Abstract
The thermal properties of light mesons, including the temperature dependence of their masses (both screening and pole masses) and thermal widths, are studied in a two-flavor (Nf = 2) soft-wall AdS/QCD model. By solving the spatial correlation functions, we extract the screening masses (mscr) from their poles. The screening masses of pseudo-scalar (π) and axial-vector (a1) mesons increase almost monotonously with the increase of temperature. The screening masses of scalar (σ) and vector (ρ) mesons decrease at low temperature and increase at high temperature. The pole masses (mpole) and the thermal widths (Γ) are extracted from the temporal correlation functions and the corresponding spectral functions. The results indicate that the pole masses have local minima at low temperature and increase at high temperature. The thermal widths increase rapidly above the chiral crossover temperature Tcp, indicating the dissociations of mesons at high temperature. Furthermore, the degeneration of the chiral partners (π and σ, ρ and a1) above Tcp is observed from the screening and pole masses, revealing the chiral symmetry restoration at the hadronic spectrum level. Finally, we numerically verify that the spectral functions in the temporal regime are strongly related to the quasi-normal modes with complex frequencies ω0 = mpole − iΓ/2.
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References
R.D. Pisarski and F. Wilczek, Remarks on the Chiral Phase Transition in Chromodynamics, Phys. Rev. D 29 (1984) 338 [INSPIRE].
P. de Forcrand and O. Philipsen, The chiral critical line of Nf = 2 + 1 QCD at zero and non-zero baryon density, JHEP 01 (2007) 077 [hep-lat/0607017] [INSPIRE].
H.-T. Ding, F. Karsch and S. Mukherjee, Thermodynamics of strong-interaction matter from Lattice QCD, Int. J. Mod. Phys. E 24 (2015) 1530007 [arXiv:1504.05274] [INSPIRE].
STAR collaboration, Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration’s critical assessment of the evidence from RHIC collisions, Nucl. Phys. A 757 (2005) 102 [nucl-ex/0501009] [INSPIRE].
E.V. Shuryak, Physics of the pion liquid, Phys. Rev. D 42 (1990) 1764 [INSPIRE].
C.E. Detar and J.B. Kogut, The Hadronic Spectrum of the Quark Plasma, Phys. Rev. Lett. 59 (1987) 399 [INSPIRE].
C.E. Detar and J.B. Kogut, Measuring the Hadronic Spectrum of the Quark Plasma, Phys. Rev. D 36 (1987) 2828 [INSPIRE].
D.T. Son and M.A. Stephanov, Pion propagation near the QCD chiral phase transition, Phys. Rev. Lett. 88 (2002) 202302 [hep-ph/0111100] [INSPIRE].
D.T. Son and M.A. Stephanov, Real time pion propagation in finite temperature QCD, Phys. Rev. D 66 (2002) 076011 [hep-ph/0204226] [INSPIRE].
I. Schmidt and J.-J. Yang, Electric screening mass of the gluon with gluon condensate at finite temperature, Phys. Lett. B 468 (1999) 138 [hep-ph/9906510] [INSPIRE].
G. Aarts et al., Light baryons below and above the deconfinement transition: medium effects and parity doubling, JHEP 06 (2017) 034 [arXiv:1703.09246] [INSPIRE].
G. Aarts, C. Allton, D. De Boni and B. Jäger, Hyperons in thermal QCD: A lattice view, Phys. Rev. D 99 (2019) 074503 [arXiv:1812.07393] [INSPIRE].
M. Cheng et al., Meson screening masses from lattice QCD with two light and the strange quark, Eur. Phys. J. C 71 (2011) 1564 [arXiv:1010.1216] [INSPIRE].
A. Bazavov et al., Meson screening masses in (2+1)-flavor QCD, Phys. Rev. D 100 (2019) 094510 [arXiv:1908.09552] [INSPIRE].
A. Ayala, C.A. Dominguez, M. Loewe and Y. Zhang, Rho-meson resonance broadening in QCD at finite temperature, Phys. Rev. D 86 (2012) 114036 [arXiv:1210.2588] [INSPIRE].
Y. Nakahara, M. Asakawa and T. Hatsuda, Hadronic spectral functions in lattice QCD, Phys. Rev. D 60 (1999) 091503 [hep-lat/9905034] [INSPIRE].
