Analysis of Z Boson Decay

Max Jenkinson
10497441
University of Manchester

(Dated: March 8, 2023)

√
A data-set collected by the ATLAS detector at the LHC of proton-proton collisions at s = 13TeV
− + − +
was analysed for the decays of Z bosons into both e e and µ µ . The integrated luminosity of
the data-set was 10.064 ± 0.171 pb−1 , with a selected invariant mass range of 75 − 145GeV. The
cross sections were measured as σ(pp → Z → ee) = 1.872 ± 0.007 (stat) ±0.052 (syst) ±0.032 (lumi)
nb and σ(pp → Z → µµ) = 1.855 ± 0.007 (stat) ±0.080 (syst) ±0.032 (lumi) nb. The Standard
model predicts that these events occur at the same rate. To test this with higher precision, a ratio
was taken with a result of σ(pp→Z→µµ)
σ(pp→Z→ee)
= 0.991 ± 0.005(stat)±0.001(syst) which is within 1.052σ of
unity, hence supporting lepton universality.

I. AN INTRODUCTION TO PROTON-PROTON
COLLISIONS AT THE LHC

The ATLAS detector consists of a superconducting

solenoid which produces a magnetic field of 2T that cov-
ers the inner detector. The inner detector tracks charged
particles in a psuedorapidity range of η < 2.5. The
Transition Radiation Tracker is used to identify electrons
by detecting the transition radiation of its straw tubes.
To measure the energy of collision products a system of FIG. 1: Diagram illustrating a cross section of ATLAS
liquid argon calorimeters operate over a psuedorapidity with the inner circle representing the particle beam, and
range of η < 4.9 (which lack tracking data for the parti- outer circle representing a detector. The two arrows
cles they detect) is comprised of multiple detectors spread show the two detected particles, recoiling from a third
between 4 layers within ATLAS. A final notable detail of undetected particle (dashed line). The third particle
ATLAS regarding this research is that the ATLAS de- can be inferred as the beam has zero transverse
tector has no ability to directly detect neutrinos, due to momentum, resulting in the products of a collision
their light and neutral nature, this means that all dis- conserving the zero total transverse momentum.
cussed instances of neutrinos are inferred by the obser-
vation of their effects such as recoil (illustrated in figure
1).[1]
Measurements of Z boson production and the subse-
quent decay provides a baseline for further understanding
of the standard model [SM] and as a result, electroweak
processes. This test of the lepton universality prediction
of SM is one of the first hurdles for SM’s validity for de-
FIG. 2: The leading order interaction for pp → Z → ll.
scribing high energy collisions.
Proton-proton collisions are an example of a hard scatter-
ing process that predominantly features interaction be-
tween virtual and valance quark, as shown in figure 2. where σ is the cross section, Nsignal is the number
Gluon-gluon interactions also occur, but as gluons do not of events measured (that pass selection cuts, see be-
directly couple with Z bosons this is less likely. low), Nbackground is the number of background events
predicted, ϵ is the fractional efficiency of the ATLAS de-
tector (estimated using the Monte Carlo data-set), and
II. PRELIMINARY THEORY L is the integrated luminosity of the data-set. The back-
ground term (Nbackground ) is taken from a Monte Carlo
A. Cross Section [MC] based simulation [2]. This is the main target of
selection cuts (selection cuts are selected restrictions to
the data-set, such as to limit invariant mass considered
The cross section of a process is measured by
to a range of 75 − 145GeV). The principle aim of cuts
made to the data was to minimise the ratio of MC pre-
Nsignal − Nbackground dicted signal made up of background events. This was
σ= , (1) important to minimise, as if the MC was out by a static
ϵL
 2

factor, say a factor of two, and in one case the signal

is 10% background and in another case (after cuts) the p
δNx = Nx , (2)
signal is made up of 1% background the impact on the
cross section will be dramatically reduced. where Nx is an data-set of independent data points
(in this case either Nsignal or Nbackground ) and δNx is
the fractional error on Nx . The error on efficiency was
B. Background Events calculated by

