002684991 001__ 2684991
002684991 005__ 20240508045829.0
002684991 0248_ $$aoai:cds.cern.ch:2684991$$pcerncds:CERN$$pcerncds:CERN:FULLTEXT$$pcerncds:FULLTEXT
002684991 0247_ $$2DOI$$9bibmatch$$a10.1140/epja/i2019-12885-0
002684991 037__ $$9arXiv$$aarXiv:1907.08218$$cnucl-ex
002684991 037__ $$9arXiv:reportnumber$$aNJU-INP 001/19
002684991 035__ $$9arXiv$$aoai:arXiv.org:1907.08218
002684991 035__ $$9Inspire$$aoai:inspirehep.net:1744597$$d2024-05-07T10:44:27Z$$h2024-05-08T02:00:10Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002684991 035__ $$9Inspire$$a1744597
002684991 041__ $$aeng
002684991 100__ $$aAguilar, Arlene C.$$tGRID:grid.411087.b$$uCampinas State U.$$vUniversity of Campinas - UNICAMP, Institute of Physics ``Gled Wataghin'', 13083-859 Campinas, São Paulo, Brazil
002684991 245__ $$9arXiv$$aPion and Kaon Structure at the Electron-Ion Collider
002684991 269__ $$c2019-07-18
002684991 260__ $$c2019-10-31
002684991 300__ $$a16 p
002684991 500__ $$9arXiv$$a16 pages, 12 figures, to appear in the European Physical Journal A - "Hadrons and Nuclei"
002684991 520__ $$9Springer$$aUnderstanding the origin and dynamics of hadron structure and in turn that of atomic nuclei is a central goal of nuclear physics. This challenge entails the questions of how does the roughly 1GeV mass-scale that characterizes atomic nuclei appear, why does it have the observed value, and, enigmatically, why are the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD) abnormally light in comparison? In this perspective, we provide an analysis of the mass budget of the pion and proton in QCD, discuss the special role of the kaon, which lies near the boundary between dominance of strong and Higgs mass-generation mechanisms, and explain the need for a coherent effort in QCD phenomenology and continuum calculations, in exa-scale computing as provided by lattice QCD, and in experiments to make progress in understanding the origins of hadron masses and the distribution of that mass within them. We compare the unique capabilities foreseen at the electron-ion collider (EIC) with those at the hadron-electron ring accelerator (HERA), the only previous electron-proton collider, and describe five key experimental measurements, enabled by the EIC and aimed at delivering fundamental insights that will generate concrete answers to the questions of how mass and structure arise in the pion and kaon, the Standard Model's NG modes, whose surprisingly low mass is critical to the evolution of our Universe.
002684991 520__ $$9arXiv$$aUnderstanding the origin and dynamics of hadron structure and in turn that of atomic nuclei is a central goal of nuclear physics. This challenge entails the questions of how does the roughly 1 GeV mass-scale that characterizes atomic nuclei appear; why does it have the observed value; and, enigmatically, why are the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD) abnormally light in comparison? In this perspective, we provide an analysis of the mass budget of the pion and proton in QCD; discuss the special role of the kaon, which lies near the boundary between dominance of strong and Higgs mass-generation mechanisms; and explain the need for a coherent effort in QCD phenomenology and continuum calculations, in exa-scale computing as provided by lattice QCD, and in experiments to make progress in understanding the origins of hadron masses and the distribution of that mass within them. We compare the unique capabilities foreseen at the electron-ion collider (EIC) with those at the hadron-electron ring accelerator (HERA), the only previous electron-proton collider; and describe five key experimental measurements, enabled by the EIC and aimed at delivering fundamental insights that will generate concrete answers to the questions of how mass and structure arise in the pion and kaon, the Standard Model's NG modes, whose surprisingly low mass is critical to the evolution of our Universe.