M. Asakawa, T. Hatsuda and Y. Nakahara, Maximum entropy analysis of the spectral functions in lattice QCD, Prog. Part. Nucl. Phys. 46 (2001) 459 [hep-lat/0011040] [INSPIRE].
G.-Q. Li, C.M. Ko and G.E. Brown, Enhancement of low mass dileptons in heavy ion collisions, Phys. Rev. Lett. 75 (1995) 4007 [nucl-th/9504025] [INSPIRE].
G. Chanfray, R. Rapp and J. Wambach, Medium modifications of the rho meson at CERN SPS energies, Phys. Rev. Lett. 76 (1996) 368 [hep-ph/9508353] [INSPIRE].
CERES collaboration, Modification of the rho-meson detected by low-mass electron-positron pairs in central Pb-Au collisions at 158-A-GeV/c, Phys. Lett. B 666 (2008) 425 [nucl-ex/0611022] [INSPIRE].
NA60 collaboration, First measurement of the rho spectral function in high-energy nuclear collisions, Phys. Rev. Lett. 96 (2006) 162302 [nucl-ex/0605007] [INSPIRE].
R. Rapp, J. Wambach and H. van Hees, The Chiral Restoration Transition of QCD and Low Mass Dileptons, Landolt-Bornstein 23 (2010) 134 [arXiv:0901.3289] [INSPIRE].
R.D. Pisarski and M. Tytgat, Propagation of cool pions, Phys. Rev. D 54 (1996) R2989 [hep-ph/9604404] [INSPIRE].
L.-f. Chen, S.-X. Qin and Y.-x. Liu, Flavor dependence of the thermal dissociations of vector and axial-vector mesons, Phys. Rev. D 102 (2020) 054015 [arXiv:2006.10582] [INSPIRE].
A. Mócsy and P. Petreczky, Quarkonia correlators above deconfinement, Phys. Rev. D 73 (2006) 074007 [hep-ph/0512156] [INSPIRE].
B.B. Brandt, A. Francis, H.B. Meyer and D. Robaina, Pion quasiparticle in the low-temperature phase of QCD, Phys. Rev. D 92 (2015) 094510 [arXiv:1506.05732] [INSPIRE].
B.B. Brandt, A. Francis, H.B. Meyer and D. Robaina, Chiral dynamics in the low-temperature phase of QCD, Phys. Rev. D 90 (2014) 054509 [arXiv:1406.5602] [INSPIRE].
H.-T. Ding, O. Kaczmarek, S. Mukherjee, H. Ohno and H.T. Shu, Stochastic reconstructions of spectral functions: Application to lattice QCD, Phys. Rev. D 97 (2018) 094503 [arXiv:1712.03341] [INSPIRE].
H. Hansen, W.M. Alberico, A. Beraudo, A. Molinari, M. Nardi and C. Ratti, Mesonic correlation functions at finite temperature and density in the Nambu-Jona-Lasinio model with a Polyakov loop, Phys. Rev. D 75 (2007) 065004 [hep-ph/0609116] [INSPIRE].
Y. Jiang, K. Ren, T. Xia and P. Zhuang, Meson Screening Mass in a Strongly Coupled Pion Superfluid, Eur. Phys. J. C 71 (2011) 1822 [arXiv:1104.0094] [INSPIRE].
D. Ebert, Y.L. Kalinovsky and M.K. Volkov, Mesons at finite temperature in the NJL model with gluon condensate, Phys. Lett. B 301 (1993) 231 [INSPIRE].
B. Sheng, Y. Wang, X. Wang and L. Yu, Pole and screening masses of neutral pions in a hot and magnetized medium: A comprehensive study in the Nambu-Jona-Lasinio model, Phys. Rev. D 103 (2021) 094001 [arXiv:2010.05716] [INSPIRE].
R.-A. Tripolt, N. Strodthoff, L. von Smekal and J. Wambach, Spectral Functions for the Quark-Meson Model Phase Diagram from the Functional Renormalization Group, Phys. Rev. D 89 (2014) 034010 [arXiv:1311.0630] [INSPIRE].
Z. Wang and P. Zhuang, Meson spectral functions at finite temperature and isospin density with the functional renormalization group, Phys. Rev. D 96 (2017) 014006 [arXiv:1703.01035] [INSPIRE].
C.S. Fischer, QCD at finite temperature and chemical potential from Dyson-Schwinger equations, Prog. Part. Nucl. Phys. 105 (2019) 1 [arXiv:1810.12938] [INSPIRE].
