Evolution of pion mass with temperature
DOI:
https://doi.org/10.31349/SuplRevMexFis.4.021124Keywords:
Contact Interaction, Finite Temperature, bound-states dissolutionAbstract
We study the evolution of light quarks with isospin symmetry and the pion masses in the presence of a thermal bath and study their temperature dependence. In addition, we analyze the inclusion of a coupling with temperature dependence. We attempt to study the dissolution of bound-states at temperatures higher than the critical temperature, but we found that the model shows that the bound-state's mass increases. We base our study on a momentum-independent symmetry-preserving truncation scheme contact interaction in the Schwinger-Dyson equations framework.
References
D. J. Gross and F. Wilczek, Ultraviolet Behavior of Nonabelian Gauge Theories, Phys. Rev. Lett. 30 (1973) 1343, https://doi.org/10.1103/PhysRevLett.30.1343
H. D. Politzer, Reliable Perturbative Results for Strong Interactions?, Phys. Rev. Lett. 30 (1973) 1346 https://doi.org/10.1103/PhysRevLett.30.1346
D. J. Gross and F. Wilczek, Asymptotically Free Gauge Theories - I, Phys. Rev. D 8 (1973) 3633 https://doi.org/10.1103/PhysRevD.8.3633
C. Bernard et al. [MILC], QCD thermodynamics with three flavors of improved staggered quarks, Phys. Rev. D 71 (2005) 034504 https://doi.org/10.1103/PhysRevD.71.034504
M. Cheng et al., The Transition temperature in QCD, Phys. Rev. D 74 (2006) 054507, https://doi.org/10.1103/PhysRevD.74.054507
Y. Aoki, S. Borsanyi, S. Durr, Z. Fodor, S. D. Katz, S. Krieg and K. K. Szabo, The QCD transition temperature: results with physical masses in the continuum limit II., JHEP 06 (2009) 088 https://doi.org/10.1088/1126-6708/2009/06/088
S. Borsanyi et al. [Wuppertal-Budapest], Is there still any Tc mystery in lattice QCD? Results with physical masses in the continuum limit III, JHEP 09 (2010) 073 https://doi.org/10.1007/JHEP09(2010)073
A. Bazavov et al., The chiral and deconfinement aspects of the QCD transition, Phys. Rev. D 85 (2012) 054503 https://doi.org/10.1103/PhysRevD.85.054503
L. Levkova, QCD at nonzero temperature and density, PoS LATTICE2011 (2011) 011, https://doi.org/10.22323/1.139.0011
P. de Forcrand, J. Langelage, O. Philipsen and W. Unger, Lattice QCD Phase Diagram In and Away from the Strong Coupling Limit, Phys. Rev. Lett. 113 (2014) 152002, https://doi.org/10.1103/PhysRevLett.113.152002
T. Bhattacharya et al., QCD Phase Transition with Chiral Quarks and Physical Quark Masses, Phys. Rev. Lett. 113 (2014) 082001 https://doi.org/10.1103/PhysRevLett.113.082001
A. Bazavov, H. T. Ding, P. Hegde, F. Karsch, E. Laermann, S. Mukherjee, P. Petreczky and C. Schmidt, Chiral phase structure of three flavor QCD at vanishing baryon number density, Phys. Rev. D 95 (2017) 074505, https://doi.org/10.1103/PhysRevD.95.074505
J. N. Guenther, Overview of the QCD phase diagram: Recent progress from the lattice, Eur. Phys. J. A 57 (2021) 136, https://doi.org/10.1140/epja/s10050-021-00354-6
S. x. Qin, L. Chang, H. Chen, Y. x. Liu and C. D. Roberts, Phase diagram and critical endpoint for strongly-interacting quarks, Phys. Rev. Lett. 106 (2011) 172301, https://doi.org/10.1103/PhysRevLett.106.172301
C. S. Fischer, J. Luecker and J. A. Mueller, Chiral and deconfinement phase transitions of two-flavour QCD at finite temperature and chemical potential, Phys. Lett. B 702 (2011) 438, https://doi.org/10.1016/j.physletb.2011.07.039
