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Springer Tracts in Modern Physics 233

George W. S. Hou

Flavor
Physics and
the TeV Scale
Second Edition
Springer Tracts in Modern Physics

Volume 233

Series editors
Yan Chen, Department of Physics, Fudan University, Shanghai, China
Atsushi Fujimori, Department of Physics, University of Tokyo, Tokyo, Japan
Thomas Müller, Institut für Experimentelle Kernphysik, Universität Karlsruhe,
Karlsruhe, Germany
William C. Stwalley, Department of Physics, University of Connecticut, Storrs,
USA
Jianke Yang, Department of Mathematics and Statistics, University of Vermont,
Burlington, VT, USA
Springer Tracts in Modern Physics provides comprehensive and critical reviews of
topics of current interest in physics. The following fields are emphasized:
– Elementary Particle Physics
– Condensed Matter Physics
– Light Matter Interaction
– Atomic and Molecular Physics
– Complex Systems
– Fundamental Astrophysics
Suitable reviews of other fields can also be accepted. The Editors encourage
prospective authors to correspond with them in advance of submitting a manuscript.
For reviews of topics belonging to the above mentioned fields, they should address
the responsible Editor as listed in “Contact the Editors”.

More information about this series at http://www.springer.com/series/426

George W. S. Hou

Flavor Physics and the TeV

Scale
Second Edition

123
George W. S. Hou
Department of Physics
National Taiwan University
Taipei, Taiwan

ISSN 0081-3869 ISSN 1615-0430 (electronic)

Springer Tracts in Modern Physics
ISBN 978-3-662-58627-3 ISBN 978-3-662-58629-7 (eBook)
https://doi.org/10.1007/978-3-662-58629-7
Library of Congress Control Number: 2018968113

1st edition: © Springer-Verlag Berlin Heidelberg 2009

2nd edition: © Springer-Verlag GmbH Germany, part of Springer Nature 2019
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part
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This Springer imprint is published by the registered company Springer-Verlag GmbH, DE part of
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The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany
To the memories of Prof. Chia-Chu Hou
and Mr. Chiao-Shen Lu, beloved father,
and father in-law.
Preface of Second Edition

It is almost exactly 10 years since the first edition. I was actually contacted by the
hardworking editor already in 2013 for a revision. However, mostly driven by the
magnificent LHCb experiment at the Large Hadron Collider, the “flavor anomalies”
were just unfolding, so it appeared too early. By 2017, I decided it was time for an
update, but the schedule was delayed by waiting ever eagerly for the “Run 2
update” on flavor anomalies by LHCb. Unfortunately, to date this has yet to hap-
pen, and with the Belle II experiment turning on, one should not delay any further.
The anomalies still stand, but alas, through Run 1 and now Run 2, we cannot say
we have uncovered any New Physics at the LHC so far. The discovery of the Higgs
boson at the LHC repeats what has happened with the discovery of the top quark at
the Tevatron: confirming the Standard Model, but No New Physics. Déjà-vu! While
that has been disappointing, it highlights the role of Flavor Physics to probe above
the TeV scale, now that we have reached the TeV scale but found ourselves
empty-handed from direct search.
We have made major updates to all chapters except the first two, with Dark
Sector entering the title of Chap. 7, reflecting the times. Furthermore, the new
Chap. 10 on “The Top and Higgs” has been added. We believe the top quark would
become part of the Flavor Physics and CP violation, or FPCP, conference theme.
Note that, echoing the absence of New Physics at the LHC, the fourth generation
(4G) has not been found, and we give a “Requiem” in an appendix. In its place,
however, the new Chap. 10 promotes extra Yukawa couplings arising from a
second Higgs boson doublet.
Just like discovering the 4G enhancement of the Jarlskog invariant, in planning
this update, we discovered that, with the extra top Yukawa coupling, together with
the possibility of first-order phase transition—both facilitated by presence of the
second Higgs doublet—electroweak baryogenesis can be readily achieved. In the
same time frame, we found that the alignment phenomenon, that the observed 125
GeV boson does not seem to mix much with the exotic neutral Higgs boson(s), can
help alleviate age-old issues with flavor-changing neutral Higgs couplings.
Inspired, we eventually called this SM2—SM with 2 Higgs doublets, and just let
Nature reveal herself.

vii
viii Preface of Second Edition

We believe a new golden decade of flavor physics is unfolding, where Belle II

would be both competitive with, and complementary to, LHCb.
Let the era begin.

Melbourne, Australia/Taipei, Taiwan George W. S. Hou

December 2018
Preface of First Edition

The flavor sector carries the largest number of parameters in the Standard Model of
particle physics. With no evident symmetry principle behind its existence, it is not
as well understood as the SU(3)
SU(2)
U(1) gauge interactions. Yet it tends to
be underrated, sometimes even ignored, by the erudite. This is especially so on the
verge of the LHC era, where the exploration of the physics of electroweak sym-
metry breaking at the high-energy frontier would soon be the main thrust of the
field.
Yet, the question of “Who ordered the muon?” by I. I. Rabi lingers.
We do not understand why there is “family” (or generation) replication. That
three generations are needed to have CP violation is a partial answer. We do not
understand why there are only three generations, but Nature insists on (just about)
only three active neutrinos. But then the CP violation with three generations fall far
short of what is needed to generate the baryon asymmetry of the Universe. We do
not understand why most fermions are so light on the weak symmetry breaking
scale (v.e.v.), yet the third-generation top quark is a v.e.v. scale particle. We do not
understand why quarks and leptons look so different, in particular, why neutrinos
are rather close to being massless, but then have (at least two) near–maximal mixing
angles. We shall not, however, concern ourselves with the neutrino sector. It has a
life of its own.
This monograph is on the usefulness of flavor physics as probes of the TeV
scale, to provide a timely interface for the emerging LHC era. Historically, the kaon
system has been a major wellspring for the emergence of the Standard Model. It
gave us the Cabibbo angle hence quark mixings, K 0 −K  0 oscillations, CP violation,
absence of FCNC and the GIM mechanism, prediction of charm (mass), and ulti-
mately the Kobayashi–Maskawa model and the prediction of the third generation.
The torch, however, has largely passed on to the B meson system, the elucidation of
which forms the bulk of this book. Following, and expanding on, the successful
paths of the CLEO and ARGUS experiments, the B factories have dominated the
scene for the past decade.

ix
x Preface of First Edition

The B factories have produced a vast amount of knowledge. Fortunately, by

concerning ourselves only with the TeV scale connection, a large part of the B
factory output can be bypassed. We do not concern ourselves with rather indirect
links to physics beyond the Standard Model, such as the measurement of CKM
sides, or the consistency of the unitary phases with three generations. The advan-
tage is that we do not need to go into the details of “precision measurement”
studies, as they are now rather involved. Our emphasis is on loop-induced pro-
cesses, which allow us to probe virtual TeV scale physics through quantum pro-
cesses, in the good traditions of muon g  2 and rare kaon processes. In this sense,
flavor physics is quite complementary to the LHC collider physics that would soon
unfold before us. If New Physics is discovered by the LHC, flavor probes would
provide extra information to help pin down parameters. If no New Physics emerges
from the LHC, then flavor physics still provides multiple probes to physics above
the TeV scale. Either way, the construction of so-called Super B factories, to go far
beyond the successful B factories in luminosity, is called for.
A glance at the Table of Contents shows that two-thirds of the book is concerned
with b ! s or bs $ sb transitions. The B factories have not uncovered strong hints
for New Physics in bd $ d b or b ! d transitions. It is remarkable that all evidence
supports the third-generation Kobayashi–Maskawa model in the so-called b ! d
 
CKM triangle, Vud Vub þ Vcd Vcb þ Vtd Vtb ¼ 0 (and the Nobel Prize has been awar-
ded). Further probes in b ! d transitions tend to be marred by hadronic or Standard
Model effects, and at best are part of the long road of third-generation Standard
Model consistency tests that we have decided to sidestep. In contrast, b ! s
transitions are not only the current frontier of flavor physics, it actually offers good
hope that New Physics may soon be uncovered, maybe even before the first physics
is repeated at the LHC. On the one hand, this is because the
 
Vus Vub þ Vcs Vcb þ Vts Vtb ¼ 0 CKM triangle is so squashed and hardly a triangle in
the Standard Model, so the expected CP violation in loop-dominated b ! s tran-
sitions is tiny. This means that any clear observation could indicate New Physics.
On the other hand, b ! s transitions offer multiple probes into physics beyond the
Standard Model that have come of age only recently. As we advocate, the mea-
surement of sin 2UBs in Bs ! J=ˆ/, analogous to sin 2/1 =b measurement in Bd !
J=ˆKS at the B factories, holds the best promise for an unequivocal discovery of
New Physics, if its measured value at the Tevatron or LHC turns out to be sizable. It
is exciting that we seem to be heading that way.
A common thread that links the several hints of New Physics in b ! s transi-
tions, to our prediction of large and negative sin 2UBs , is the existence of a fourth
generation. Of course, there are strong arguments against the existence of a fourth
generation, by the aforementioned “neutrino counting,” and by electroweak pre-
cision tests. However, these objections arise from outside of flavor physics. While
these should be taken seriously, one should not throw the fourth generation away
when considering flavor physics, since the richness of flavor physics rests on the
existence of three generations, and extending to four generations provide consid-
erable enrichment, particularly in b ! s transitions. It also provides multiple links
Preface of First Edition xi

between different flavor processes, through the unitarity of the 4
4 CKM matrix.
As emphasized in this book, a fourth generation could most easily enter box and
electroweak penguin diagrams. Accounts of these are scattered throughout the
book, as we touch upon different processes. These are effects due to large Yukawa
couplings, which link flavor physics to the Higgs, or electroweak symmetry
breaking sector.
While writing this book, we observed that adding a fourth quark generation
could enhance the so-called Jarlskog invariant for CP violation by a factor of
10 þ 13 or more, and the (fourth generation) KM model could provide the source of
CP violation for the baryon asymmetry of the Universe. A sketch of this insight is
given in the final discussion chapter, which also serves as justification for our
frequent mentioning of the fourth generation throughout the book. Flavor physics
could provide CP violation for the Heaven and the Earth.
Two other chapters, on D0 mixing and K ! …””, and on lepton number vio-
lating ¿ decays, are loop-induced probes of New Physics that are analogous to the
emphasis of our main text on B physics. Interestingly, there are still tree-level
processes that can probe New Physics, such as the probe of charged Higgs boson
H+ through B þ ! ¿ þ ” ¿ , or light dark matter or pseudoscalar Higgs boson search
in  ðnSÞ decays.
We have taken an experimental perspective in writing this book. This means
selecting processes, rather than the theories or models, as the basis to explore flavor
physics as probe of the TeV scale. In the first few chapters, emphasis is on CP
violation measurables in b ! s transitions. We then switch to using a particular
process to illustrate the probe of a special kind of physics. We therefore also spend
some time in elucidating what it takes to measure these processes. However, this is
not a worker’s manual for experimental analysis, but on bringing out the physics.
For the same reason, we do not go into any detail on theoretical models. Our
guiding principle has been: Unless it can be identified as the smoking gun, it is
better to stick to the simplest (rather than elaborate) explanation of an effect that
requires New Physics.
The origins of this monograph are the plenary talk I gave at the SUSY 2007
conference held in Karlsruhe, Germany. It was interesting to attend the SUSY
conference for the first time, while giving an experimental plenary talk. I thank the
Belle spokespersons, Masa Yamauchi in particular, for nominating me as “that
special physicist” to give this talk. I also thank my old friend and former colleague,
Hans Kühn, for encouraging and inviting me to expand the talk into a monograph
for Springer Tracts of Modern Physics. It is impossible to thank the numerous
colleagues in the field of flavor physics for benefits of discussion and insight.
I acknowledge the help from Yeong-jyi Lei for help on figures. Last, and above all,
I thank my family for the understanding and support throughout the period of
writing this book.