Background events are defined by interactions that s

produce a similar or identical final state to the signal ϵ(1 − ϵ)
δϵ = , (3)
event, in this case Z → ll (where l are leptons, in this NM C − 1
case either an electron or muon pair). The Feynman di-
where ϵ is the efficiency, δϵ is the error on the efficiency,
agrams for the main contributions to the background for
and NM C is the total number of events predicted by the
this process are shown in figure 3.
MC simulation. These errors were simply combined in
quadrature to produce the statistical uncertainty.
The method of cut selection involved an amount of sub-
jective decision making. The cuts were selected based
on balancing preservation of sections where MC fit the
real data best, minimising the number of background
events, and maximising the number of data-set elements
resulted in a range of possible cuts that could have been
made. To calculate the systematic error resulting from
this range, the cross sections were calculated with the ex-
tremes of each possible cut range. The difference between
the largest and smallest cross sections were calculated to
FIG. 3: The leading order diagrams for the two give the systematic uncertainty by
dominant background events predicted by the MC data.
(Left) A W boson is produced in the collision of two σmax − σmin
δsystematic = , (4)
protons and decays into an antineutrino and a lepton. 2σ
The second (detectable) lepton is produced by the where δsystematic is the systematic error, σmax is the
hadronising jet produced by a gluon emitted by a quark largest cross section, σmin is the smallest cross section,
just prior to the collision. (Right) A top quark pair are and σ is the cross section with the unaltered cuts.
produced by a decaying gluon and each decay into a Error on the ratio, σ(pp→Z→µµ)
σ(pp→Z→ee) was able to be reduced
bottom quark via a W boson which subsequently decays compared to the individual measurements as the uncer-
into a neutrino and lepton, this is the most common tainty of the luminosity was a constant factor on both,
background event observed within the invariant mass therefore being cancelled. The systematic uncertainty
range used by this experiment. was also greatly reduced by demonstrating that an identi-
cal change of cuts produced similar (within 0.5%) changes
In the effort to filter background events from the data, to the cross section. This subsequently allowed an order
limits on certain variables [cuts] were made. For exam- of magnitude increase in precision.
ple, to filter figure 3 (Left) from the data, the hadronis-
ing jets were identified using the energy readings taken
in the angular region about the trajectory of the lepton III. EXPERIMENTAL RESULTS
detected. If this energy was too high (as a result of other
particles formed by the jet) it was assumed to have been A. Measurement of σ(pp → Z → ee) and
produced in a jet and therefore removed from the data. σ(pp → Z → µµ)
**CITE?**
Prior to cuts being made, the MC data simulated a
background that made up 1% of the total signal, as seen
C. Error Analysis in figure 4. These initial plots also recognised areas of
disagreement between the MC and real data-sets. After
Uncertainty on the measurement of the two cross sec- the cuts, listed in figure 5, were made the real and MC
tions using equation 1, are affected by the uncertainties data-sets demonstrated satisfactory agreement, allowing
carried by each of its terms. The error on the luminos- the confident measurement both σ(pp → Z → ee) =
ity is a given of the ATLAS detector and is quoted as a 1.872 ± 0.007 (stat) ±0.052 (syst) ±0.032 (lumi) nb and
fractional uncertainty of 1.7% [3]. The error on Nsignal σ(pp → Z → µµ) = 1.855 ± 0.007 (stat) ±0.080 (syst)
and Nbackground are simply the standard statistical error ±0.032 (lumi) nb.
 3

B. Test of Lepton Universality

IV. CONCLUSIONS

FIG. 4
The aim of this experiment was to test the capabilities
of holographic interferometry by measuring the deforma-
tion of a block of iron undergoing a temperature change.
The collected data was compared with the established
relation between the average atomic volume and tem-
perature. This data was used to predict a deformation
of 33.6λ which was within the 34 ± 0.5λ measured. A
further check of accuracy used the same data set to pre-
dict the temperature difference between the top and bot-
tom of the iron block using the path length difference
measured from the fringe count. The temperature dif-
ference predicted was 21.5◦ C which was within error for
the measured value of 21.3 ± 0.3◦ C. This demonstrated
that holographic interferometry is a precise and useful
measurement method for small distances on the order
of µm. This level of precision could be even further re-
duced with the use of a laser with a shorter wavelength
FIG. 5
than used here.

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keywords = Simulation, Particle interactions, Geometrical