A. Ayala, A. Bashir, C. A. Dominguez, E. Gutierrez, M. Loewe and A. Raya, QCD phase diagram from finite energy sum rules, Phys. Rev. D 84 (2011) 056004, https://doi.org/10.1103/PhysRevD.84.056004
E. Gutierrez, A. Ahmad, A. Ayala, A. Bashir and A. Raya, The QCD phase diagram from Schwinger–Dyson equations, J. Phys. G 41 (2014) 075002, https://doi.org/10.1088/0954-3899/41/7/075002
K. l. Wang, Y. x. Liu, L. Chang, C. D. Roberts and S. M. Schmidt, Baryon and meson screening masses, Phys. Rev. D 87 (2013) 074038, https://doi.org/10.1103/PhysRevD.87.074038
F. Gao, J. Chen, Y. X. Liu, S. X. Qin, C. D. Roberts and S. M. Schmidt, Phase diagram and thermal properties of stronginteraction matter, Phys. Rev. D 93 (2016) 094019, https://doi.org/10.1103/PhysRevD.93.094019
G. Eichmann, C. S. Fischer and C. A. Welzbacher, Baryon effects on the location of QCD’s critical end point, Phys. Rev. D 93 (2016) 034013, https://doi.org/10.1103/PhysRevD.93.034013
F. Gao and Y. x. Liu, QCD phase transitions via a refined truncation of Dyson-Schwinger equations, Phys. Rev. D 94 (2016) 076009, https://doi.org/10.1103/PhysRevD.94.076009
C. S. Fischer, QCD at finite temperature and chemical potential from Dyson–Schwinger equations, Prog. Part. Nucl. Phys. 105 (2019) 1, https://doi.org/10.1016/j.ppnp.2019.01.002
C. Shi, X. T. He, W. B. Jia, Q. W. Wang, S. S. Xu and H. S. Zong, Chiral transition and the chiral charge density of the hot and dense QCD matter, JHEP 06 (2020) 122, https://doi.org/10.1007/JHEP06(2020)122
A. Ahmad, A. Bashir, M. A. Bedolla and J. J. Cobos-Martínez, Flavor, temperature and magnetic field dependence of the QCD phase diagram: magnetic catalysis and its inverse, J. Phys. G 48 (2021) 075002; A. Ahmad and A. Raya, Inverse magnetic catalysis and confinement within a contact interaction model for quarks, J. Phys. G 43 (2016) 065002
J. L. Goity and H. Leutwyler, On the Mean Free Path of Pions in Hot Matter, Phys. Lett. B 228 (1989) 517, https://doi.org/10.1016/0370-2693(89)90985-4
A. Schenk, Pion propagation at finite temperature, Phys. Rev. D 47 (1993) 5138, https://doi.org/10.1103/PhysRevD.47.5138
J. Gasser and H. Leutwyler, Light Quarks at Low Temperatures, Phys. Lett. B 184 (1987) 83, https://doi.org/10.1016/0370-2693(87)90492-8
P. Gerber and H. Leutwyler, Hadrons Below the Chiral Phase Transition, Nucl. Phys. B 321 (1989) 387, https://doi.org/10.1016/0550-3213(89)90349-0
V. P. Gusynin, V. A. Miransky and I. A. Shovkovy, Dimensional reduction and dynamical chiral symmetry breaking by a magnetic field in (3+1)-dimensions, Phys. Lett. B 349 (1995) 477, https://doi.org/10.1016/0370-2693(95)00232-A
D. S. Lee, C. N. Leung and Y. J. Ng, Chiral symmetry breaking in a uniform external magnetic field, Phys. Rev. D 55 (1997) 6504, https://doi.org/10.1103/PhysRevD.55.6504
D. K. Hong, Magnetic catalysis in quantum electrodynamics, Phys. Rev. D 57 (1998) 3759, https://doi.org/10.1103/PhysRevD.57.3759
E. J. Ferrer and V. de la Incera, Magnetic catalysis in the presence of scalar fields, Phys. Lett. B 481 (2000) 287, https://doi.org/10.1016/S0370-2693(00)00482-2
A. Ayala, A. Bashir, A. Raya and E. Rojas, Dynamical mass generation in strongly coupled quantum electrodynamics with weak magnetic fields, Phys. Rev. D 73 (2006) 105009, https://doi.org/10.1103/PhysRevD.73.105009
E. Rojas, A. Ayala, A. Bashir and A. Raya, Dynamical mass generation in QED with magnetic fields: Arbitrary field strength and coupling constant, Phys. Rev. D 77 (2008) 093004, https://doi.org/10.1103/PhysRevD.77.093004
