Chiral Symmetry Restoration Using the Running Coupling Constant from the Light-Front Approach to QCD
DOI:
https://doi.org/10.15407/ujpe67.3.151Keywords:
confinement potential, running coupling, chiral symmetryAbstract
In this work, the distance between a quark-antiquark pair is analyzed through both the confinement potential and the hadronic total cross- section. Using the Helmholtz free energy, the entropy is calculated near the minimum of the total cross-section through the confinement potential. A fitting procedure for the proton-proton total cross- section is carried out, defining the fit parameters. Therefore, the only remaining free parameter in the model is the mass-scale к used to define the running coupling constant of the light-front the approach to QCD. The mass scale controls the distance r between the quark-antiquark pair and, under some conditions, allows the appearance of free quarks even within the confinement regime of QCD.
References
Y. Aoki et al. The QCD transition temperature: results with physical masses in the continuum limit II. J. High. Energ. Phys. 0906, 088 (2009).
https://doi.org/10.1088/1126-6708/2009/06/088
S. Borsanyi et al. (Wuppertal-Budapest Collaboration). Is there still any Tc mystery in lattice QCD? Results with physical masses in the continuum limit III. J. High. Energ. Phys. 1009, 073 (2010).
https://doi.org/10.1007/JHEP09(2010)073
C. Ratti. Lattice QCD and heavy ion collisions: a review of recent progress. Rept. Prog. Phys. 81(8), 084301 (2018).
https://doi.org/10.1088/1361-6633/aabb97
A. Bazavov et al. (USQCD Collaboration). Hot-dense lattice QCD: USQCD whitepaper 2018. Eur. Phys. J. A 55 (11), 194 (2019).
https://doi.org/10.1140/epja/i2019-12922-0
L. Adamczyk et al. (STAR Collaboration). Bulk properties of the medium produced in relativistic heavy-ion collisions from the beam energy scan program. Phys. Rev. C 96(4), 044904 (2017).
A. Andronic et al. Decoding the phase structure of QCD via particle production at high energy. Nature 561 (7723), 321 (2018).
https://doi.org/10.1038/s41586-018-0491-6
M. Cveti˘c, H. L¨u, C.N. Pope. Entropy-product rules for charged rotating black holes. Phys. Rev. D 88, 044046 (2013).
https://doi.org/10.1103/PhysRevD.88.044046
M. Li. Note on the production of scale-invariant entropy perturbation in the ekpyrotic universe. Phys. Lett. B 724, 192 (2013).
https://doi.org/10.1016/j.physletb.2013.06.035
L. Herrera et al. Vorticity and entropy production in tilted Szekeres spacetimes. Phys. Rev. D 86, 044003 (2012).
https://doi.org/10.1103/PhysRevD.86.044003
S. Mattiello. Entropy production for an interacting quarkgluon plasma. Nucl. Phys. A 894, 1 (2012).
https://doi.org/10.1016/j.nuclphysa.2012.09.003
Y.K. Vermani, R.K. Puri. Entropy and light cluster production in heavy-ion collisions at intermediate energies. Nucl. Phys. A 847, 243 (2010).
https://doi.org/10.1016/j.nuclphysa.2010.07.005
R.J. Fries, B. Muller, A. Sch¨afer. Decoherence and entropy production in relativistic nuclear collisions. Phys. Rev. C 79, 034904 (2009).
https://doi.org/10.1103/PhysRevC.79.034904
K. Kutak. Gluon saturation and entropy production in proton-proton collisions. Phys. Lett. B 705, 217 (2011).
https://doi.org/10.1016/j.physletb.2011.09.113
D. Kharzeev, K. Tuchin. From color glass condensate to quark-gluon plasma through the event horizon. Nucl. Phys. A 753, 316 (2005).
https://doi.org/10.1016/j.nuclphysa.2005.03.001
S.D. Campos. Chiral symmetry in the confinement phase of QCD. Mod. Phys. Lett. A 36 (19), 2150135 (2021).
https://doi.org/10.1142/S0217732321501352
R. Hagedorn. Statistical thermodynamics of strong interactions at high energies. Il Nuovo Cimento Suppl. 3, 147 (1965).
R. Hagedorn. Hadronic matter near the boiling point. Il Nuovo Cimento A 56, 1027 (1968).
https://doi.org/10.1007/BF02751614
L. McLerran, R.D. Pisarski. Phases of dense quarks at large Nc. Nucl. Phys. A 796, 83 (2007).
https://doi.org/10.1016/j.nuclphysa.2007.08.013
L.YA. Glozman, R.F. Wagenbrunn. Chirally symmetric but confined hadrons at finite density. Mod. Phys. Lett. A 23, 2385 (2008).
https://doi.org/10.1142/S0217732308029435
V.L. Berezinskii. Destruction of long range order in onedimensional and two-dimensional systems having a continuous symmetry group. I. Classical systems. Zh. Eksp. Teor. Fiz. 59, 907 (1970)
Sov. Phys. JETP 32, 493 (1971).