002684991 540__ $$3preprint$$aarXiv nonexclusive-distrib 1.0$$uhttp://arxiv.org/licenses/nonexclusive-distrib/1.0/
002684991 542__ $$3publication$$dSociet`a Italiana di Fisica / Springer-Verlag GmbH Germany$$g2019
002684991 65017 $$2arXiv$$anucl-th
002684991 65017 $$2SzGeCERN$$aNuclear Physics - Theory
002684991 65017 $$2arXiv$$ahep-ph
002684991 65017 $$2SzGeCERN$$aParticle Physics - Phenomenology
002684991 65017 $$2arXiv$$ahep-lat
002684991 65017 $$2SzGeCERN$$aParticle Physics - Lattice
002684991 65017 $$2arXiv$$ahep-ex
002684991 65017 $$2SzGeCERN$$aParticle Physics - Experiment
002684991 65017 $$2arXiv$$anucl-ex
002684991 65017 $$2SzGeCERN$$aNuclear Physics - Experiment
002684991 690C_ $$aCERN
002684991 690C_ $$aARTICLE
002684991 693__ $$aDESY$$eHERA
002684991 700__ $$aAhmed, Zafir$$mzahmed@jlab.org$$tGRID:grid.57926.3f$$uRegina U.$$vUniversity of Regina, Regina, Saskatchewan, S4S 0A2, Canada
002684991 700__ $$aAidala, Christine$$jORCID:0000-0001-9540-4988$$mcaidala@umich.edu$$tGRID:grid.214458.e$$uMichigan U.$$vUniversity of Michigan, Ann Arbor, Michigan 48109-1040, USA
002684991 700__ $$aAli, Salina$$m95ali@cua.edu$$tGRID:grid.39936.36$$uCatholic U.$$vCatholic University of America, Washington DC 20064, USA
002684991 700__ $$aAndrieux, Vincent$$tGRID:grid.35403.31$$tGRID:grid.9132.9$$uIllinois U., Urbana (main)$$uCERN$$vUniversity of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA$$vCERN, 1211 Geneva 23, Switzerland
002684991 700__ $$aArrington, John$$tGRID:grid.187073.a$$uArgonne (main)$$vArgonne National Laboratory, Lemont, IL 60439, USA
002684991 700__ $$aBashir, Adnan$$tGRID:grid.412205.0$$uIFM-UMSNH, Michoacan$$vInstituto de Física y Matemáticas, UniversidadMichoacana de San Nicolás de Hidalgo Edificio C-3, Ciudad Universitaria, C. P. 58040, Morelia, Michoacán, México
002684991 700__ $$aBerdnikov, Vladimir$$iINSPIRE-00687455$$mberdnik@jlab.org$$tGRID:grid.39936.36$$uCatholic U.$$vCatholic University of America, Washington DC 20064, USA
002684991 700__ $$aBinosi, Daniele$$tGRID:grid.469918.b$$uECT, Trento$$uFond. Bruno Kessler, Trento$$vEuropean Centre for Theoretical Studies in Nuclear Physicsand Related Areas (ECT$^\ast$) and Fondazione Bruno Kessler Villa Tambosi, Strada delle Tabarelle 286, I-38123 Villazzano (TN) Italy
002684991 700__ $$aChang, Lei$$jORCID:0000-0002-4339-2943$$mleichang@nankai.edu.cn$$tGRID:grid.216938.7$$uNankai U.$$vSchool of Physics, Nankai University, Tianjin 300071, China
002684991 700__ $$aChen, Chen$$mchen.chen@theo.physik.uni-giessen.de$$tGRID:grid.8664.c$$uGiessen U.$$vInstitut für Theoretische Physik, Justus-Liebig-Universität Gießen, 35392 Gießen, Germany
002684991 700__ $$aChen, Muyang$$tGRID:grid.216938.7$$uNankai U.$$vSchool of Physics, Nankai University, Tianjin 300071, China
002684991 700__ $$aPacheco B.C. de Melo, João$$mjpachecodm@gmail.com$$tGRID:grid.412268.b$$uCruzeiro do Sul U.$$vUniversidade Cruzeiro do Sul, Sao Paulo, Brazil
002684991 700__ $$aDiefenthaler, Markus$$mmdiefent@jlab.gov$$tGRID:grid.450315.6$$uJefferson Lab$$vThomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
002684991 700__ $$aDing, Minghui$$tGRID:grid.469918.b$$tGRID:grid.216938.7$$uECT, Trento$$uFond. Bruno Kessler, Trento$$uNankai U.$$vEuropean Centre for Theoretical Studies in Nuclear Physicsand Related Areas (ECT$^\ast$) and Fondazione Bruno Kessler Villa Tambosi, Strada delle Tabarelle 286, I-38123 Villazzano (TN) Italy$$vSchool of Physics, Nankai University, Tianjin 300071, China