Les Houches, France/Geneva, Switzerland/Taipei, Taiwan George W. S. Hou

September 2008
Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Outline, Strategy, and Apologies . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 A Parable: What if? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 The Template: DmBd , Heavy T op, and Vtd . . . . . . . . . . . . . . . . 6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 CP Violation in Charmless b ! sqq Transitions . . . . . . . . . . . . . . . 11
2.1 The DS Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Measurement of TCPV at the B Factories . . . . . . . . . . 12
2.1.2 TCPV in Charmless b ! sqq Modes . . . . . . . . . . . . . . 15
2.2 The DAK… Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Measurement of DCPV in B0 ! K þ … Decay . . . . . . 18
2.2.2 DAK… and New Physics? . . . . . . . . . . . . . . . . . . . . . . 21
2.3 ACP ðB þ ! J=ˆK þ Þ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 An Appraisal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Bs Mixing and sin 2UBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Bs Mixing Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.1 Standard Model Expectations . . . . . . . . . . . . . . . . . . . 34
3.1.2 Tevatron Measurement of DmBs . . . . . . . . . . . . . . . . . 38
3.2 Search for TCPV in Bs System . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 DCBs Approach to /Bs : cos 2UBs . . . . . . . . . . . . . . . . . 42
3.2.2 Prospecting for sin 2UBs , ca. 2008 . . . . . . . . . . . . . . . . 44
3.2.3 Hints at Tevatron in 2008 . . . . . . . . . . . . . . . . . . . . . . 50
3.2.4 Anticlimax: sin 2UBs ’ 0 . . . . . . . . . . . . . . . . . . . . . . 54
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

xiii
xiv Contents

4 H+ Probes: b ! s
, and B ! ¿”, D(*)¿” . . . . . . . . . . . . . . . . . . . . 59

4.1 b ! s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.1 QCD Enhancement and the CLEO Observation . . . . . . 59
4.1.2 Measurement of b ! s at the B Factories . . . . . . . . . 61
4.1.3 Implications for H þ . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.2 Measuring B ! ¿”, DðÞ ¿” . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.1 Enhanced H þ Effect in b ! c¿” and B þ ! ¿ þ ” ¿ . . . 66
4.2.2 B ! ¿” and B ! DðÞ ¿” Rate Measurement . . . . . . . . 69
4.3 RD , RD Anomaly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3.1 BaBar Bombshell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3.2 Assessment: Towards Belle II + LHCb Era . . . . . . . . . 79
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 Electroweak Penguin: b ! s‘‘, Anomalies, Z′ . . . . . . . . . . . . . . . . . 85
5.1 AFB ðB ! K  ‘ þ ‘ Þ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.1.1 Observation of mt -enhanced b ! s‘ þ ‘ . . . . . . . . . . . 85
5.1.2 AFB ðB ! K  ‘ þ ‘ Þ Problem and Its Demise . . . . . . . . 89
5.2 P05 and RK ðÞ Anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2.1 P05 Anomaly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2.2 RK , RK  Anomaly . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3 B ! K ðÞ ”” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3.1 Experimental Search . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3.2 Constraint on Light Dark Matter . . . . . . . . . . . . . . . . . 102
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6 Scalar Interactions and Right-Handed Currents . . . . . . . . . . . . . . . 107
6.1 Bs ! „ þ „ (and B0 ! „ þ „ ) . . . . . . . . . . . . . . . . . . . . . . . 107
6.1.1 Tevatron Versus LHC . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.1.2 Observation of Bs ! „ þ „ at LHC . . . . . . . . . . . . . . 111
6.2 TCPV in B ! KS0 …0 , X 0  . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7 Probes of the Dark Sector at Flavor Facilities . . . . . . . . . . . . . . . . 121
7.1  Decay Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.1.1  ð3SÞ ! … þ …  ð1SÞ ! … þ … þ Nothing . . . . . . . . . 121
7.1.2  ð1SÞ ! a01 Search . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.2 The Quest for Dark Photons . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.2.1 Exotic Higgs-Strahlung: e þ e ! A0 h0 , h0 ! A0 A0 . . . . . 128
7.2.2 Dark Photon from ISR: e þ e !  ISR A0 . . . . . . . . . . . 129
7.2.3 Inclusive A0 ! „ þ „ Search at LHC . . . . . . . . . . . . . 131
7.2.4 Muonic Dark Force: e þ e ! „ þ „ Z 0 ,
Z 0 ! „ þ „ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Contents xv

8 D and K Systems: Box and EWP Redux . . . . . . . . . . . . . . . . . . . . . 135

8.1 D0 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8.1.1 SM Expectations and Observation at B Factories . . . . . 136
8.1.2 Interpretation, DACP Interlude, and Prospects . . . . . . . . 141
8.2 Rare K Decays: K ! …” ” Pursuit . . . . . . . . . . . . . . . . . . . . . . 143
8.2.1 Path to K ! …”” . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8.2.2 Pushing the Frontier: NA62 and KOTO . . . . . . . . . . . . 147
8.2.3 Kaon Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
9 Lepton Number Violation and „, ¿ Systems . . . . . . . . . . . . . . . . . . 155
9.1 „ ! e Transitions, g  2 and EDM . . . . . . . . . . . . . . . . . . . . . 156
9.1.1 „ ! e Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
9.1.2 Muon g  2 and EDMs . . . . . . . . . . . . . . . . . . . . . . . 159
9.2 LFV ¿ ! ‘, ‘‘‘0 Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
9.2.1 Lepton Universality and ¿ Lifetime . . . . . . . . . . . . . . . 162
9.2.2 ¿ ! „, ‘‘‘0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
9.3 ¿ ! K…,  p…0 and Baryon Number Violation . . . . . . . . . . . . . . 165
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
10 The Top and The Higgs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
10.1 Top Changing Neutral Couplings . . . . . . . . . . . . . . . . . . . . . . . 170
10.1.1 TCNC: t ! cZ ð0Þ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
10.1.2 TCNH: t ! ch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
10.2 New Yukawa Couplings with Extra Higgs Bosons . . . . . . . . . . 174
10.2.1 Flavor Changing Neutral Higgs: h0 ! „ ¿  . . . . . . . . 174
10.2.2 2HDM-III: Two Higgs Doublets Without Z2 . . . . . . . . 177
10.3 SM2: SM, But with Two Higgs Doublets . . . . . . . . . . . . . . . . . 178
10.3.1 Lagrangian for Yukawa Couplings in SM2 . . . . . . . . . 179
10.3.2 Prognosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Appendix A: A CP Violation Primer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Appendix B: Requiem to 4th Generation . . . . . . . . . . . . . . . . . . . . . . . . . 201
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Chapter 1
Introduction

As humans, we aspire to reach up to the heavens. It is our unquenchable nature. An

old fable illustrates the point: Jack and the Beanstalk. It is simply impossible for Jack
not to climb the Beanstalk, when it stands in front of him, extending all the way up,
to beyond the clouds.
Let us illustrate Jack and the Beanstalk as an allegory in Fig. 1.1. In particle
physics, we have strived to surpass the threshold and reach beyond the veiling clouds
of the “v.e.v. scale” (the “v.”, “e.” and “v.”, unfortunately do not show up clearly in
Fig. 1.1 in BW, which seems fitting), as we know firmly that a vacuum expectation
value of order v  246 GeV had developed in the early Universe, which broke
the electroweak symmetry (EWSB) down to electromagnetism. This is the scale
for all fundamental masses1 in the Standard Model (SM). The conventional high
energy approach is like Jack climbing straight up the Beanstalk. In 2012, the Large
Hadron Collider (LHC) at CERN spectacularly discovered the Higgs boson with
mass mh  125 GeV, i.e. in the Castle floating on a low cloud in Fig. 1.1. But going
up in energy from 7 and 8 TeV in Run 1 to 13 TeV in Run 2 (which would finish
by end of 2018), the LHC uncovered No New Physics Beyond the SM (BSM) so far!
While the Higgs boson is relatively light, there seems to be vast emptiness beyond
the darker clouds of the v.e.v., with no sign of treasures, nor the “Giant”.
In the direct ascent approach, Jack has to fear the Giant, which could even be
the projects like ILC (International Linear Collider) or the 100 km circumference
CEPC-SppC (Circular Electron-Positron Collider & Super proton-proton Collider).
The cost of machines is becoming so prohibitive, Jack may not be able to survive
or return, whatever the riches he may or may not uncover. However, “Jack” may not
have to actually climb the Beanstalk: quantum physics allows him to stay on Earth,
and let virtual “loops” do the work. The virtual Jack has no fear of getting eaten by
the Giant.

1 Themass of the proton (hence most Earthly masses) actually arises predominantly from a similar
phenomena of chiral symmetry breaking, induced by QCD.
© Springer-Verlag GmbH Germany, part of Springer Nature 2019 1
G. W. S. Hou, Flavor Physics and the TeV Scale, Springer Tracts
in Modern Physics 233, https://doi.org/10.1007/978-3-662-58629-7_1
2 1 Introduction

Child
Eating
Giant
e. (LHC/ILC?)
v. v.

Higgs
Castle
clouds

http://pbjc-lib.state.ar.us/mural.htm

Down to Earth
Flavor/ TeV

Fig. 1.1 Parable of Jack and the Beanstalk (adapted from the mural by Henri Linton and Ariston
Jacks, originally located at the Pine Bluff Public Library, Pine Bluff, Arkansas, U.S.A.; used with
permission)

This parable illustrates how flavor physics offers probes of the TeV scale, at much
reduced costs. The flavor connection to TeV scale physics is typically through loops.
Interestingly, the current indications for “anomalies”,2 or deviations from SM, all
seem to arise from the flavor sector.

1.1 Outline, Strategy, and Apologies

The outline of this book is as follows.