J.M. Kosterlitz, D.J. Thouless. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181 (1973).
https://doi.org/10.1088/0022-3719/6/7/010
A. Deur, S.J. Brodsky, G.F. de T'eramond. The QCD running coupling. Prog. Part. Nuc. Phys. 90, 1 (2016).
https://doi.org/10.1016/j.ppnp.2016.04.003
V. de Alfaro, S. Fubini, G. Furlan. Conformal invariance in quantum mechanics. Il Nuovo Cimento 34 (4), 569 (1976).
https://doi.org/10.1007/BF02785666
J. Terrell. Invisibility of the Lorentz contraction. Phys. Rev. 116 (4), 1041 (1959).
https://doi.org/10.1103/PhysRev.116.1041
R. Penrose. The apparent shape of a relativistically moving sphere. Mathematical Proceedings of the Cambridge Philosophical Society 55 (1), 137 (1959).
https://doi.org/10.1017/S0305004100033776
D. Bohm. A suggested interpretation of the quantum theory in terms of "hidden" variables. I. Phys. Rev. 85, 166 (1952); ibid 180 (1952).
https://doi.org/10.1103/PhysRev.85.180
Sh. F.Y. Liu, R. Rapp. An in-medium heavy-quark potential from the QQ free energy. ArXiv: 1501.07892[hep-ph].
G. Dennis et al. Fermi's ansatz and Bohm's quantum potential. Phys. Lett. A 378, 2363 (2014).
https://doi.org/10.1016/j.physleta.2014.05.020
G. Dennis, M.A. de Gosson, B.J. Hiley. Bohm's quantum potential as an internal energy. Phys. Lett. A 379, 1224 (2015).
https://doi.org/10.1016/j.physleta.2015.02.038
C. Quigg, J.L. Rosner. Quarkonium level spacings. Phys. Lett. B 71, 153 (1977).
https://doi.org/10.1016/0370-2693(77)90765-1
C. Quigg, J.L. Rosner. Quantum mechanics with applications to quarkonium. Phys. Rep. 56 (4), 167 (1979).
https://doi.org/10.1016/0370-1573(79)90095-4
E. Eichten et al. Spectrum of charmed quark-antiquark bound states. Phys. Rev. Lett. 34, 369 (1975).
https://doi.org/10.1103/PhysRevLett.34.369
E. Eichten et al. Charmonium: the model. Phys. Rev. D 17, 3090 (1978).
https://doi.org/10.1103/PhysRevD.17.3090
E. Eichten et al. Charmonium: comparison with experiment. Phys. Rev. D 21, 203 (1980).
https://doi.org/10.1103/PhysRevD.21.203
M.G. Olsson, S. Vesell, K. Williams. Observations on the potential confinement of a light fermion. Phys. Rev. D 51, 5079 (1995).
https://doi.org/10.1103/PhysRevD.51.5079
D. Ebert, V.O. Galkin, R.N. Faustov. Mass spectrum of orbitally and radially excited heavy-light mesons in the relativistic quark model. Phys. Rev. D 57, 5663 (1998)
https://doi.org/10.1103/PhysRevD.57.5663
Erratum Phys. Rev. D 59, 019902 (1998).
E.J. Eichten, C. Quigg. Mesons with beauty and charm: spectroscopy. Phys. Rev. D 49, 5845 (1994).
https://doi.org/10.1103/PhysRevD.49.5845
S. Aoki et al. 2 + 1 flavor lattice QCD toward the physical point. Phys. Rev. D 79, 034503 (2009).
https://doi.org/10.1103/PhysRevD.79.034503
A.P. Trawi'nski et al. Effective confining potentials for QCD. Phys. Rev. D 90, 074017 (2014).
https://doi.org/10.1103/PhysRevD.90.074017
D.V. Shirkov, I.L. Solovtsov. Analytic model for the QCD running coupling with universal as(0) value. Phys. Rev. Lett. 79, 1209 (1997).
https://doi.org/10.1103/PhysRevLett.79.1209
S. J.Brodsky et al. Meson/baryon/tetraquark supersymmetry from superconformal algebra and light-front holography. Int. J. Mod. Phys. A 31 (19), 1630029 (2016).