002684991 700__ $$aEnt, Rolf$$iINSPIRE-00079670$$ment@jlab.org$$tGRID:grid.450315.6$$uJefferson Lab$$vThomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
002684991 700__ $$aFrederico, Tobias$$mtobias@ita.br$$tGRID:grid.419270.9$$uSao Paulo, Inst. Tech. Aeronautics$$vInstituto Tecnológico de Aeronáutica, 12. 228-900 São José dos Campos, Brazil
002684991 700__ $$aGao, Fei$$tGRID:grid.7700.0$$uHeidelberg U.$$vInstitut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
002684991 700__ $$aGothe, Ralf W.$$tGRID:grid.254567.7$$uSouth Carolina U.$$vUniversity of South Carolina, Columbia, SC 29208, USA
002684991 700__ $$aHattawy, Mohammad$$mmhattawy@odu.edu$$tGRID:grid.261368.8$$uOld Dominion U.$$vOld Dominion University, Norfolk, Virginia 23529, USA
002684991 700__ $$aHobbs, Timothy J.$$jORCID:0000-0002-2729-0015$$mtjhobbs@smu.edu$$tGRID:grid.263864.d$$uSouthern Methodist U.$$vSouthern Methodist University, Dallas, TX 75275-0175, USA
002684991 700__ $$aHorn, Tanja$$mhornt@cua.edu$$tGRID:grid.39936.36$$uCatholic U.$$vCatholic University of America, Washington, DC 20064, USA
002684991 700__ $$aHuber, Garth M.$$iINSPIRE-00091430$$mhuberg@uregina.ca$$tGRID:grid.57926.3f$$uRegina U.$$vUniversity of Regina, Regina, Saskatchewan, S4S 0A2, Canada
002684991 700__ $$aJia, Shaoyang$$jORCID:0000-0002-8226-2279$$msjia@iastate.edu$$tGRID:grid.34421.30$$uIowa State U.$$vIowa State University, Ames, IA 50011, USA
002684991 700__ $$aKeppel, Cynthia$$jORCID:0000-0002-7516-8292$$mkeppel@jlab.org$$tGRID:grid.450315.6$$uJefferson Lab$$vThomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
002684991 700__ $$aKrein, Gastão$$jORCID:0000-0003-1713-8578$$mgkrein@ift.unesp.br$$tGRID:grid.410543.7$$uSao Paulo, IFT$$vInstituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. ~Bento Teobaldo Ferraz, 271, 01140-070 São Paulo, SP, Brazil
002684991 700__ $$aLin, Huey-Wen$$jORCID:0000-0001-6281-944X$$mhwlin@pa.msu.edu$$tGRID:grid.17088.36$$uMichigan State U.$$vMichigan State University, East Lansing, Michigan, 48824, USA
002684991 700__ $$aMezrag, Cédric$$tGRID:grid.470218.8$$uINFN, Rome$$vIstituto Nazionale di Fisica Nucleare, Sezione di Roma, P. le A. Moro 2, I-00185 Roma, Italy
002684991 700__ $$aMokeev, Victor$$tGRID:grid.450315.6$$uJefferson Lab$$vThomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
002684991 700__ $$aMontgomery, Rachel$$mrachel.montgomery@glasgow.ac.uk$$tGRID:grid.8756.c$$uGlasgow U.$$vUniversity of Glasgow, G128QQ Scotland, UK
002684991 700__ $$aMoutarde, Hervé$$tGRID:grid.457342.3$$uAIM, Saclay$$vIRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
002684991 700__ $$aNadolsky, Pavel$$jORCID:0000-0003-3732-0860$$mnadolsky@physics.smu.edu$$tGRID:grid.263864.d$$uSouthern Methodist U.$$vSouthern Methodist University, Dallas, TX 75275-0175, USA
002684991 700__ $$aPapavassiliou, Joannis$$tGRID:grid.5338.d$$uValencia U.$$uValencia U., IFIC$$vDepartment of Theoretical Physics and IFIC, University of Valencia and CSIC, E-46100, Valencia, Spain
002684991 700__ $$aPark, Kijun$$mparkkj@jlab.org$$tGRID:grid.450315.6$$uJefferson Lab$$vThomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
002684991 700__ $$aPegg, Ian L.$$mianp@vsl.cua.edu$$tGRID:grid.39936.36$$uCatholic U.$$vCatholic University of America, Washington DC 20064, USA
002684991 700__ $$aPeng, Jen-Chieh$$jORCID:0000-0003-4198-9030$$mjcpeng@illinois.edu$$tGRID:grid.35403.31$$uIllinois U., Urbana (main)$$vUniversity of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