D. Horvatic, D. Blaschke, D. Klabucar and O. Kaczmarek, Width of the QCD transition in a Polyakov-loop DSE model, Phys. Rev. D 84 (2011) 016005 [arXiv:1012.2113] [INSPIRE].
F. Gao and M. Ding, Thermal properties of π and ρ meson, Eur. Phys. J. C 80 (2020) 1171 [arXiv:2006.05909] [INSPIRE].
W. Florkowski and B.L. Friman, Spatial dependence of the finite temperature meson correlation function, Z. Phys. A 347 (1994) 271 [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].
J. Erlich, E. Katz, D.T. Son and M.A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett. 95 (2005) 261602 [hep-ph/0501128] [INSPIRE].
A. Karch, E. Katz, D.T. Son and M.A. Stephanov, Linear confinement and AdS/QCD, Phys. Rev. D 74 (2006) 015005 [hep-ph/0602229] [INSPIRE].
S.S. Gubser and A. Nellore, Mimicking the QCD equation of state with a dual black hole, Phys. Rev. D 78 (2008) 086007 [arXiv:0804.0434] [INSPIRE].
S.S. Gubser, A. Nellore, S.S. Pufu and F.D. Rocha, Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics, Phys. Rev. Lett. 101 (2008) 131601 [arXiv:0804.1950] [INSPIRE].
O. DeWolfe, S.S. Gubser and C. Rosen, A holographic critical point, Phys. Rev. D 83 (2011) 086005 [arXiv:1012.1864] [INSPIRE].
U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [INSPIRE].
U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: Part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [INSPIRE].
S.J. Brodsky, G.F. de Teramond, H.G. Dosch and J. Erlich, Light-Front Holographic QCD and Emerging Confinement, Phys. Rept. 584 (2015) 1 [arXiv:1407.8131] [INSPIRE].
T. Gherghetta, J.I. Kapusta and T.M. Kelley, Chiral symmetry breaking in the soft-wall AdS/QCD model, Phys. Rev. D 79 (2009) 076003 [arXiv:0902.1998] [INSPIRE].
T.M. Kelley, S.P. Bartz and J.I. Kapusta, Pseudoscalar Mass Spectrum in a Soft-Wall Model of AdS/QCD, Phys. Rev. D 83 (2011) 016002 [arXiv:1009.3009] [INSPIRE].
D. Li, M. Huang and Q.-S. Yan, A dynamical soft-wall holographic QCD model for chiral symmetry breaking and linear confinement, Eur. Phys. J. C 73 (2013) 2615 [arXiv:1206.2824] [INSPIRE].
D. Li and M. Huang, Dynamical holographic QCD model for glueball and light meson spectra, JHEP 11 (2013) 088 [arXiv:1303.6929] [INSPIRE].
Y.-Q. Sui, Y.-L. Wu, Z.-F. Xie and Y.-B. Yang, Prediction for the Mass Spectra of Resonance Mesons in the Soft-Wall AdS/QCD with a Modified 5D Metric, Phys. Rev. D 81 (2010) 014024 [arXiv:0909.3887] [INSPIRE].
P. Colangelo, F. De Fazio, F. Giannuzzi, F. Jugeau and S. Nicotri, Light scalar mesons in the soft-wall model of AdS/QCD, Phys. Rev. D 78 (2008) 055009 [arXiv:0807.1054] [INSPIRE].
A. Ballon-Bayona and L.A.H. Mamani, Nonlinear realization of chiral symmetry breaking in holographic soft wall models, Phys. Rev. D 102 (2020) 026013 [arXiv:2002.00075] [INSPIRE].
E. Folco Capossoli, M.A. Martín Contreras, D. Li, A. Vega and H. Boschi-Filho, Hadronic spectra from deformed AdS backgrounds, Chin. Phys. C 44 (2020) 064104 [arXiv:1903.06269] [INSPIRE].
P. Colangelo, F. Giannuzzi, S. Nicotri and V. Tangorra, Temperature and quark density effects on the chiral condensate: An AdS/QCD study, Eur. Phys. J. C 72 (2012) 2096 [arXiv:1112.4402] [INSPIRE].
K. Chelabi, Z. Fang, M. Huang, D. Li and Y.-L. Wu, Realization of chiral symmetry breaking and restoration in holographic QCD, Phys. Rev. D 93 (2016) 101901 [arXiv:1511.02721] [INSPIRE].