We take an experimental view on the physics of flavor and the TeV scale connec-
tion. In the remainder of this chapter, we entertain a “What if?” question to elucidate
the possible surprises from flavor physics, then use B0 –B̄0 mixing as a template to
illustrate loop effects. In the next chapter we cover New Physics (NP) CP violation
(CPV) search in loop-induced b → s transitions: the mixing-dependent CPV differ-
ence ΔS between b → cc̄s and sq̄q processes, and the direct CPV difference ΔAKπ
between B+ and B0 decay to K + π. These were highlight studies of the B factory era.
In Chap. 3, we continue with the New Physics CPV search in loop-induced bs̄ ↔ b̄s

2 “Anomalies”, put in quotation here, are discrepancies between experimental measurement and
theoretical (i.e. SM) expectation. They come and go, and mostly, go. The most famous “anomaly”
at the LHC was the 750 GeV diphoton excess, which came with early 13 TeV data of 2015 run, but
went away within a year.
1.1 Outline, Strategy, and Apologies 3

transitions, namely the status and prospects for measuring the CPV phase in Bs
mixing. There was some hope during 2008–2010 that it could be large, but ended up
again SM-like, which was a disappointing triumph of the LHCb experiment in the
LHC era. It remains a focus of flavor physics. In Chap. 4, we turn to the traditional
probes of charged Higgs boson (H + ) effects, namely b → sγ and B+ → τ + ν, where
the latter arises from a tree diagram. The B → D(∗) τ ν anomaly is also discussed here,
together with possible New Physics. In Chap. 5, we use B → K (∗) + − to show how
these electroweak penguin processes provide exquisite probes of New Physics. The
forward-backward asymmetry (AFB ) “anomaly” rose and fell, but the P5 and RK (∗)
anomalies unveiled by LHCb are recent highlights. The B → K (∗) νν modes emerge
analogously in SM, but because the experimental signature is B → K (∗) + nothing,
their search provide a window on light dark matter, which connects also with the
kaon section. In Chap. 6, the LHC Run 1 highlight of Bs → μ+ μ− observation is
discussed in the context as a probe of the extended Higgs sector, but again turned out
SM-like. We then use time-dependent CPV in B0 → KS π 0 γ to illustrate the probes
of right-handed dynamics. In Chap. 7 we detour from loop physics to discuss the
bottomonium system as probe of light dark matter and exotic light Higgs bosons.
This is further expanded to the broad interest of flavor facilities as probes of the
Dark Sector. We then return to loop effects in D0 mixing and rare K → πνν decays
in Chap. 8, and lepton flavor violation in μ and τ decays in Chap. 9, where we also
discuss briefly muon g − 2 and electric dipole moments. Chapter 10 discusses the
emerging field of Top-Higgs connections with flavor physics. We close with some
discussions and insight, and offer our conclusions in Chap. 11. In Appendix A, we
elucidate and demystify the mechanism of CPV; Appendix B is a requiem to the
fourth generation.
Flavor physics is a vast subject with many rather elaborate and specialized top-
ics. Our selection of topics is simplified by focusing on those that are pertinent to
BSM physics, while avoiding those that are too intricate or too long to present. The
emphasis is on bringing out the physics, rather than on the experimental or theoretical
details. As the (Chinese) saying goes, one should avoid “See tree(s), not see forest”,
which often happens to experts that get lost in the details.
Another criteria for selection of topics is our emphasis on the nearer-term impact.
We have seen the spectacular success of the LHCb experiment, which has completely
superseded the Tevatron era, while after long preparations, we are finally at the
juncture where the “Super B factory” era is dawning. The unprecedented luminosities
of KEKB (see Fig. 1.2) would soon take another leap upward by a factor of 40–50 to
SuperKEKB, with a total of 50 ab−1 integrated luminosity delivered to Belle II by
∼ 2025. We can finally enjoy the competition, and complementarity, between LHCb
and Belle II.
We have largely picked traditional theoretical models for BSM or “New Physics”.
Thanks to the B factories, flavor physics experienced a tremendous leap forward from
the CLEO era of the 1990s. While the frontier has been pushed back considerably
(see Fig. 1.2 again), no smoking gun BSM signal has yet emerged in an unequivocal
way. With the advent of LHCb, we have seen quite a few flavor “anomalies” emerge,
which is intriguing. In contrast, “No New Physics” at the LHC energy frontier has
4 1 Introduction

10 36

Peak luminosity (cm s )

-2 -1
Peak Luminosity trends in last 40 years SuperKEKB
35
10
KEKB
LHC
10 34
PEP II
10 33 CESR DAFNE
TEVATRON
10 32 ISR
PEP
LEP2 BEPC2
PETRA TRISTAN
31 HERA
10 DORIS LEP1
SPEAR BEPC
10 30 SppS
DCI
10 29
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
Year

Fig. 1.2 The luminosity frontier up to 2010. Note that the LHC has already achieved luminosities
comparable to KEKB, while SuperKEKB only started in 2018. [Source http://sabotin.p-ng.si/
~sstanic/kekb/trends.html, by Samo Stanič, used with permission]

brought on some anxiety in the theory community, not least the absence of any
signal for supersymmetry (SUSY). We will not enter the “naturalness” debate, but
emphasize that the current situation elevates the importance of the flavor physics and
TeV scale link. EWSB physics and flavor physics are orthogonal but complementary
directions. They overlap in the Yukawa coupling sector, hence our new chapter on
the Top-Higgs intersection. It is gratifying that SuperKEKB would soon allow Belle
II to probe, together with LHCb, the flavor frontier, hand in hand with ATLAS and
CMS on the energy frontier.
Having said all this, we apologize for incomplete citations of theoretical work. We
cite what we deem to be of key importance, again, to illustrate the physics. However,
we are not impartial in promoting our own phenomenological work. But our previous
favorite, having a fourth generation of quarks in Nature, is placed in an Appendix.

1.2 A Parable: What if?

Another “parable” illustrates the potential of heavy flavor physics to make impact.
Let us entertain a hypothetical “What if ?” question.
Forwarding to the recent past, on July 31, 2000, at the ICHEP conference in Osaka,
the BaBar experiment announced the low value of sin 2β ∼ 0.12 [2],

sin 2β = 0.12 ± 0.37 (stat) ± 0.09 (syst). (BaBar, ICHEP2000) (1.1)

We will gradually define what sin 2β means. The result of (1.1) was analyzed with
a data set of 9 fb−1 integrated luminosity on the ϒ(4S) resonance, corresponding to
1.2 A Parable: What if? 5

Fig. 1.3 Measurement of sin 2β/φ1 , 2000–2005, illustrating how the combined result of Belle and
BaBar settled already in 2001. [Source talk by Cahn [1] given at 2006 SLAC Summer Institute,
used with permission.]

about 10M BB̄ meson pairs produced in the clean e+ e− collider environment. The
value for the equivalent sin 2φ1 = 0.45+0.43+0.07
−0.44−0.09 [3] measurement from the Belle
experiment (using 6.2 fb−1 data, or almost 7M BB̄ pairs) was slightly higher, but
also consistent with zero. Note that the errors are quite large. Within the same day,
however, a theory paper appeared on the arXiv [4], entertaining the implications
of the low sin 2β value for the strategy of exploring New Physics. It seems that3
some theorists have the power to “wormhole” into the future! A year later, however,
both BaBar and Belle claimed the observation [6, 7] of sin 2β/φ1 ∼ 1, which turned
out to be consistent with Standard Model (SM) expectations, i.e. confirming the
Kobayashi–Maskawa [8] source of CPV.
In Fig. 1.3 we illustrate how the summer 2001 measurements by Belle and BaBar
“settled” the value for sin 2β/φ1 . The band is some mean value, roughly of 2002.
With impressive accumulation of data, as seen in the bars at the bottom of the figure,
the measured mean remains more or less the same.
What if sin 2β/φ1 stayed close to zero? Well, as stated already, it certainly didn’t.
Otherwise, you would have heard much more about it—a definite large deviation
from the SM has been found! For even in the last century, one expected from indirect
data that sin 2β/φ1 had to be nonzero within SM (see Fig. 1.4). Note that within SM,
with the standard phase convention of taking Vcb to be real, and placing the unique
CPV phase in Vub , one has β/φ1 = − arg Vtd [10]. The awkward notation of β/φ1
(like the original J /ψ) is just to respect the friendly competition across the Pacific
Ocean.

3 This parable was meant as a joke, but as I was preparing for my SUSY2007 talk (the starting point

of this volume), the paper “Search for Future Influence from L.H.C.” appeared [5]. So it was not a
joke after all. The future can wormhole back!? It seems to have received preliminary confirmation
with the magnet accident right after successful first beam at LHC in September 2008.
6 1 Introduction

_
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
_

Fig. 1.4 Expectation for sin 2β/φ1 measurement ca. 1998. [Source BaBar Physics Book, SLAC
Report R-504, [9]; used with permission] This figure should be compared with Fig. 1.6; for definition
of ρ̄ and η̄, as well as a discussion of the CKM matrix and CPV in SM, see Appendix A

The measurement of sin 2β/φ1 is the measurement of the CPV phase in the
Bd0 –B̄d0 mixing matrix element M12 d
. We recall that the discovery of Bd0 –B̄d0 mix-
ing itself by the ARGUS experiment [11] more than 30 years ago was the first clear
indication that the top is heavy, that it is a v.e.v. scale quark, a decade before the
top quark was actually discovered at the Tevatron. The ARGUS discovery caused
a Gestalt switch, and to this day we do not yet quite understand why the top is so
heavy compared to other fermions.
Such is the impact of loop effects, and the power of the Flavor and TeV link. If
an “anomaly” turns out4 to be the harbinger, it becomes the page-turning discovery
that we are looking for. With the Bd0 –B̄d0 mixing frequency ΔmBd proportional to
|Vtd |2 m2t , it is the template for flavor loops as probes into high energy scales. So let
us learn from it.

1.3 The Template: ΔmBd , Heavy T op, and Vtd

As shown in Fig. 1.5, the Bd0 –B̄d0 mixing amplitude M12d

is generated by the box
diagram involving two internal W bosons and top quarks in the loop.
Normally, heavy particles such as the top quark would decouple from the loop in
the heavy mt → ∞ limit. After all, our daily experience does not seem to depend
on yet-unknown heavy particles. This is the case for QED and QCD. However, for
chiral gauge theories, such as the electroweak theory, the longitudinal component
of the W boson, which is a charged Higgs scalar that got “eaten” by the W through
spontaneous symmetry breaking, couples to the top quark mass. This gives rise to

4 Twoother more recent “What if ?” situations are the measurements of sin 2ΦBs (Chap. 3), i.e. the
CPV phase in Bs mixing, and Bs0 → μ+ μ− (Chap. 6), both ended up being consistent with SM.
What if not !?
1.3 The Template: ΔmBd , Heavy T op, and Vtd 7

b d b d
u , c, t
u , c, t

d¯ b̄ d¯ b̄

Fig. 1.5 The box diagrams that induce Bd0 –B̄d0 mixing. The top quark dominates the loop, and
brings in the CPV phase though (Vtd∗ Vtb )2

the phenomenon of nondecoupling of the top quark effect from the box diagram, i.e.
d
M12 ∝ (Vtd∗ Vtb )2 m2t to first approximation. It illustrates the Higgs affinity of heavy
SM-like (chiral) quarks, namely λt ∼ 1 for the top quark Yukawa coupling. It is
the Yukawa coupling to the Higgs boson that links the left- and right-handed chiral
quarks, which are in different representations of the SU(2) × U(1) electroweak gauge
group, that generates quark masses. The rather large Yukawa coupling of the top quark
compensates for the suppression of Vtd∗ 2 (∼10−4 in strength), bringing forth the CPV
phase sin 2β/φ1 that was measured by the B factories in 2001.
d
The formula for M12 is very well known. Since the top quark dominates, one has

G 2F mB  2
d
M12 − 2
× ηB m2W S0 (m2t /m2W ) × fB2d BBd × Vtd∗ Vtb . (1.2)
12π
From this formula, we can get a feeling of what a loop calculation involves. The first
factor with G 2F counts the number of W propagators. The second factor is from short
distance physics and calculable, with ηB ≈ 0.6 a QCD correction factor, and

S0 (m2t /m2W ) ≈ 0.55 m2t /m2W , (1.3)

for our purpose, which is proportional to m2t as stated before. For the third factor, the
decay constant fBd accounts for the probability for the b and d̄ quarks to meet and anni-
hilate (“wave function at the origin”), and the “bag” parameter BBd is to compensate
for the so-called vacuum insertion approximation, of separating the [b̄d ][d̄ b] 4-quark
operator into a product of two currents, then taking the matrix element of e.g. [b̄d ]
between the |Bd and |0 states. The decay constant fBu is accessible in B+ decay, the
measurement of which can help infer fBd . But in general we rely on nonperturbative
calculational methods like lattice QCD for information on fB2d BBd . Finally, (Vtd∗ Vtb )2
is just the product of the four CKM factors from the weak interaction vertices.
We recall that K 0 –K̄ 0 mixing, or ΔmK , provided the basic source of insight for the
Glashow–Iliopoulos–Maiani (GIM) mechanism [12], which lead to the prediction
of the charm quark before it was actually discovered, even an estimation of the
charm mass (using a formula similar to (1.2)). With 3 generations, as suggested by
Kobayashi and Maskawa [8] (KM), the top quark in the box diagram provided the
SM explanation for the origin of CPV in KL → 2π decay [13], the εK parameter.
None of this, however, prepared people for the Bd system. It is curious to note
that the charm contribution to K 0 –K̄ 0 mixing gives the correct order of magnitude
8 1 Introduction