002684991 700__ $$aPlatchkov, Stephane$$mstephane.platchkov@cea.fr$$tGRID:grid.457342.3$$uAIM, Saclay$$vIRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
002684991 700__ $$aQin, Si-Xue$$tGRID:grid.190737.b$$uChongqing U.$$vDepartment of Physics, Chongqing University, Chongqing 401331, P. \, R. China
002684991 700__ $$aRaya, Khépani$$tGRID:grid.216938.7$$uNankai U.$$vSchool of Physics, Nankai University, Tianjin 300071, China
002684991 700__ $$aReimer, Paul$$jORCID:0000-0002-0301-2176$$mreimer@anl.gov$$tGRID:grid.187073.a$$uArgonne (main)$$vArgonne National Laboratory, Lemont, IL 60439, USA
002684991 700__ $$aRichards, David G.$$jORCID:0000-0002-7516-8292$$mkeppel@jlab.org$$tGRID:grid.450315.6$$uJefferson Lab$$vThomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
002684991 700__ $$aRoberts, Craig D.$$jORCID:0000-0002-2937-1361$$mcdroberts@anl.gov$$tGRID:grid.41156.37$$uArgonne (main)$$vArgonne National Laboratory, Lemont, IL 60439, USA
002684991 700__ $$aRodríguez-Quintero, Jose$$tGRID:grid.18803.32$$uHuelva U.$$uIPM, Tehran$$vDepartment of Integrated Sciences and Centre for Advanced Studies in Physics, Mathematics and Computation, University of Huelva, E-21071 Huelva, Spain
002684991 700__ $$aSato, Nobuo$$jORCID:0000-0002-1535-6208$$mnsato@jlab.org$$tGRID:grid.450315.6$$uJefferson Lab$$vThomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
002684991 700__ $$aSchmidt, Sebastian M.$$iINSPIRE-00302278$$ms.schmidt@fz-juelich.de$$tGRID:grid.494742.8$$uIAS, Julich$$uJARA, Aachen$$vInstitute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany
002684991 700__ $$aSegovia, Jorge$$tGRID:grid.15449.3d$$uPablo de Olavide U., Seville$$vDepartamento de Sistemas Físicos, Químicos y Naturales, Universidad Pablo de Olavide, E-41013 Sevilla, Spain
002684991 700__ $$aTadepalli, Arun$$marunts@jlab.org$$tGRID:grid.450315.6$$uJefferson Lab$$vThomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
002684991 700__ $$aTrotta, Richard$$mtrotta@cua.edu$$tGRID:grid.39936.36$$uCatholic U.$$vCatholic University of America, Washington, DC 20064, USA
002684991 700__ $$aYe, Zhihong$$jORCID:0000-0002-1873-2344$$myez@anl.gov$$tGRID:grid.187073.a$$uArgonne (main)$$vArgonne National Laboratory, Lemont, IL 60439, USA
002684991 700__ $$aYoshida, Rikutaro$$mryoshida@jlab.org$$tGRID:grid.450315.6$$uJefferson Lab$$vThomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA
002684991 700__ $$aXu, Shu-Sheng$$tGRID:grid.453246.2$$uNUAA, Nanjing$$vCollege of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
002684991 773__ $$c190$$n10$$pEur. Phys. J. A$$v55$$y2019
002684991 8564_ $$82210912$$s298572$$uhttp://cds.cern.ch/record/2684991/files/F1.png$$y00000 Twist-two parton distribution amplitudes at a resolving scale $\zeta=2 \,$GeV$=:\zeta_2$. \textbf{A} solid (green) curve – pion $\Leftarrow$ emergent mass generation is dominant; \textbf{B} dot-dashed (blue) curve – $\eta_c$ meson $\Leftarrow$ Higgs mechanism is the primary source of mass generation; \textbf{C} solid (thin, purple) curve -- asymptotic profile, 6x(1 - x); and \textbf{D} dashed (black) curve – ``heavy-pion'', \emph{i.e}.\ a pion-like pseudo-scalar meson in which the valence-quark current masses take values corresponding to a strange quark $\Leftarrow$ the boundary, where emergent and Higgs-driven mass generation are equally important.