A. Ayala, A. Bashir, E. Gutierrez, A. Raya and A. Sanchez, Chiral and Parity Symmetry Breaking for Planar Fermions: Effects of a Heat Bath and Uniform External Magnetic Field, Phys. Rev. D 82 (2010) 056011, https://doi.org/10.1103/PhysRevD.82.056011
G. S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S. D. Katz, S. Krieg, A. Schafer and K. K. Szabo, The QCD phase diagram for external magnetic fields, JHEP 02 (2012) 044, https://doi.org/10.1007/JHEP02(2012)044
G. S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S. D. Katz and A. Schafer, QCD quark condensate in external magnetic fields, Phys. Rev. D 86 (2012) 071502, https://doi.org/10.1103/PhysRevD.86.071502
G. S. Bali, F. Bruckmann, G. Endrodi, F. Gruber and A. Schaefer, Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD, JHEP 04 (2013) 130, https://doi.org/10.1007/JHEP04(2013)130
V. G. Bornyakov, P. V. Buividovich, N. Cundy, O. A. Kochetkov and A. Schafer, Deconfinement transition in two-flavor lattice ¨ QCD with dynamical overlap fermions in an external magnetic field, Phys. Rev. D 90 (2014) 034501, https://doi.org/10.1103/PhysRevD.90.034501
V. P. Pagura, D. Gomez Dumm, S. Noguera and N. N. Scoccola, Magnetic catalysis and inverse magnetic catalysis in nonlocal chiral quark models, Phys. Rev. D 95 (2017) 034013, https://doi.org/10.1103/PhysRevD.95.034013
A. Ahmad and A. Farooq, Schwinger Pair Production in QCD from Flavor-Dependent Contact Interaction Model of Quarks, [arXiv:2302.13265 [hep-ph]]
The Committee on the Assessment of and Outlook for Nuclear Physics; Board on Physics and Astronomy; Division on Engineering and Physical Sciences; National Research Council, Nuclear Physics: Exploring the Heart of Matter (National Academies Press, 2012)
S. x. Qin, L. Chang, Y. x. Liu and C. D. Roberts, Quark spectral density and a strongly-coupled QGP, Phys. Rev. D 84 (2011) 014017, https://doi.org/10.1103/PhysRevD.84.014017
C. E. Detar and J. B. Kogut, Measuring the Hadronic Spectrum of the Quark Plasma, Phys. Rev. D 36 (1987) 2828, https://doi.org/10.1103/PhysRevD.36.2828
I. Pushkina et al. [QCD-TARO], Properties of hadron screening masses at finite baryonic density, Phys. Lett. B 609 (2005) 265, https://doi.org/10.1016/j.physletb.2005.01.006
M. Cheng et al. Meson screening masses from lattice QCD with two light and the strange quark, Eur. Phys. J. C 71 (2011) 1564, https://doi.org/10.1140/epjc/s10052-011-1564-y
P. Petreczky, Lattice QCD at non-zero temperature, J. Phys. G 39 (2012) 093002, https://doi.org/10.1088/0954-3899/39/9/093002
H. L. L. Roberts, L. Chang, I. C. Cloet and C. D. Roberts, Masses of ground and excited-state hadrons, Few Body Syst. 51 (2011) 1, https://doi.org/10.1007/s00601-011-0225-x
M. A. Bedolla, J. J. Cobos-Mart´ınez and A. Bashir, Charmonia in a contact interaction, Phys. Rev. D 92 (2015) 054031, https://doi.org/10.1103/PhysRevD.92.054031
M. A. Bedolla, K. Raya, J. J. Cobos-Mart´ınez and A. Bashir, ηc elastic and transition form factors: Contact interaction and algebraic model, Phys. Rev. D 93 (2016) 094025, https://doi.org/10.1103/PhysRevD.93.094025
K. Raya, M. A. Bedolla, J. J. Cobos-Martínez and A. Bashir, Heavy quarkonia in a contact interaction and an algebraic model: mass spectrum, decay constants, charge radii and elastic and transition form factors, Few Body Syst. 59 (2018) 133, https://doi.org/10.1007/s00601-018-1455-y