φ CKM
3 Δms & Δmd
εK
fitter

excluded area has CL > 0.95

0.6 Δmd Summer 2007

0.5 sin2φ
1
sol. w/ cos2φ < 0
(excl. at CL > 10.95)
φ
3
0.4
η

0.3 φ φ
εK 2 2
0.2

0.1
φ3
φ V ub φ
1
0 2
-0.4 -0.2 0 0.2 0.4 0.6 0.8 1
ρ

Fig. 1.6 CKM unitarity fit to all data as of summer 2007 [from the CKMfitter group [19], used
∗ V + V∗ V + V∗V = 0
with permission]. The triangle corresponds to Vud ub cd cb td tb

for ΔmK , i.e. xK ≡ ΔmK /ΓKS ∼ 0.5. This lead people to expect that xBd ≡ ΔmBd /
ΓB < 1%, even when the B lifetime was found [14, 15] to be greatly prolonged
(which was itself 5 a great discovery). This is because the B meson decay width is
still so much larger than that of the kaon, and since people tacitly assumed that the top
quark was “just around the corner”, meaning of order 20–30 GeV or less (remember
the march of the e+ e− colliders, from PEP, PETRA to Tristan, even SLC and LEP).
Thus, when ΔmBd was found to be comparable to ΓB , it was quite a shock to realize
that the top quark is actually a special, v.e.v. scale particle.
So, loop effects in B physics provided insight into the TeV scale. But that was
just the beginning. It is truly remarkable that the measured xBd ∼ 0.8 was just right
to allow the beautiful, but originally somewhat esoteric (because of the xBd 1
mindset), method [16, 17] for measuring mixing-dependent CPV, to suddenly appear
realistic in the late 1980s. This paved the way for the construction of the B factories,
but not without the key experimental insight, i.e. to boost the ϒ(4S), hence the
produced BB̄ pair. This allowed one to capitalize on vertex detector development by
going to an asymmetric energy collider [18]. After intense studies, two B factories,
one at SLAC in California, one at KEK in Japan, were constructed in the 1990s.
All this impact, stimulated by the observation of the nondecoupled loop effect of
the heavy top quark in Fig. 1.5, at the tiny DORIS e+ e− collider. Rather cost-effective
indeed. Providing diverse probes of flavor physics, often using loop effects, the B
factories themselves were quite cost-effective, as we shall see.
As we will only be interested in New Physics (NP), we note that extensive studies
at the B factories (and elsewhere) indicate that b → d transitions are consistent with
the SM [20]. As illustrated in Fig. 1.6, no discrepancy is apparent with the CKM
(Cabibbo–Kobayashi–Maskawa) unitarity triangle6

5 Thefact |Vub |2 |Vcb |2 ∼ 1 came only through experiment, and is not yet explained,
|Vtb |2 =
not within SM.
6 We will often refer to the Particle Data Group [10] for many useful discussions.
1.3 The Template: ΔmBd , Heavy T op, and Vtd 9

∗
Vud Vub + Vcd∗ Vcb + Vtd∗ Vtb = 0, (1.4)

which is the db element of V † V = I , where V is the quark mixing matrix. An enor-

mous amount of information and effort has gone into this figure (compare Fig. 1.4),
the phase of Vtd∗ Vtb being only one of the prominent entries that emerged through the
B factory studies. Although there are some tensions here and there, e.g. in the value
of |Vub |, in general, we see remarkable consistency with CKM expectations. And the
CKM fit continues to improve.
What about loop-induced b → s transitions? This frontier for heavy flavor physics
offers a window into a multitude of possible TeV scale physics. It will therefore be
our starting point of the next chapter.

References

1. Cahn, R.: Talk at SLAC Summer Institute 2006, Stanford, 25 July 2006
2. Hitlin, D.: Plenary Talk at the XXXth International Conference on High Energy Physics
(ICHEP2000), Osaka, Japan. 31 July 2000
3. Aihara, H.: Plenary Talk at the XXXth International Conference on High Energy Physics
(ICHEP2000), Osaka, Japan. 31 July 2000
4. Kagan, A.L., Neubert, M.: Phys. Lett. B 492, 115 (2000). arXiv:hep-ph/0007360
5. Nielsen, H.B., Ninomiya, M.: Int. J. Mod. Phys. A 23, 919 (2008). arXiv:0707.1919 [hep-ph]
6. Aubert, B., et al.: [BaBar Collaboration]: Phys. Rev. Lett. 87, 091801 (2001)
7. Abe, K., et al.: [Belle Collaboration]: Phys. Rev. Lett. 87, 091802 (2001)
8. Kobayashi, M., Maskawa, T.: Prog. Theor. Phys. 49, 652 (1973)
9. BaBar Physics Book. http://www.slac.stanford.edu/pubs/slacreports/slac-r-504.html
10. Tanabashi, M., et al.: [Particle Data Group]: Phys. Rev. D 98, 030001 (2018). http://pdg.lbl.
gov/
11. Albrecht, H., et al.: [ARGUS Collaboration]: Phys. Lett. B 192, 245 (1987)
12. Glashow, S.L., Iliopoulos, J., Maiani, L.: Phys. Rev. D 2, 1285 (1970)
13. Christenson, J.H., Cronin, J.W., Fitch, V.L., Turlay, R.: Phys. Rev. Lett. 13, 138 (1964)
14. Fernandez, E., et al.: [MAC Collaboration]: Phys. Rev. Lett. 51, 1022 (1983)
15. Lockyer, N.S., et al.: [MARK II Collaboration]: Phys. Rev. Lett. 51, 1316 (1983)
16. Carter, A.B., Sanda, A.I.: Phys. Rev. Lett. 45, 952 (1980); Phys. Rev. D 23, 1567 (1981)
17. Bigi, I.I.Y., Sanda, A.I.: Nucl. Phys. B 193, 85 (1981)
18. Oddone, P.: At UCLA Workshop on Linear Collider BB̄ Factory Conceptual Design. Los
Angeles, California (1987). January
19. CKMfitter group: http://ckmfitter.in2p3.fr
20. Heavy Flavor Averaging Group: (HFLAV; acronym changed from HFAG to HFLAV (2017)).
http://www.slac.stanford.edu/xorg/hflav
Chapter 2
CP Violation in Charmless b → sq̄q
Transitions

With the study of CP violation in b → d transitions seemingly in good agreement

with Standard Model expectations, the subject of CPV studies in charmless b → s
transitions (including bs̄ ↔ sb̄) became the frontier of heavy flavor research. Because
there is little CPV weak phase in the controlling product of CKM matrix elements
for loop induced b → s transitions, Vts∗ Vtb , any observed deviation could indicate
New Physics. As transitions between 3rd to 2nd generation quarks, the subject also
has τ → μ transition echoes in the lepton sector, which is covered in Chap. 9. More
generally, with the Sakharov conditions [1] that link CPV with the Baryon Asymme-
try of the Universe (BAU), i.e. why there is no trace of antimatter in our Universe,
we do expect NP sources for CPV. It is well known that the 3 generation SM falls
short by many orders of magnitude from the CPV that is needed to generate the
observed BAU, which has been the strongest motivation to search for New Physics
in CP violation.
In this Chapter, we focus on three topics: the measurement of mixing- or time-
dependent CPV (TCPV) in charmless b → sq̄q modes versus b → cc̄s modes, ΔS,
where we elucidate also how TCPV studies are conducted; the discovery of ΔAKπ
between direct CPV (DCPV) in B+ → K + π 0 and B0 → K + π − decays; and the
DCPV asymmetry AB+ →J /ψK + . We close with an appraisal of New Physics search
in hadronic b → s transitions. The pursuit of sin 2ΦBs measurement (analogous to
sin 2φ1 /β for Bd system) at the Tevatron and LHC, the frontier of the past decade,
will be discussed in the next Chapter. Further charmless b → s probes of different
New Physics are covered in subsequent Chapters.

2.1 The ΔS Pursuit

The B factories were built to measure mixing-, or time-dependent CPV (TCPV) in

the B0 → J /ψKS mode [2, 3]. This is the billion dollar question that started with the
ARGUS discovery of large B0 –B̄0 mixing [4]. With the suggestion by Oddone [5]
of boosting the Υ (4S), thereby boosting the B0 and B̄0 mesons, by the late 1980s,
© Springer-Verlag GmbH Germany, part of Springer Nature 2019 11
G. W. S. Hou, Flavor Physics and the TeV Scale, Springer Tracts
in Modern Physics 233, https://doi.org/10.1007/978-3-662-58629-7_2
12 2 CP Violation in Charmless b → sq̄q Transitions

both SLAC and KEK initiated feasibility studies for e+ e− colliders with asymmetric
beam energies. The push towards asymmetric beam energies also contributed partly
to the demise, in 1989, of the proposed PSI machine, which had a symmetric double
ring design. By 1994 or so, both the PEP-II/BaBar and KEKB/Belle accelerator and
detector complexes entered construction phase.
Several miraculous points that aid B factory studies are worthy of note. First, mB is
so close to mΥ (4S) /2, such that not only the Υ (4S) decays practically 100% to B0 B̄0
and B+ B− pairs, the B mesons are produced with rather small momenta. Second,
mB+ and mB0 are rather close in mass, such that charged and neutral B mesons are
almost equally produced. Their production ratio is of course measured. One third
point, which will be immediately discussed in the following, is the “EPR” coherence
(or entanglement) of the B0 B̄0 meson pair from Υ (4S) decay. That is, although each
meson starts to oscillate between B0 and B̄0 after being produced, the pair remains in
coherence, such that the determination of the B0 (or B̄0 ) nature of one meson at time
t in the Υ (4S) frame, the other meson starts to oscillate from a B̄0 (or B0 ) from time
t onwards. This quantum coherence has in fact been tested at Belle [6]. Of course,
Quantum Mechanics is again affirmed. The fraction of produced B0 and B̄0 pairs (out
of 76M) that disentangle and decay incoherently is measured to be 0.029 ± 0.057,
which is consistent with zero.