002684991 8564_ $$82210913$$s12708$$uhttp://cds.cern.ch/record/2684991/files/F2.png$$y00001 Lattice-QCD computations of the pion’s electromagnetic charge radius (green circles \cite{Wang:2018pii}, red down-triangle \cite{Chambers:2017tuf}, cyan cross \cite{Koponen:2017fvm}) as a function of $m_\pi^2$, compared with a continuum theory prediction \cite{Chen:2018rwz} (blue curve within bands, which indicate response to reasonable parameter variation). The continuum analysis establishes $f_\pi r_\pi \approx\,$constant, from which it follows that the size of a Nambu-Goldstone mode decreases in inverse proportion to the active strength of the dominant mass generating mechanism. The empirical value of $r_\pi$ is marked by the gold star.
002684991 8564_ $$82210914$$s31143$$uhttp://cds.cern.ch/record/2684991/files/F3.png$$y00002 Sullivan processes. In these examples, a nucleon's pion cloud is used to provide access to the pion's (a) elastic form factor and (b) parton distribution functions. $t = –(k-k^\prime)^2$ is a Mandelstam variable and the intermediate pion, $\pi^\ast(P=k-k^\prime)$, $P^2= –t$, is off-shell.
002684991 8564_ $$82210915$$s123725$$uhttp://cds.cern.ch/record/2684991/files/F4.png$$y00003 Virtuality-dependence of pion twist-two PDA. Solid (blue) curve: $v_\pi =0$ result; and dot-dashed (green) curve, PDA at $v_\pi=31$. Even this appreciable virtuality only introduces a modest rms relative-difference between the computed PDAs; namely, 13\%. Measured equivalently, the zero virtuality result differs by 34\% from that appropriate to QCD's asymptotic limit (dotted, red curve).
002684991 8564_ $$82210916$$s50210$$uhttp://cds.cern.ch/record/2684991/files/F5.png$$y00004 Geometric acceptances for detection of leading neutrons and the decay products of $\Lambda$ and $\Sigma$ particles in the integrated JLEIC detector concept, to tag the pion and kaon Sullivan processes.
002684991 8564_ $$82210917$$s138124$$uhttp://cds.cern.ch/record/2684991/files/F6.png$$y00005 Ratio of the component of the $F_2$ structure function related to the pion Sullivan process as compared to the proton $F_2$ structure function in the low-$t$ vicinity of the pion pole, as a function of $t$ for various values of Bjorken-$x$.
002684991 8564_ $$82210918$$s196902$$uhttp://cds.cern.ch/record/2684991/files/F7.png$$y00006 A sample EIC extraction of valence quark, sea quark and gluon PDFs in the pion, at a scale $Q^2 =10\,$GeV$^2$. The extraction is done with the following assumptions on PDFs: the $u$ PDF equals the $\bar d$ PDF in the pion and the $\bar u$ PDF is the same as the other sea quark PDFs ($d$, $s$ and $\bar s$). The extraction at $x_\pi < 10^{-2}$, at this $Q^2$ scale, is constrained by the existing HERA data.
002684991 8564_ $$82210919$$s316050$$uhttp://cds.cern.ch/record/2684991/files/F9.png$$y00009 Projected EIC pion form factor data as extracted from a combination of electron-proton and electron-deuteron scattering, each with an integrated luminosity of $20\,{\rm fb}^{-1}$ -- black stars with error bars. Also shown are projected JLab 12-GeV data from a Rosenbluth-separation technique -- orange diamonds and green triangle. The long-dashed green curve is a monopole form factor whose scale is determined by the pion radius. The black solid curve is the QCD-theory prediction bridging large and short distance scales, with estimated uncertainty \cite{Chen:2018rwz}. The dot-dashed blue and dotted purple curves represent the short-distance views \cite{Lepage:1979zb, Efremov:1979qk, Lepage:1980fj}, comparing the result obtained using a modern DCSB-hardened PDA and the asymptotic profile, respectively.
002684991 8564_ $$82210920$$s2420195$$uhttp://cds.cern.ch/record/2684991/files/1907.08218.pdf$$yFulltext
002684991 8564_ $$82210921$$s8421$$uhttp://cds.cern.ch/record/2684991/files/F12A.png$$y00012 Projected uncertainties for measurements of the $u$-quark to pion (\emph{upper panel}) and kaon (\emph{lower panel}) fragmentation function at EIC for an integrated luminosity of $10\,{\rm fb}^{-1}$, for the large $z$ region, $z > 0.5$, and transverse momentum $k_\perp$ (as picked up in the fragmentation process) of $k_\perp = 0.1, 0.3, 0.5\,$GeV, respectively.