https://doi.org/10.1142/S0217751X16300295
S.J. Brodsky, G.F. de T'eramond, A. Deur. Nonperturbative QCD coupling and its beta function from light-front holography. Phys. Rev. D 81, 096010 (2010).
https://doi.org/10.1103/PhysRevD.81.096010
S.J. Brodsky, H.G. Dosch, J. Erlich. Light-front holographic QCD and emerging confinement. Phys. Rept. 584, 1 (2015).
https://doi.org/10.1016/j.physrep.2015.05.001
A. Karch et al. Linear confinement and AdS/QCD. Phys. Rev. D 74, 015005 (2006).
https://doi.org/10.1103/PhysRevD.74.015005
P. Zhang. Linear confinement for mesons and nucleons in AdS/QCD. J. High. Energ. Phys. 2010 (5), 39 (2010).
https://doi.org/10.1007/JHEP05(2010)039
A.J.G. Hey, R.L. Kelly. Baryon spectroscopy. Phys. Rep. 96, 71 (1983).
https://doi.org/10.1016/0370-1573(83)90114-X
T. Branz et al. Light and heavy mesons in a soft-wall holographic approach. Phys. Rev. D 82, 074022 (2010).
https://doi.org/10.1103/PhysRevD.82.074022
D. Chakrabarti, C. Mondal. Nucleon and flavor form factors in a light front quark model in AdS/QCD. Eur. Phys. J. C 73, 2671 (2013).
https://doi.org/10.1140/epjc/s10052-013-2671-8
A. Bacchetta, S. Cotogno, B. Pasquini. The transverse structure of the pion in momentum space inspired by the AdS/QCD correspondence. Phys. Lett. B 771, 546 (2017).
https://doi.org/10.1016/j.physletb.2017.05.072
D.V. Shirkov. Fourier transformation of the renormalization-invariant coupling. Theor. Math. Phys. 136 (1), 893 (2003).
A. Erd'elyi et al. Tables of integral transforms (McGrawHill, 1954) [ISBN: 978-0070195509].
H.G. Dawson. On the numerical value of ∫︀h0ex2dx. Proceedings of the London Mathematical Society, s1-29 (1), 519 (1897).
https://doi.org/10.1112/plms/s1-29.1.519
M. Abramowitz, I.A. Stegun. Error function and Fresnel integrals. Handbook of mathematical functions with formulas, graphs, and mathematical tables (9th ed. New York, 1972) [ISBN: 9780486612720].
F.G. Lether, P.R. Wenston. Elementary approximations for Dawson's integral. Journal of Quantitative Spectroscopy and Radiative Transfer 46 (4), 343 (1991).
https://doi.org/10.1016/0022-4073(91)90099-C
S.D. Campos. Logarithmic Regge pole. Chin. Phys. C 44, 103103 (2020).
https://doi.org/10.1088/1674-1137/ababf8
M. Tanabashi et al. (Particle Data Group). Review of particle physics. Phys. Rev. D 98, 030001 (2018).
E.A. Kuraev, L.N. Lipatov, V.S. Fadin. Multiregge processes in the Yang-Mills theory. Sov. Phys. JETP 44, 443 (1976).
Y.Y. Balitsky, L.N. Lipatov. The Pomeranchuk singularity in quantum chromodynamics. Sov. J. Nucl. Phys. 28, 822 (1978).
J. Bartels. High-energy behaviour in a non-abelian gauge theory (II). First corrections to T n → m beyond the leading In s approximation. Nucl. Phys. B 175 (3), 365 (1980).
https://doi.org/10.1016/0550-3213(80)90019-X
G. Antchev et al. (TOTEM Collaboration). First determination of the p parameter at √s = 13 TeV: probing the existence of a colourless C-odd three-gluon compound state. Eur. Phys. J. C 79, 785 (2019).
I.M. Dremin. Interaction region of high energy protons. Phys. Uspekhi 58, 61 (2015).
https://doi.org/10.3367/UFNe.0185.201501d.0065
I.M. Dremin. Unexpected properties of interaction of highenergy protons. Phys. Uspekhi 60 (4), 333 (2017).
https://doi.org/10.3367/UFNe.2016.11.037977
S.D. Campos, V.A. Okorokov, C.V. Moraes. The Tsallis entropy and the BKT-like phase transition in the impact parameter space for pp and ¯ pp collisions. Phys. Scr. 95, 025301 (2020). https://doi.org/10.1088/1402-4896/ab429e
S.D. Campos, A.M. Amarante. The effects of the Tsallis entropy in the proton internal pressure. Int. J. Mod. Phys A 35, 2050095 (2020). https://doi.org/10.1142/S0217751X20500955
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