2.1.1 Measurement of TCPV at the B Factories

At B factories, TCPV measurement utilizes the coherent production of B0 B̄0 pairs

from Υ (4S) decay. That is, as the produced B0 (and vice versa the B̄0 ) undergoes
oscillations back and forth from B0 to B̄0 , the pair remains coherent. As the original
B0 and B̄0 are produced at the same time, if one measures at time t the decay of one
B meson, and find that it decays as, say, B0 , we then know from quantum coherence
that the other B meson is a B̄0 meson at time t. From then on, this B̄0 meson again
oscillates back and forth from B̄0 to B0 , until time Δt later, where it also decays.
Having this picture visualized, we can go further and discuss what is done experi-
mentally to measure TCPV. We repeat (A.9) of Appendix A.3 for TCPV asymmetry,

Γ (B̄0 (Δt) → f ) − Γ (B0 (Δt) → f )

ACP (Δt) ≡
Γ (B̄0 (Δt) → f ) + Γ (B0 (Δt) → f )
= −ξf (Sf sin ΔmΔt + Af cos ΔmΔt), (2.1)

where ξf is the CP eigenvalue of final state f , and Δm ≡ ΔmBd . This asymmetry

measures, at time Δt, the difference in rate between a state tagged at t = 0 as B̄0
versus B0 . Thus, the Γ ’s are really shorthands for differential decay rates. With the
Δt distribution of ACP (Δt), which are actually done by fitting Γ (B̄0 (Δt) → f ) and
Γ (B0 (Δt) → f ) distributions, the CPV parameters Sf and Af are just the Fourier
coefficients of the sine and cosine Δt oscillation terms. Of course, experimentally
2.1 The ΔS Pursuit 13

Fig. 2.1 Figure illustrating TCPV measurement. The Υ (4S), which decays into a B0 –B̄0 pair, is
boosted in the z direction. After one B is tagged by its decay, quantum coherence dictates the other B
would start evolving from the conjugate of the tagged state. At time Δt = γβcΔz (can be negative),
where Δz is the measured difference between the decay vertices, the other B decays into a CP
eigenstate such as J /ψ KS . See text for further discussion

Fig. 2.2 Schematic side

view of the Belle detector,
with markings of the
subdetector systems.
[Source http://belle.kek.jp/
belle/transparency/detector1.
html]

one has to correct for inefficiencies and dilution factors, which we do not go into.
As discussed in Chap. 1 and Appendix A, SJ /ψK 0 is just sin 2β/φ1 , the CPV phase
of B0 –B̄0 mixing amplitude, while AJ /ψK 0 is the direct CPV for this mode.
To conduct ACP (Δt) measurement, as illustrated in Fig. 2.1, one needs to,
(1) Tag the flavor of one B decay (B0 or B̄0 ) at “t = 0”, and
(2) Reconstruct the other B in a CP eigenstate (cannot tell B0 versus B̄0 ),
(3) Measure decay vertices for both B decays.
For the last point, one utilizes the boost along the z or beam direction, and
Δz ∼= γβcΔt is the measured difference between the two B decay vertices. The
γβ factor is 0.56 and 0.43 for PEP-II and KEKB, respectively. With B lifetime of
order picosecond, γβcτB is of order 200 micron or so. For the CP side, one therefore
demands a σz resolution of less than 100 micron.
The BaBar and Belle detectors are rather similar to each other. A side view of
the Belle detector is given in Fig. 2.2 showing subdetectors. The subdetectors of
14 2 CP Violation in Charmless b → sq̄q Transitions

BaBar and Belle consist of a silicon vertex detector (SVT/SVD), a central drift
chamber (DCH/CDC), an electromagnetic calorimeter (EMC/ECL) based on CsI(T),
a particle identification detector (PID) system, superconducting solenoid magnet, and
an iron flux return that is instrumented (IFR for BaBar) for KL and muon detection
(hence KLM for Belle).
The difference between the two detectors are basically only in the PID system
that is crucial for flavor tagging, in particular the task of charged K/π separation at
various energies. Note that, even for B → J /ψ K decay, pK is almost 1.7 GeV/c and
rather relativistic, and in addition one has the boost. The Belle PID system consists
of Aerogel Cherenkov Counters (ACC), a threshold device with several indices of
refraction n for the silica aerogel for different angular coverage, plus a TOF counter
system. BaBar uses the DIRC, basically a system of quartz bars that generate and
guide the Cherenkov photons (by internal reflection) and project them into a water
tank at the back end (called the Stand-off-box, or SOB) of the detector. It provides
more dynamical information, but the large SOB is a little unwieldy.1 One other
difference between Belle and BaBar is the Interaction Region (IR), which is at the
intersection between detector and accelerator. PEP-II made the conservative choice
of zero angle crossing (electrostatic beam separation by permanent magnets), while
KEKB used finite angle crossing. This eventually became a main limiting factor for
the luminosity reach of PEP-II, although it ensured faster accelerator turn-on. In any
case, it is truly impressive that both accelerators reached beyond design luminosities,
especially since the asymmetric energy design was a new challenge.
The real novelty of the B factories, of course, is the asymmetric beam energies.
The γβ factor for the produced Υ (4S) is 0.56 and 0.43, respectively, for PEP-II and
KEKB. Boosting the B0 and B̄0 mesons allowed the time difference Δt ∼ = Δz/βγc
used in (2.1) to be inferred from the decay vertex difference Δz in the boost direction,
while the proximity of 2mB0 to mΥ (4S) means rather minimal lateral motion. Both
the PEP-II and KEKB accelerators were commissioned in 1999 with a roaring start.
By 2001, KEKB outran PEP-II in the instantaneous luminosity, and in integrated
luminosity as well by the following year (see Fig. 2.3). In April 2008, PEP-II dumped
its beam for the last time.
With the good performance of the accelerators, and with relatively standard detec-
tors, by 2001, the measurement of the gold-plated mode of B0 → J /ψK 0 (including
KL0 ), was settled. As can be seen from Fig. 1.3, the mean value between Belle and
BaBar remained largely unchanged since then. It would seem that the raison d’être
of the B factories was accomplished just two years after commissioning!

1 The aerogel technique was originally developed at BaBar, and adopted by Belle when there was
insufficient confidence in the original design of a RICH detector system. When BaBar adopted
the innovative DIRC, the extra space available, together with budget pressures, lead to a slight
compromise of the EMC system.
2.1 The ΔS Pursuit 15

Fig. 2.3 Comparison of

integrated luminosities
achieved by KEKB/Belle
and PEP-II/BaBar, up to
early summer 2007

2.1.2 TCPV in Charmless b → sq̄q Modes

With the measurement of TCPV in B0 → J /ψKS settled in summer 2001, attention

quickly turned to the b → s penguin modes, where a virtual gluon is emitted from
the virtual top quark in the vertex loop.
Let us take B0 → φKS as example [7], where, as shown in Fig. 2.4a, the virtual
gluon pops out an ss̄ pair. The b → s penguin amplitude is practically real within SM,
just like the tree level B0 → J /ψKS . This is because Vus∗ Vub is very suppressed, so the
c and t contributions carry equal and opposite CKM coefficients Vts∗ Vtb ∼ = −Vcs∗ Vcb ,
which is practically real, as can be seen from (A.3). Thus, one has the SM prediction,

SφKS ∼
= sin 2φ1 /β, (SM) (2.2)

where SφKS is the analogous TCPV measure in the B0 → φKS mode, following the
Sf notation of (2.1). New physics induced flavor changing neutral current (FCNC)
and CPV effects, such as having supersymmetric (SUSY) particles in the loop (for
example, b̃–s̃ squark mixing, Fig. 2.4b), could break this equality. That is, deviations
from (2.2) would indicate New Physics. This prospect prompted the experiments to
search vigorously.

Fig. 2.4 a Strong penguin (a) W (b) g̃

(P) diagram for B̄0 → φK̄ 0
in SM, and b a possible s
b s b
diagram in SUSY with b̃–s̃ s̄ s̄
squark mixing, which is g g
illustrated by the cross on the s s
squark line inside the loop d¯ d¯ d¯ d¯
16 2 CP Violation in Charmless b → sq̄q Transitions

The first ever TCPV study in charmless b → sq̄q modes was performed for
B0 → η  KS [8] by Belle in 2002 with 45M BB̄ pairs [9]. Part of the motivation is the
large enhanced rate, which is still not fully understood. But many might remember
better the big splash made by Belle in summer 2003, where SφKS was found to be
opposite in sign [10] to sin 2φ1 /β, where the significance of deviation was more than
3σ. However, the situation softened by 2004, and became far less dramatic. What
happened was that the Belle value for SφKS changed by 2.2σ, shifting from ∼ −1
in 2003, to ∼ 0 in 2004. 123M BB̄ pairs were added to the analysis in 2004, but
they gave the results with sign opposite to the earlier data of 152M BB̄ pairs. The
new data was taken with the upgraded SVD2 silicon detector, which was installed
in summer 2003. The SVD2 resolution was studied with B lifetime and mixing and
was well understood, while sin 2φ1 measured in J /ψKS and J /ψKL modes showed
good consistency between SVD2 and SVD1. Many other systematics checks were
also done. By Monte Carlo study of pseudo-experiments, Belle concluded [11] that
there is 4.1% probability for the 2.2σ shift. This is a sobering and useful reminder,
especially when one is conducting New Physics search, that large fluctuations do
happen.
The study at Belle and BaBar expanded to include many charmless b → sq̄q
modes. After several years of vigorous pursuit, some deviation persisted in an inter-
esting but somewhat nagging kind of way. Let us not dwell on analysis details,
except stress that this became one of the major, concerted efforts at the B factories.
For a snapshot, compared with the 2007 average of Scc̄s = 0.681 ± 0.025 [12] over
b → cc̄s transitions, Sf is smaller in practically all measured b → sq̄q modes (see
Fig. 2.5), with the naive mean2 of Ssq̄q = 0.56 ± 0.05 [12]. That is,

Ssq̄q = 0.56 ± 0.05, vs Scc̄s = 0.681 ± 0.025. (HFAG 2007) (2.3)

The deviation ΔS ≡ Ssq̄q − Scc̄s < 0 was only 2.2σ from zero, and the significance
was slowly diminishing. However, it is worthwhile to stress that the persistence
over several years, and in multiple modes, taken together made this “ΔS problem”
a potential indication for New Physics from the B factories. Despite the lack in
significance, it was not taken lightly, as the experiments were not able to “make
it go away”. By Summer 2008 and onwards, however, HFAG updates suggest no
deviation, and the “ΔS problem” now rests in the errors.
One reason that kept the interest is that theoretical studies, although troubled by
hadronic effects, all gave Ssq̄q values that are above (see e.g. [13–16] Scc̄s , or

ΔS|TH > 0. (2.4)