L. X. Gutiérrez-Guerrero, A. Bashir, M. A. Bedolla and E. Santopinto, Masses of Light and Heavy Mesons and Baryons: A Unified Picture, Phys. Rev. D 100 (2019) 114032, https://doi.org/10.1103/PhysRevD.100.114032
P. Boucaud, J. P. Leroy, A. L. Yaouanc, J. Micheli, O. Pene and J. Rodriguez-Quintero, The Infrared Behaviour of the Pure Yang-Mills Green Functions, Few Body Syst. 53 (2012) 387, https://doi.org/10.1007/s00601-011-0301-2
D. Binosi, C. Mezrag, J. Papavassiliou, C. D. Roberts and J. Rodriguez-Quintero, Process-independent strong running coupling, Phys. Rev. D 96 (2017) 054026, https://doi.org/10.1103/PhysRevD.96.054026
A. Deur, S. J. Brodsky and G. F. de Teramond, The QCD Running Coupling, Nucl. Phys. 90 (2016) 1, https://doi.org/10.1016/j.ppnp.2016.04.003
D. Ebert, T. Feldmann and H. Reinhardt, Extended NJL model for light and heavy mesons without q - anti-q thresholds, Phys. Lett. B 388 (1996) 154, https://doi.org/10.1016/0370-2693(96)01158-6
C. D. Roberts, Hadron Properties and Dyson-Schwinger Equations, Prog. Part. Nucl. Phys. 61 (2008) 50, https://doi.org/10.1016/j.ppnp.2007.12.034
R. L. S. Farias, G. Dallabona, G. Krein and O. A. Battistel, Extension of the Nambu-Jona-Lasinio model at high densities and temperatures using an implicit regularization scheme, Phys. Rev. C 77 (2008) 065201, https://doi.org/10.1103/PhysRevC.77.065201
E. E. Salpeter and H. A. Bethe, A Relativistic equation for bound state problems, Phys. Rev. 84 (1951) 1232, https://doi.org/10.1103/PhysRev.84.1232
G. S. Bali et al. [SESAM], Observation of string breaking in QCD, Phys. Rev. D 71 (2005) 114513, https://doi.org/10.1103/PhysRevD.71.114513
L. Chang, I. C. Cloet, B. El-Bennich, T. Klahn and C. D. Roberts, Exploring the light-quark interaction, Chin. Phys. C 33 (2009) 1189, https://doi.org/10.1088/1674-1137/33/12/022
A. Bochkarev and J. I. Kapusta, Chiral symmetry at finite temperature: Linear versus nonlinear sigma models, Phys. Rev. D 54 (1996) 4066, https://doi.org/10.1103/PhysRevD.54.4066
S. Ferreres-Sole, A. Gómez Nicola and A. Vioque-Rodríguez, Role of the thermal f0(500) in chiral symmetry restoration, Phys. Rev. D 99 (2019) 036018, https://doi.org/10.1103/PhysRevD.99.036018
A. Bender, C. D. Roberts and L. Von Smekal, Goldstone theorem and diquark confinement beyond rainbow ladder approximation, Phys. Lett. B 380 (1996) 7, https://doi.org/10.1016/0370-2693(96)00372-3
L. Chang, C. D. Roberts and P. C. Tandy, Selected highlights from the study of mesons, Chin. J. Phys. 49 (2011) 955
S. x. Qin, L. Chang, Y. x. Liu, C. D. Roberts and D. J. Wilson, Investigation of rainbow-ladder truncation for excited and exotic mesons, Phys. Rev. C 85 (2012) 035202, https://doi.org/10.1103/PhysRevC.85.035202
H. L. L. Roberts, A. Bashir, L. X. Gutierrez-Guerrero, C. D. Roberts and D. J. Wilson, pi- and rho-mesons, and their diquark partners, from a contact interaction, Phys. Rev. C 83 (2011) 065206, https://doi.org/10.1103/PhysRevC.83.065206
C. Chen, L. Chang, C. D. Roberts, S. Wan and D. J. Wilson, Spectrum of hadrons with strangeness, Few Body Syst. 53 (2012) 293, https://doi.org/10.1007/s00601-012-0466-3
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York, 1980).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Jose Luis Flores-Pon, Marco Antonio Bedolla, Peter Sloane, Alfredo Raya
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Suplemento de la Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