K. Chelabi, Z. Fang, M. Huang, D. Li and Y.-L. Wu, Chiral Phase Transition in the Soft-Wall Model of AdS/QCD, JHEP 04 (2016) 036 [arXiv:1512.06493] [INSPIRE].
Z. Fang, S. He and D. Li, Chiral and Deconfining Phase Transitions from Holographic QCD Study, Nucl. Phys. B 907 (2016) 187 [arXiv:1512.04062] [INSPIRE].
D. Li, M. Huang, Y. Yang and P.-H. Yuan, Inverse Magnetic Catalysis in the Soft-Wall Model of AdS/QCD, JHEP 02 (2017) 030 [arXiv:1610.04618] [INSPIRE].
D. Li and M. Huang, Chiral phase transition of QCD with Nf = 2 + 1 flavors from holography, JHEP 02 (2017) 042 [arXiv:1610.09814] [INSPIRE].
S.P. Bartz and T. Jacobson, Chiral Phase Transition and Meson Melting from AdS/QCD, Phys. Rev. D 94 (2016) 075022 [arXiv:1607.05751] [INSPIRE].
Z. Fang, Y.-L. Wu and L. Zhang, Chiral phase transition and meson spectrum in improved soft-wall AdS/QCD, Phys. Lett. B 762 (2016) 86 [arXiv:1604.02571] [INSPIRE].
S.P. Bartz and T. Jacobson, Chiral phase transition at finite chemical potential in 2+1 -flavor soft-wall anti-de Sitter space QCD, Phys. Rev. C 97 (2018) 044908 [arXiv:1801.00358] [INSPIRE].
Z. Fang, Y.-L. Wu and L. Zhang, Chiral Phase Transition with 2+1 quark flavors in an improved soft-wall AdS/QCD Model, Phys. Rev. D 98 (2018) 114003 [arXiv:1805.05019] [INSPIRE].
X. Cao, H. Liu, D. Li and G. Ou, QCD phase diagram at finite isospin chemical potential and temperature in an IR-improved soft-wall AdS/QCD model, Chin. Phys. C 44 (2020) 083106 [arXiv:2001.02888] [INSPIRE].
J. Erdmenger, M. Kaminski and F. Rust, Holographic vector mesons from spectral functions at finite baryon or isospin density, Phys. Rev. D 77 (2008) 046005 [arXiv:0710.0334] [INSPIRE].
J. Erdmenger, M. Kaminski, P. Kerner and F. Rust, Finite baryon and isospin chemical potential in AdS/CFT with flavor, JHEP 11 (2008) 031 [arXiv:0807.2663] [INSPIRE].
M. Kaminski, K. Landsteiner, F. Pena-Benitez, J. Erdmenger, C. Greubel and P. Kerner, Quasinormal modes of massive charged flavor branes, JHEP 03 (2010) 117 [arXiv:0911.3544] [INSPIRE].
P. Colangelo, F. Giannuzzi and S. Nicotri, Holographic Approach to Finite Temperature QCD: The Case of Scalar Glueballs and Scalar Mesons, Phys. Rev. D 80 (2009) 094019 [arXiv:0909.1534] [INSPIRE].
M. Fujita, T. Kikuchi, K. Fukushima, T. Misumi and M. Murata, Melting Spectral Functions of the Scalar and Vector Mesons in a Holographic QCD Model, Phys. Rev. D 81 (2010) 065024 [arXiv:0911.2298] [INSPIRE].
L.-X. Cui, Z. Fang and Y.-L. Wu, Thermal Spectral Function and Deconfinement Temperature in Bulk Holographic AdS/QCD with Back Reaction of Bulk Vacuum, Chin. Phys. C 40 (2016) 063101 [arXiv:1404.0761] [INSPIRE].
N.R.F. Braga, M.A. Martin Contreras and S. Diles, Holographic Picture of Heavy Vector Meson Melting, Eur. Phys. J. C 76 (2016) 598 [arXiv:1604.08296] [INSPIRE].
A. Vega and A. Ibañez, Analysis of soft wall AdS/QCD potentials to obtain the melting temperature of scalar hadrons, Eur. Phys. J. A 53 (2017) 217 [arXiv:1706.01994] [INSPIRE].