2 We use the LP2007 update by HFAG that excludes the Sf0 (980)KS result from BaBar at that time.
The Heavy Flavor Averaging Group (HFAG) itself warns “treat with extreme caution” when using
this BaBar result [12]. The value is larger than Scc̄s and is very precise, with errors 3 times smaller
than the φKS mode. But f0 (980)KS actually has smaller branching ratio than φKS !
Another random document with
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knows. But they found the peaceful and sedentary pueblo Indians an
easy prey, and gradually they drove them all out of these cliff
dwellings in the mountains to build themselves defensive villages on
the high mesas of the Painted Desert to the north.
Sid and Big John stopped at that natural doorway to look out below.
Cañon Honanki lay a green-spired paradise below them. Bare,
barren cliffs, streaked with color, rose opposite. A short way down
the valley the horses could be picked out grazing placidly. The
watchful Blaze lay near them and he rose and barked at sight of his
master, his faint volleys echoing up the cliffs.
“Now for Mr. Inaccessible—the cavate dwelling!” exclaimed Sid
triumphantly. He led on upward until he came to a low door built in a
stone wall laid up without mortar. Entering it, they saw that a round
window cut through the cliff stone lit up the small cave room.
Baskets, finely woven, of a texture and quality seldom seen
nowadays, greeted Sid’s delighted eyes. There were shallow
marriage and ceremonial baskets; bottle-shaped ones waterproofed
with piñon gum, the kind now called tus and used in medicine
dances; large granary baskets still filled with dry kernels of blue,
black, red, and white corn. A few black pottery jars, decorated with
white lightning zigzags, stood in the corners. Strings of corn ears,
red peppers, and dried onions, all musty and shriveled, hung from
poles let into the roof of the cave.
“The old bird was a rain-maker, all right,” said Big John, pointing
irreverently at the zigzags on the jars and baskets. “Claimed he
invented the lightning, all-same as Benjamin Franklin.”
But Sid did not answer. Instead his eyes were riveted in sheer
astonishment on the smooth rock wall of the cave, and he grabbed
Big John’s sleeve and pointed, speechless with wonder.
“Gorry!—Look there, John!” he finally found breath to exclaim. “Here
is the last place a fellow would expect to see the writing of a white
man, I’ll say!”
“Well, I’ll be durned!” growled Big John, peering at the letters with
Sid.
Written on the wall, in red earth letters and still as bright as the day
they were made, was—a name! a Spanish name!
Fra Pedro Del Vacas, 1680.
“Can you beat it!” cried Sid, breathlessly. “Gorry, what a find!—Le’s
see, John,” he went on excitedly, “1680 was the year of the big
massacre, wasn’t it?”
“Search me!” said Big John whimsically. “All I know about them
greasers is that you shore don’t have to oil yore bullets none to slip
’em through their feathers.”
“Sure it was 1680!” continued Sid, ignoring Big John’s observation
upon our Mexican neighbors. “That year all the tribes rose against
their Spanish friars. Most of them were murdered or martyred—
especially those that the Apaches got hold of. This Fra came up here
to the old shaman for refuge. Why did he write that inscription then?
Because he was dying, of course! Escaped from the Apaches
somehow, wounded perhaps, and was carried up here by the pueblo
people. The Spanish missionaries did not carve their initials on every
rock. He left his name for the next missionary to find, if ever one
should visit this pueblo again. It means something, John. We’ll look
for pueblo graves, next, and maybe get some more light on it.”
Sid’s idea of searching for graves might seem astounding to any one
but an ethnologist. But the richest prehistoric relics are always
obtained from exhumed graves, usually located near some shaman’s
cave. The body was always mummied, and with it were buried most
of the pueblo Indian’s possessions. Here the early cotton blankets,
yucca sandals, baskets, pottery, and weapons are found in a
tolerable state of preservation, and they all show that the prehistoric
pueblo dwellers lived very much as their descendants do to-day.
Big John was used to Sid’s intense enthusiasms in ethnological
matters and was accustomed to following him around—to see that
he “didn’t break his fool neck an’ so cheat that rope that’s waitin’ fer
him” as he always put it. He bent his tall frame in pursuit as Sid
dodged out of the house and darted for a deep and dusty grotto that
lay behind it. A huge horizontal fissure, not over four feet high, had
been worn out here by the waters, undermining the cliffs above for a
considerable distance. A stratum of mud, long since dried to dust,
covered the floor of the fissure. Closely dotted over it were slabs of
stone, under each of which one would find a small stone kiva or dry
well. The mummy would be discovered sitting upright in it, swathed
about with cotton blanketing made long before the first wool from the
first sheep that gave it was stolen from the Spaniards by the Navaho.
Generally also the mummy was covered with ceremonial basketry.
But Sid passed them all by, for the present. What he was searching
for now was a white man’s grave. And, far back under the rock he
found it, a long mound with a rude cross set in the dust at its head. A
single flat stone lay across the center of the mound.
Raising it, the persistent Indian burial customs proved to have been
still adhered to. A long black robe, with a ghastly skull peeping from
the cowl, lay flat on the bottom of the niche, which was a sort of
stone coffin, its sides lined with stone slabs built in shallow walls
precisely like the Indian rivas. The top was roofed over with stone,
on which the earth had been mounded up as the white priest had
evidently directed it should be. There was nothing else in the grave.
Nothing, that is, but a flat slab of pottery, lying across the dead friar’s
chest!
Its square shape at once attracted Sid as unusual and not Indian. He
picked it up with queer thrills running all through him. A message
from that white man of long ago! For there was writing graven on the
clay, and the three letters “D. O. M.” stood at the head of the plaque.
“A Dominican friar, he was, John,” said Sid, reverently. He began to
read aloud the sonorous Latin written on the plaque, conjuring up his
forgotten Cæsar of high-school days.
“What’s that stuff, huh?” inquired Big John. “Sounds like spig talk, but
’tain’t. I’m a hundred per cent American, Sid, I am, an’ I don’t like it,”
he growled, shaking his head sturdily.
“Can’t make it out myself,” confessed Sid, after reading it a little
farther. He found that he had forgotten his Latin so much that merely
to pronounce the words was an effort. “Here’s a few that I do know,
though, John: ‘Aurum et Argentum,’ that’s gold and silver; ‘Pinacate,’
‘Sonoyta,’ those are places; ‘Papagoii’, the Papagoes; ‘Mesa Rubra’
that’s Red Mesa——”
“Never heard tell of it,” declared Big John, promptly. “Thar’s a red
mesa up Zuñi way, but there’s no gold or silver thar; an’ Pinacate is a
long thirsty ride down over the lava country into Mexico. Ain’t no
mesas in that country nohow. She’s all red lava saw-teeth an’ spiny
choyas—if you asks me.”
“It’s an old Spanish mine—that’s what the plaque’s all about!”
shouted Sid, excitedly. “Some of the Papagoes must have told this
old fra about a gold and silver mine, located in Red Mesa down
Pinacate way—say, Scotty will have to hear of this John!” whooped
Sid, carried away by the enthusiasm of the moment.
Big John shook his head solemnly: “Son, folks has died of thirst in
thousands, chasing lost Spanish mines in that country! Santa Fé’s
full of old priest reports like this-yer. The Indians shore did stuff ’em
with gauzy tales! Thar’s mineral down thar, I’ll ’low; but after ye find
it, what ye got? Reminds me of the recipe for cookin’ a fish-duck. Ye
take an’ soaks him in three kinds of soup; bile him four days; stuff
him with an apple an’ a onion; tie a bunch of celery ’round his neck,
wrap him in a couple of slabs of bacon; stick in a hunk of garlic; add
salt, pepper, and a bottle of wine; bake him three hours—an’ presto,
the gosh-darn fish-duck is gone! That’s how a feller feels when he
finds a mine in that country, Sid; ye cayn’t git the miner’l out nohow!”
Sid’s laughter pealed out. “Well, we’ll hunt up old Scotty just the
same and then go get some one to translate this Latin. Scotty’ll just
go crazy over this tablet, and he needs the money, John. We can
come back here for the Indian relics some other time. Scotty and
Niltci are prospecting down in the Santa Catalinas for mineral, right
now, you know——”
“An’ they won’t find nawthin’ down thar thet ain’t been found long
ago, jest as I told him,” interjected Big John.
“Sure! We’ll ride down there and give him this tablet. It will be a life-
saver for old Scotty! Red Mesa or bust! John—how’s that for a new
motto?”
“Looks handsome, but she ain’t edible,” said Big John, enigmatically.
But Sid just couldn’t get over his enthusiasm for his chum Scotty’s
sake about this Latin tablet. What a find for good old Les! That mine
would be his big chance! Friendship was sweet; to be able to do
something for a chum was keen pleasure. He sat down and went on
studying over the tablet, balking at strange Latin words, digging up
more of them out of his memories of his school Cæsar. The old
pottery plaque fascinated him. He kept speculating about it, how it
came to be made, where the old fra had got his information about
the mine. What an ancient old story this was!
“This fra used to live with the cavate dwellers here, John, I tell you!
He made this plaque and had them fire it when they baked their own
pottery. Imperishable record, you see. It’s a real find, I tell you! One
of those lost Spanish mines that really is so! ‘In regione Papagoii’
that’s the Papago country of Pinacate, all right. ‘XXI milia S-O ab
Pinacate’ plain as shootin’, twenty-one miles northeast from
Pinacate, ‘Mesa Rubra’—there’s a hill that looks like a red mesa
down there—that’s the dope! Gee! What a start for good old Scotty!
Le’s go! We’ll ride straight for his camp in the Catalinas!”
Big John grinned saturnine grins as he deposited the pottery plaque
in the small rucksack without which he never left his horse. Then he
got up and followed the eager Sid down the long, dark ascent of
steps up which they had come.
 CHAPTER II
THE LURE OF THE MINE
“IT’S panning out mighty low-grade stuff!—Dog-gone it!”
The young man who made this ejaculation, and in a most
discouraged tone, too, was slender and wiry, with sandy reddish hair
surmounting a Scotch cast of features. His face was freckled and
sunburned. The inextinguishable hope of youth still flickered in his
blue eyes, but there was worry, anxiety, there, too—the sign of that
nagging, cankering care that keeps a fellow thin.
He shook his head as he held up a test tube in its wooden holder to
the sunlight.
“Won’t do!” he muttered. “Anybody can find a mine in Arizona—but
few can find a paying one.”
He looked about him at the silent and colorful mountains surrounding
him, hopeless misery in his eyes. They had no answer for him! The
brush sunshade that he and the Indian boy who was his companion
had established was Scotty Henderson’s base camp for mine
prospecting. Our readers may have met him before—on the trip for
the Ring-necked Grizzly in Montana or when after the Black Panther
of the Painted Desert country of Arizona.
Leslie Henderson—Scotty’s real name—had a heavy load to carry,
for a youth of nineteen. It weighed nothing physically but mentally it
was a burden far beyond his years. And the letter from his mother
that he was now carrying in a hip pocket of his riding breeches had
added a sickening load upon a mind already worn with anxiety. It had
told him, as gently and self-sacrificingly as possible, of his mother’s
decision to sell the old Henderson place back east. The cost of living
had gradually come to exceed Major Henderson’s pension, which
was all the Great War had left them of his father, the good old
Doctor. To a woman used to comforts and a roof over her head as a
matter of course, to say nothing of the ancestral associations of that
homestead, that decision of Scotty’s mother was a far heavier blow
to her than her words would admit. Delicately put, it meant in plain
words that Scotty would either have to strike a paying mine claim
soon or else give up his heritage of independence, that heritage that
every real man claims as his birthright, and take a position
somewhere in some great mining corporation. And the outlook was
pretty black, now.
“No go, Niltci!” groaned Scotty, emptying the green fluid in the test
tube with a gesture of discouragement, “we’ll have to break camp
and move on.”
With that decision the hopelessness of all this endless prospecting
surged over Scotty in an overwhelming wave. Arizona had been
combed all over for mines! There was plenty of this sort of thing, this
scanty and scattered deposit of copper carbonate, poor in per cent of
metal, all through its mountains. The real thing was far different. Not
impossible to locate; for each year, even now, sees some new and
fabulous lode opened up. But the scattered, thin deposit of this gulch
would take a mountain railroad to develop it and the most expensive
of electric process works to reduce it to metal. Take this ore back
east and men could make money out of it, but that “take,” that train-
haul which would cost more than the ore was worth, was the rub!