002684991 8564_ $$82210922$$s8383$$uhttp://cds.cern.ch/record/2684991/files/F12B.png$$y00013 Projected uncertainties for measurements of the $u$-quark to pion (\emph{upper panel}) and kaon (\emph{lower panel}) fragmentation function at EIC for an integrated luminosity of $10\,{\rm fb}^{-1}$, for the large $z$ region, $z > 0.5$, and transverse momentum $k_\perp$ (as picked up in the fragmentation process) of $k_\perp = 0.1, 0.3, 0.5\,$GeV, respectively.
002684991 8564_ $$82210923$$s136734$$uhttp://cds.cern.ch/record/2684991/files/F10.png$$y00010 Ratio of valence $u$-quark PDFs in the pion and the kaon at $\zeta = 5.2\,$GeV$=:\zeta_5$. Data are from Drell-Yan measurements \cite{Badier:1980jq}. The computed results are taken from Ref.\,\cite{Chen:2016sno}, with the dashed, solid, and dot-dashed curves representing, respectively, $0$, $5$\%, $10$\% of the kaon's light-front momentum carried by glue at the scale, $\zeta_K = 0.51\,$GeV. For the projected EIC data (brown points drawn at $u_K(x)/u_\pi(x)=1.2$) we assumed $u$-quark dominance. (For reference, the horizontal dotted line marks $u_K(x)/u_\pi(x)=1$.)
002684991 8564_ $$82210924$$s288144$$uhttp://cds.cern.ch/record/2684991/files/F11.png$$y00011 Pion valence-quark momentum distribution function, $x {\mathpzc u}^\pi(x;\zeta_5)$: dot-dot-dashed (grey) curve within shaded band -- lQCD result \cite{Sufian:2019bol}; long-dashed (black) curve -- early continuum analysis \cite{Hecht:2000xa}; and solid (blue) curve embedded in shaded band -- modern, continuum calculation \cite{Ding:2019lwe}. Gluon momentum distribution in pion, $x g^\pi(x;\zeta_5)$ -- dashed (green) curve within shaded band; and sea-quark momentum distribution, $x S^\pi(x;\zeta_5)$ -- dot-dashed (red) curve within shaded band. (In all cases, the shaded bands indicate the size of calculation-specific uncertainties, as described elsewhere \cite{Ding:2019lwe}.) Data (purple) from Ref.\,\cite{Conway:1989fs}, rescaled according to the analysis in Ref.\,\cite{Aicher:2010cb}.
002684991 8564_ $$82210925$$s44414$$uhttp://cds.cern.ch/record/2684991/files/F8A.png$$y00007 \emph{Upper panel}. Two dressed-quark mass functions distinguished by the amount of DCSB: emergent mass generation is 20\% stronger in the system characterized by the solid green curve, which describes the more realistic case. \emph{Lower panel}. $F_\pi(Q^2)$ obtained with the mass function in the upper panel: $r_\pi = 0.66\,$fm with the solid green curve and $r_\pi = 0.73\,$fm with the dashed blue curve. The long-dashed green and dot-dashed blue curves are predictions from the QCD hard-scattering formula, obtained with the related, computed pion PDAs. The dotted purple curve is the result obtained from that formula if the asymptotic profile is used for the PDA: $\varphi(x)=6x(1-x)$.
002684991 8564_ $$82210926$$s58258$$uhttp://cds.cern.ch/record/2684991/files/F8B.png$$y00008 \emph{Upper panel}. Two dressed-quark mass functions distinguished by the amount of DCSB: emergent mass generation is 20\% stronger in the system characterized by the solid green curve, which describes the more realistic case. \emph{Lower panel}. $F_\pi(Q^2)$ obtained with the mass function in the upper panel: $r_\pi = 0.66\,$fm with the solid green curve and $r_\pi = 0.73\,$fm with the dashed blue curve. The long-dashed green and dot-dashed blue curves are predictions from the QCD hard-scattering formula, obtained with the related, computed pion PDAs. The dotted purple curve is the result obtained from that formula if the asymptotic profile is used for the PDA: $\varphi(x)=6x(1-x)$.
002684991 960__ $$a13
002684991 980__ $$aARTICLE