R. Zöllner and B. Kämpfer, Quarkonia Formation in a Holographic Gravity-Dilaton Background Describing QCD Thermodynamics, Particles 4 (2021) 159 [arXiv:2007.14287] [INSPIRE].
M.A. Martin Contreras, S. Diles and A. Vega, Heavy quarkonia spectroscopy at zero and finite temperature in bottom-up AdS/QCD, Phys. Rev. D 103 (2021) 086008 [arXiv:2101.06212] [INSPIRE].
V.P. Frolov and I.D. Novikov, Black hole physics: Basic concepts and new developments, Kluwer Academic Publishers, Berlin, Germany (1998).
K.D. Kokkotas and B.G. Schmidt, Quasinormal modes of stars and black holes, Living Rev. Rel. 2 (1999) 2 [gr-qc/9909058] [INSPIRE].
A.S. Miranda, C.A. Ballon Bayona, H. Boschi-Filho and N.R.F. Braga, Black-hole quasinormal modes and scalar glueballs in a finite-temperature AdS/QCD model, JHEP 11 (2009) 119 [arXiv:0909.1790] [INSPIRE].
H.R. Grigoryan, P.M. Hohler and M.A. Stephanov, Towards the Gravity Dual of Quarkonium in the Strongly Coupled QCD Plasma, Phys. Rev. D 82 (2010) 026005 [arXiv:1003.1138] [INSPIRE].
L.A.H. Mamani, A.S. Miranda, H. Boschi-Filho and N.R.F. Braga, Vector meson quasinormal modes in a finite-temperature AdS/QCD model, JHEP 03 (2014) 058 [arXiv:1312.3815] [INSPIRE].
L.A.H. Mamani, A.S. Miranda and V.T. Zanchin, Melting of scalar mesons and black-hole quasinormal modes in a holographic QCD model, Eur. Phys. J. C 79 (2019) 435 [arXiv:1809.03508] [INSPIRE].
N.R.F. Braga and L.F. Ferreira, Quasinormal modes for quarkonium in a plasma with magnetic fields, Phys. Lett. B 795 (2019) 462 [arXiv:1905.11309] [INSPIRE].
D. Bak, A. Karch and L.G. Yaffe, Debye screening in strongly coupled N = 4 supersymmetric Yang-Mills plasma, JHEP 08 (2007) 049 [arXiv:0705.0994] [INSPIRE].
S.I. Finazzo and J. Noronha, Debye screening mass near deconfinement from holography, Phys. Rev. D 90 (2014) 115028 [arXiv:1411.4330] [INSPIRE].
N.R.F. Braga and L.F. Ferreira, Thermal spectrum of pseudo-scalar glueballs and Debye screening mass from holography, Eur. Phys. J. C 77 (2017) 662 [arXiv:1703.07851] [INSPIRE].
O. Andreev, Color screening masses from string models, Phys. Rev. D 94 (2016) 126003 [arXiv:1608.08026] [INSPIRE].
X. Cao, H. Liu and D. Li, Pion quasiparticles and QCD phase transitions at finite temperature and isospin density from holography, Phys. Rev. D 102 (2020) 126014 [arXiv:2009.00289] [INSPIRE].
D.T. Son and M.A. Stephanov, QCD and dimensional deconstruction, Phys. Rev. D 69 (2004) 065020 [hep-ph/0304182] [INSPIRE].
A. Cherman, T.D. Cohen and E.S. Werbos, The chiral condensate in holographic models of QCD, Phys. Rev. C 79 (2009) 045203 [arXiv:0804.1096] [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
J. Chen, S. He, M. Huang and D. Li, Critical exponents of finite temperature chiral phase transition in soft-wall AdS/QCD models, JHEP 01 (2019) 165 [arXiv:1810.07019] [INSPIRE].
G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
S. Kalyana Rama and B. Sathiapalan, On the role of chaos in the AdS / CFT connection, Mod. Phys. Lett. A 14 (1999) 2635 [hep-th/9905219] [INSPIRE].
A. Sirlin, Theoretical considerations concerning the Z0 mass, Phys. Rev. Lett. 67 (1991) 2127 [INSPIRE].
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Cao, X., Qiu, S., Liu, H. et al. Thermal properties of light mesons from holography. J. High Energ. Phys. 2021, 5 (2021). https://doi.org/10.1007/JHEP08(2021)005
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DOI: https://doi.org/10.1007/JHEP08(2021)005