For a moment a gorgeous vista of temptation opened up before
Scotty. All he really needed to do to become rich was to go east with
some of these picked specimens and float a “paper” copper mine,
the kind that robs thousands of poor people of their earnings by false
and visionary “literature”; that were never intended to do more than
line the pockets of those scoundrels who make their living cheating
the public that way.
But the mute reproach of the silent mountains to that temptation was
enough for Scotty. Even the poor prospector with burro and pick who
had come this way before had been too honest for that! He, some
one of him, had without doubt explored this very valley long before
Scotty; he had looked over this ore and gone on, knowing well that in
practice it would never pay.
“Nothing doing!” said Scotty to himself, his honest soul recoiling in
horror before the gilded prospect of a wildcat mine floated back east.
“But, while there’s life there’s dope!” he grinned. “Where next?
Dashed if I know! Le’s break camp anyhow, Niltci.”
The Indian youth grunted inquiringly from where he squatted, with
the stoic patience of the Indian, under their brush shade. He pointed
a coppery finger out at a lariat rope stretched between two
mesquites in the sunlight of the hill slope. On it hung a ragged
collection of meat strips, like stockings on a clothesline. They still
glistened, raw and red, in the hot blaze of the cloudless sky
overhead.
“Charqui no done,” he demurred, shaking his head. “Three sleeps
yet.”
He was referring to their store of dried venison; “jerky” as the
cowmen call it, only he used the original Spanish name for it, charqui
—dried meat.
“Gee, I’d forgot about our grub stake! Hope,” observed Scotty,
“springs infernal in the human breast, Niltci! Grub’s our real problem,
now. Let’s let the mine wait and play hunters a bit, eh?”
As if to answer him the musical notes of a hound belled down from a
distant mountain flank. There was sparse, dry-soil timber all over
these hills, piñon, spruce, stunted western yellow pine and the
inevitable aspens. The hills were bare and bony, and they blazed
with orange and lavender color, for it was November, but there was
game in the valley timber, lots of it, deer, cougar, bobcat, and an
occasional cinnamon bear. Wild turkey inhabited the depths of the
cañons, so plentiful that they formed the daily fresh meat of their
camp in addition to the abundant trout which the Apaches disdained
to catch and eat.
Scotty listened a moment to the musical notes floating down through
the valley.
“There goes Ruler!” he cried. “Let’s get the horses and see what he’s
after!”
Niltci, the Navaho boy, sprang to his feet grunting assent eagerly. His
lithe form bounded down the slope towards a grass meadow, his red
bandanna a blazing note of color, set off by an equally blazing white
cotton shirt contrasting with his long, dark blue leggins which
sparkled with rows of barbaric silver buttons. In a trice he was
leading back Scotty’s chestnut mare and his own flea-bitten desert
pony. Ever since Niltci had miraculously “disappeared” during the
religious excitements of his own people over the Black Panther, he
had been with Scotty on his mining expeditions down here, far to the
south in the Apache country of White River and far away from his
own people. To his white friends he had owed his life that time—a
debt that, to a Navaho, is never paid.
He handed Scotty the mare’s halter and started deftly saddling his
own pony. Ruler’s bays came unceasingly down through the
mountains. Their giant coonhound was of an indomitable
persistence; he could be depended upon to follow that trail, whatever
it was, for days on end without relenting.
“Up the coulée, Niltci!” shouted Scotty, vaulting his horse and
clattering down the slope from camp. Behind him the fast hoofbeats
of the Navaho’s pony followed. The mare crossed the creek bottom
in a single jump and began working up the opposite flank in a long
slant. On ahead an occasional yelp from Ruler gave inkling of his
whereabouts. He was traveling fast, for the distance between them
did not seem to close up. Frightened deer burst from cover and
dashed down and across the stream bottom as they rode. A wild
turkey, scared into flight by the showers of rolling stones struck loose
by the horses, soared over the willows in the ravine and disappeared
in a mass of thick green.
Then, behind Scotty, Niltci grunted eagerly and made a queer sound
that was half a yelp.
“Yep! I see him, Niltci—cougar! There he goes!—regular old he-one!”
gasped Scotty, jouncing in his saddle as he bent to drag his rifle from
the holster. The mare shied as the heavy .405 swung out around her
flanks. Scotty’s knees gripped her fast and he let the horse go with
the bridle reins dropped over the pommel.
Ruler’s deep tones now came back in explosive volleys.
“Ow-ow-ow! Ow-ow-ow!” he sang, belling a hot trail.
“Heading north, up the cañon!” yelled Scotty, galloping through the
timber at full speed. “Look at him go!”
He pointed out a running cougar far up on the yellow mountain sides,
galloping along in easy bounds that seemed effortless. His tawny
body doubled and stretched out in the queer lope of the cat tribe,
now trotting with fast-moving feet, now humping up in the swinging
bounds of the gallop. He seemed very like a buff and white
household cat magnified to enormous size. His tail drooped behind,
tapering from a thick root seemingly as wide as his hips to a ropy
furry length that undulated as he sprang easily up over the rock
ledges.
“Gee, he’s an old Tom, Niltci!” called back Scotty over his shoulder,
“Hi-Hi!—Go it, Ruler!”
The big reddish brown coonhound yodeled in answer. He was racing
along perhaps halfway between them and the cougar, a red dot on
the hot sunlight, bellowing forth bursts of hound music as he ran.
Above them soared the high walls of the cañon, at least a mile up to
the rim, yellow and blue-shadowed and dotted with dark green
conifers. A hideous gulch, as it would look to a city dweller,
terminated the cañon walls as they narrowed, and it was cleft high
above by a dry arroyo that was all stones and boulders. But to Scotty
this was the finest place on earth, and it was a jolly old world anyhow
—in spite of mines that failed to pan out! His one anxiety was that
the cougar might reach the timber up on the rim plateau and then
turn on Ruler before they could get up there. The cat was far up,
near the head of the gulch, and going even faster than they were.
Like tiny Japanese pines the distant trees on the rim seemed to
welcome him, and, while the panting horses and men labored hard
up the slope, the cougar bounded over a ledge of broken rock and
was gone into the timber.
Niltci grunted. “Wah!” he exclaimed disgustedly. “Lose dog! Cougar
kill him! No good! Take pony quick—me climb up straight.”
His little horse clattered close behind and Scotty reached back for
the bridle. Niltci vaulted from the saddle and with quick lithe
movements he began to climb vertically up the cañon slope. Scotty
urged the mare on up the long slant that would bring him out
somewhere near the beginning of the cleft that made the arroyo. He
got two glimpses of Niltci’s blue leggins swarming up over vertical
ledges far above him; one brief sight of Ruler scrambling up over the
rim ahead on the cougar’s trail; and then he was all alone, with the
empty, silent, gorgeous mountains brooding majestically around him.
With his passing and the shower of stones that his pony was sending
down, they would return again to the eternal peace that was theirs.
Apache, frontiersman, cavalryman, prospector, all in their turn had
come and gone, to disturb their meditations for a brief moment, to
pass on leaving these lonely cliffs and pines their silent and
inscrutable witnesses.
Scotty leaned over and whispered a word in the mare’s ear. The
noble creature was giving him her best, with the boundless
generosity and disinterestedness of our four-footed hunting
companions, but somehow, somewhere, she found it in her to call
upon an extra burst of speed, some hidden reserve in response to
her master’s whisper. The top of the gulch was near now. With
distended nostrils, with heaving flanks, and hoarse soughing breath
the mare toiled up the last ledges and then vaulted over the rim.
An open country of great pines was that plateau. Shadows and
sunlight flecked the needles under the huge ponderosas. Scotty saw
a white flash running like a deer through the tree trunks—Niltci, who
could run faster than a horse for a short spurt. He was far ahead,
and as for Ruler, only a deep ringing bay told of his whereabouts.
“Wahoo!—Wahoo!” sang out Scotty, his whoops intended more to let
them know he was up and coming than anything else. The pony he
led behind him snorted and whickered at sight of Niltci and Scotty let
him go free at the hint. The flea-bitten little mustang immediately
loped on ahead in a fast clatter. This urged the mare to top speed
again, for she would let no horse pass her, if wind and legs could
prevent it!
Came a wild piercing screech and a savage miauling on ahead
somewhere. It sounded hoarse and ropy and vengeful; terrifying;
intended to strike a paralysis of fright into the creature attacked.
Scotty realized that the cougar had turned to the attack, finding that
only a dog was following him. Then Ruler’s voice floated back,
yelping and barking in a mixed medley of pain and fury. Scotty knew
instantly what had happened. The old Tom was mauling the dog
unmercifully. He would kill Ruler if help did not come instantly. Ruler
was all of eighty pounds in weight but the cougar was at least two
hundred and fifty and could beat him easily in a single combat.
A piercing whoop came from Niltci in answer to Ruler’s cry of
distress. Scotty at once whipped out the heavy .405 and its
thunderous roar rang out. The mare ducked and shied under its
cannonlike reports, but Scotty fired again and again, for he hoped
the sound of the bullets ripping through the timber would frighten the
cat into treeing if not too savagely engaged with Ruler.
As the mare burst out into an open glade, a wild drama under the
pines across from it met Scotty’s eyes. Ruler was dodging and giving
back, the cat following up and striking again and again with a tawny
and scimitar-clawed forepaw—bright flashes in the sunlight as of
curved steel hooks. Niltci was racing across the clearing, his bright
knife flashing in the sun, his wild black hair streaming out behind
him. He was sprinting his utmost to save the hound but he would be
too late if one of those terrible blows ever got home on Ruler!
Scotty threw the mare back on her haunches and raised a wabbling
rifle barrel. The scene through the sights was not reassuring. Dog
and cougar were so instantly changing places that it was impossible
to fire. All this was happening with the quickness of thought, and
Scotty felt reluctant to fire even a flash shot, for Ruler was whirling
about so fast that he might run into the bullet while it was getting
there.
And then a queer thing happened. Another tawny and grizzled body
suddenly projected itself into the fray! Where he came from Scotty
could not imagine, but a volleying bay of savage barks told him that it
was no cougar but another dog.
Scotty stared for a moment, rifle lowered. Then—“Blaze!” he yelled
in amazed delight—“Yeeoow!—Tear him, puppy!” he whooped. The
giant Airedale launched himself like a gray thunderbolt surcharged
with vim and power at the cougar’s throat. As Scotty watched them,
not daring to fire, the cat spun around and Ruler instantly seized a
hock hold. Claws flew through the air. Blaze bounded about the cat
like a rubber ball, just out of reach. A whoop of triumph came from
Niltci as he closed in swiftly with upraised knife. For a tense instant
Scotty sat watching a chance to fire from his saddle, his heart
beating so that he could hear the pulses through his own open
mouth. Then the cat whirled and soared through the air in one
tremendous bound that carried him twenty feet away. He hit the
ground running. There is no such speed as an old Tom can put on
when in a tight place! He seemed literally to fly through the air, Blaze
and Ruler a jump or two behind him. Niltci gave up the chase and
snatched at the bridle of his pony as that faithful creature raced up
after him. Scotty put spurs to the mare and galloped off in hot
pursuit.
“Hi! Blaze! Hi! Ruler!—Wahoo!” he yelled, throwing the bridle over
the mare’s neck. In answer a stentorian Whoopee! came ringing
back through the forest. That was a man’s voice, and almost
immediately following it there was a crash in the timber and a white
horse thundered through the pines at right angles to Scotty’s course,
the tree trunks seeming to pass the white flash of the horse like
fence pickets.
“Left!—Left!—You pisen—li’l—horned—toad!” came Big John’s iron
voice, jolting to the rhythm of his gallop. Scotty whooped back
greeting at him and then wheeled obediently. The cat and both dogs
were in plain sight ahead of him but Big John had an uncanny
foresight in the ways of big game, and he had no doubt foreseen
some sort of twist or short cut on the cougar’s part. The timber
cleared ahead of Scotty now, and out to the left in it he saw a giant
pine, already dying of old age. For it the cougar had turned and was
now racing at top speed. He ran up its huge bole like a cat climbing a
tree, a shower of bark spalls raining down from his claws. At the first
big dead branch he stopped and turned below his black muzzle,
spitting and snarling from an open pink mouth at the dogs
underneath. Ruler was prancing around on his hind legs, yelling with
eagerness, while Blaze savagely scrambled up the trunk, to lose his
grip and tumble down and indomitably attempted it again.
Big John reined in the white horse. “Now’s yore chance to do the
pretty, Scotty, old-timer—afore he jumps down—shoot!” he yelled.
Scotty quieted the mare and raised the .405. Its enormous bellow
rang out. The cat screeched and launched forth with all four claws
spread in the convulsive flurry of death. He struck the pine needles
with a heavy thud and instantly the dogs charged in, growling and
worrying at him, while old Tom rolled over on his back and spun his
claws in the instinctive defense of a cat in his last throes. Niltci
clattered up on the mustang at that instant. In a flash he had leaped
from his horse, bounded to the cougar’s side and jumped away,
leaving a red knife-handle sticking out behind the cougar’s shoulder
blades. Again there was a flash of his nimble body and the knife
came out, while blood spurted six feet from the gash. The cougar
groaned and stretched out on his side, quivering and sighing
peacefully as if falling asleep. His eyes glazed; then the body
stiffened and stretched in a last tremor.
Blaze ran up on the carcass and bared white fangs at Ruler. His
attitude was crinky, cocky as a prize fighter’s, and he honestly
believed that he had killed that whole cougar all by himself! He dared
Ruler to come on. As the latter had convictions of his own
concerning that cat, a royal dog-fight seemed imminent—but Niltci
seized the hound’s collar and held him back by main force.
Big John laughed uproariously. “Hol’ him, Injun!” he roared. “Ruler’ll
be gobblin’ more’n he kin chow, fust ye know! That Blazie boy’s
feelin’ reel mean an’ ornery, danged ef he ain’t!”
Scotty laughed as Big John dismounted to boot the Airedale off the
cougar, for Niltci had signified that he wanted to begin skinning out
but wasn’t any too anxious to go near the belligerent Blaze.
“Where’s Sid, John?” asked Scotty, collecting his thoughts for the
first coherent greeting that the swift action of the hunt so far had
allowed.
The big cowman’s eyes twinkled. “Sid, he ain’t travelin’ none, these
days,” he grinned. “He’s back thar, somewhar, nursin’ along a sort of
present for ye, Scotty.” He winked enigmatically at the youth.
“How come?” asked Scotty, mystified. “Present, eh?”
“Yaas, he’ll come a-singin’ with it, pronto. Some dago writin’ on a
piece of Injun pottery, ’tis. We-all was headin’ for yore camp when we
heard Ruler kyoodlin’ back thar a-piece,” he explained, “so Blazie
and I, we ’lows to set in the game. But Sid he’s afear’d to ride, which-
same’s because he mought break that thar curio. We found it in one
of them caves, after the most all-fired climb this hombre ever got
inter, I’m settin’ here to tell ye——”
“Here he comes, now!” interrupted Scotty, whipping off his sombrero
to wave it at a new rider who came plodding through the pines with a
led pack cayuse following him. “Whoopee!—Oh, Sid!” he yelled.
The rider waved back. The dogs put out for him pell-mell, Ruler
leaping and fawning up on his saddle flanks, so overjoyed was he at
seeing Sid again, the Airedale jealously shoving in to get his share of
the caresses. Presently Sid rode up to where Big John and Niltci
were busily skinning out the cougar and butchering big sections of
the delicious meat.
“Hi, Sid!—what’s all this Big John’s telling me about a present?”
Scotty greeted him. “Gosh knows, I was feeling pretty blue not so
very long ago! Did you remember it was my birthday or anything?”
he bantered.
“It’s a mine for you, Scotty!” announced Sid, breathlessly, his eyes
alight with the joy of him who gives, “an old Spanish mine! Got the
dope here on a pottery tablet that we found in a cave dwelling.”
“Gorry!—a mine!—le’s see it!” cried Scotty. “A real, sure-enough
mine? I’d begun to think there was no such thing left in Arizona.”
“It’s at a place called Red Mesa, down near Pinacate, Scotty,” said
Sid. “The dope’s all in Latin and I can’t read much of it, but we’ll hunt
up a priest somewhere and get him to translate it——”
Scotty’s face fell, even while Sid was speaking. “‘Down near
Pinacate!’” he echoed, huge disappointment in his tones. “It can’t be,
Sid! Why, that’s all lava country! There’s no mesa or mineral down
there.”
“How about the Ajo Mines?” challenged Sid. “And there’s lots of ore
north of Sonoyta, only it costs too much to work it. You know that
yourself.”
“By gosh, you never can tell!” exclaimed Scotty, excitedly. “It’s
possible, though! There’s granite outcropping, even down at
MacDougal Pass, only fifteen miles from Pinacate. We’ll try it!”
“Hope it isn’t in Mexican territory—but no, ‘twenty-one miles
northeast of Pinacate,’ the plaque says——”
“Gee! Le’s see it!” cried Scotty eagerly.
Big John grinned sardonic grins as the two youths got the plaque out
of Sid’s saddlebags and held it between them, scanning it excitedly.
He heard Scotty eagerly bark out the word “‘aurum’—gold?” and
shook his head.
“’Pears to me that every white man but me goes crazy over that word
‘gold’!” he growled whimsically. “Fellers will lie, steal, murder, get
themselves killed with thirst or et by grizzlies—an’ all for somethin’
that they don’t want when they’ve got it!” he exclaimed. “Scotty, ef it
warn’t for you bein’ a minin’ engineer I’d warn ye to leave it alone!”
he said positively. “Exceptin’ it’s now November and the tanks is
probably full down thar, I wouldn’t let you go, nohow.”
But Scotty was hardly listening to him. A planning look was in his eye
and his engineer mind was already envisioning not the mine itself but
the practical ways to get out the metal.
“Ship base in Adair Bay; burros up to the mine; carry the ore in
bottoms through the Panama Canal to the East, where we can get
cheap process reduction—Gee! There’s nothing to it!” he averred
enthusiastically.
“C’rect—nawthin’ a-tall, li’l hombre!” grinned Big John sardonically.
“No water; no feed for yore burros; no road—an’ no mine!” he
declared.
“Yes, but ships, John!” urged Scotty. “That’s different. We can send
out a year’s supply of hay, oats and supplies for the camp just as
they do at Las Pintas, and bring back the bottoms in ore. It’s mighty
different from some inland proposition, hundreds of miles from either
rail or sea routes. If this tablet is reliable, the engineering side of it is
a cinch! Le’s hear the ethnologist.”
Sid spoke up on this prompting: “We know well that all that country
has been explored since the earliest times by the Spaniards,” he
contributed. “Sonoyta has been inhabited by them for over two
hundred years, and one of their oldest missions is San Xavier, the
one for Papago Indians who used to hunt all that country. The friars
were Dominicans—D.O.M., you see. This Fra Pedro undoubtedly got
his information from some Papago visitors to the pueblo tribes. He
made that pottery record and had it fired while proselyting among the
pueblos of the San Pedro River—probably named the river himself
after his patron saint. It all fits in, see, John? Then he got wounded
or hurt, somehow, in the general massacre of the friars in 1680 and
died in the refuge of that cavate dwelling. The Indians buried his
plaque with him in a sort of kiva. The thing seems straight enough to
me,” concluded Sid.
“Me too!” grinned Big John. “I gotto nurse you two pisen mean young
reptyles down into that no-man’s land—I see that!” he snorted.
“Waal, le’s git back to yore camp, Scotty, an’ I’ll git the outfit ready.
Niltci’s goin’, of course. We gotto hev at least one Injun down in that
country. Thar’s lots of mountain sheep down thar, an’ that means
hoss feed, galleta grass. We’ll git a few pronghorns (antelope),
mebbe, out’n them lava craters. Ef the tanks is not dry, we kin resk
it.”
 CHAPTER III
VASQUEZ
LEAVING Big John and Niltci hard at work making pemmican from
the cougar and deer meat, and bags of pinole or parched corn meal
from corn purchased at a near-by Apache encampment, Sid and
Scotty rode a day’s march through the mountains to where there was
a mission school—San Mateo of the Apaches. Scotty’s idea was to
get the Red Mesa tablet translated by the teacher, who no doubt still
remembered his Latin.
A small adobe schoolhouse of primitive Spanish architecture came in
sight shortly after noon, surmounting a little knoll in the mountains.
As they rode toward it Indian children, boys and girls, came running
and yelling around them to beg pennies, and with them as an escort
they rode up to the hitching rail before the school, dismounted and
entered.
A lone Mexican teacher, poor and of uncertain temper apparently,
sat reading at the school desk as they entered. With an annoyed
exclamation in Spanish he put down his book and came toward them
during the time that their eyes were becoming accustomed to the
dim light of the interior of the building.
“And what can I do for the señores?” inquired the man suspiciously,
after the usual polite Spanish greetings had been exchanged.
Sid had already sized him up with a sense of misgiving, even then,
before a word of their object had been disclosed. The Mexican—his
nationality oozed out all over him—was a little weazened man, dirty,
old, with one eye drooping nearly shut from some violent slash
gotten during his past history. His face bore a sardonic, cynical,
rascally expression, even under the smooth suavity of the crooked
smile that now leered upon them. Sid felt like taking Scotty’s arm and
leading him away, right then and there! Surely this man was no one
to trust with such a mining secret as might be written on the Red
Mesa tablet.
But Scotty had already guilelessly begun explaining their visit. His
simple, “We have a Latin inscription here, señor, that we would like
you to translate for us,” had settled it, for the man was already
holding out his hand for the plaque which Scotty bore.
“You understand Latin, señor?” put in Sid, hoping that he didn’t.
“Vasquez,” supplied the Mexican, “ees my name. For the Latin, si!—
indifferently,” he shrugged. “Anything that my poor efforts can do to
help you, though—” Once more he held out his hand for the plaque.
Again Sid felt that queer inner warning not to let the matter go
further. He disliked any man who depreciated his own worth with
every other word. Due modesty was admirable, but this groveling
disdain of one’s self was in truth but the inevitable expression of a
fundamental lack of esteem for one’s own integrity—and that usually
came from a guilty conscience.
But it was too late now. Before Sid could obey a mad impulse to
snatch the tablet away—no matter what explanations might be
needed—no matter how absurd and incomprehensible and rude it
might seem—the Mexican had begun reading the script on the
pottery.
“D.O.M.—Deo Optimo Maximo,” he rolled out in the sonorous Latin
tongue. That was as far as he got in reading it out aloud to the boys.
For, immediately thereafter, an expression of amazed, puzzled
surprise came into his eyes as the boys watched him reading over
the script to himself. Then Sid noted intense concentration, and this
gradually gave way to an expression of crafty cupidity, an air of
envisioning something other than the words that his eyes were falling
on, of planning big enterprise, great affairs in connection with this
tablet. Vasquez went on to read the script entirely through in a still,
tense silence. Before he had finished, those snaky black eyes of his
were fairly blazing with avarice. Talk of the power of the word “gold”
to excite man! This man’s primitive nature stood stripped before the
boys; revealed was an elemental desire for possession before which
the rights of others, the entire veneer of civilization were stricken off
as phantoms. He might as well have been some Mexican greaser
griping at a pile of gold on some disreputable faro table along the
border!
As Sid watched, the face before him looked up. Instantly it went
blank, expressionless. There was a period of reflection, while the
boys waited expectantly, then a crafty, planning look came into the
eyes.
He folded the plaque under his arm—gesture of possession, which
we are told, is nine points of the law.
Vasquez smiled—a practical declaration of ownership—a
maddening, infuriating smile; the superior smile of the older man
toward youth, which seems to question the right of the young man to
busy himself with anything at all but the toys of childhood. Sid found
it particularly unbearable. He had been smiled at that way before,
when some staid and sophisticated professor had smiled indulgently
at him over some of his own theories in Indian ethnology, theories
which Sid propounded with all the fire of his youthful enthusiasm and
conviction.
“Caballeros,” said the Mexican craftily, “this matter can have no
possible interest to you, since it happens to refer to the work of the
missionary brothers among the—ah, the Papagoes—” he hesitated,
referring to the script as if to refresh his memory, his thought
evidently being that the boys might have recognized that word in the
Latin. “Over two hundred years ago this—ah, yes, missionary matter
it is, my young friends—was written concerning our poor red brothers
who lived down near Pinacate,” Vasquez smiled down at them
suavely.
Sid glanced at Scotty. The latter’s Scotch nature was so incensed
over this bald smiling perversion of what even his limited knowledge
of Latin had told him was the truth that he was utterly speechless.
“Minem Argenti” indeed! That meant “silver mine” at any rate!
Scotty’s faced blazed red, his eyes burned blue fire. As for Sid, he
saw no use in prolonging this conversation further, for in craft the