Abstract
We study the mass spectra and spin alignment of vector meson J/ψ in a thermal magnetized background using a generalized theoretical framework based on gauge/gravity duality. Utilizing a soft wall model for the QGP background and a massive vector field for the J/ψ meson, we delve into the meson’s spectral function and spin parameters (λθ, λφ, λθφ) for different cases, assessing their response to variations in magnetic field strength, momentum, and temperature. We initially examine scenarios where a meson’s momentum aligns parallel to the magnetic field in helicity frame. Our results reveal a magnetic field-induced positive \( {\lambda}_{\theta}^{\textrm{H}} \) for low meson momentum, transitioning to negative with increased momentum. As a comparison, we also study the case of momentum perpendicular to the magnetic field and find the direction of magnetic field does not affect the qualitative behavior for the eB-dependence of \( {\lambda}_{\theta}^{\textrm{H}} \). Moreover, we apply our model to real heavy-ion collisions for three different spin quantization directions. Further comparisons with experimental data show qualitative agreement for spin parameters λθ and λφ in the helicity and Collins-Soper frames.
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References
V. Skokov, A.Y. Illarionov and V. Toneev, Estimate of the magnetic field strength in heavy-ion collisions, Int. J. Mod. Phys. A 24 (2009) 5925 [arXiv:0907.1396] [INSPIRE].
D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The effects of topological charge change in heavy ion collisions: ’Event by event P and CP violation’, Nucl. Phys. A 803 (2008) 227 [arXiv:0711.0950] [INSPIRE].
L. McLerran and V. Skokov, Comments About the Electromagnetic Field in Heavy-Ion Collisions, Nucl. Phys. A 929 (2014) 184 [arXiv:1305.0774] [INSPIRE].
U. Gursoy, D. Kharzeev and K. Rajagopal, Magnetohydrodynamics, charged currents and directed flow in heavy ion collisions, Phys. Rev. C 89 (2014) 054905 [arXiv:1401.3805] [INSPIRE].
K. Tuchin, Electromagnetic field and the chiral magnetic effect in the quark-gluon plasma, Phys. Rev. C 91 (2015) 064902 [arXiv:1411.1363] [INSPIRE].
H. Li, X.-L. Sheng and Q. Wang, Electromagnetic fields with electric and chiral magnetic conductivities in heavy ion collisions, Phys. Rev. C 94 (2016) 044903 [arXiv:1602.02223] [INSPIRE].
Y. Chen, X.-L. Sheng and G.-L. Ma, Electromagnetic fields from the extended Kharzeev-McLerran-Warringa model in relativistic heavy-ion collisions, Nucl. Phys. A 1011 (2021) 122199 [arXiv:2101.09845] [INSPIRE].
L. Yan and X.-G. Huang, Dynamical evolution of a magnetic field in the preequilibrium quark-gluon plasma, Phys. Rev. D 107 (2023) 094028 [arXiv:2104.00831] [INSPIRE].
Z. Wang et al., Incomplete electromagnetic response of hot QCD matter, Phys. Rev. C 105 (2022) L041901 [arXiv:2110.14302] [INSPIRE].
K. Fukushima, D.E. Kharzeev and H.J. Warringa, The Chiral Magnetic Effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].
D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].
D.E. Kharzeev and H.-U. Yee, Chiral Magnetic Wave, Phys. Rev. D 83 (2011) 085007 [arXiv:1012.6026] [INSPIRE].
S.K. Das et al., Directed Flow of Charm Quarks as a Witness of the Initial Strong Magnetic Field in Ultra-Relativistic Heavy Ion Collisions, Phys. Lett. B 768 (2017) 260 [arXiv:1608.02231] [INSPIRE].
U. Gürsoy et al., Charge-dependent Flow Induced by Magnetic and Electric Fields in Heavy Ion Collisions, Phys. Rev. C 98 (2018) 055201 [arXiv:1806.05288] [INSPIRE].
J.-J. Zhang et al., Charge-dependent directed flows in heavy-ion collisions by Boltzmann-Maxwell equations, Phys. Rev. Res. 4 (2022) 033138 [arXiv:2201.06171] [INSPIRE].
STAR collaboration, Observation of the electromagnetic field effect via charge-dependent directed flow in heavy-ion collisions at the Relativistic Heavy Ion Collider, Phys. Rev. X 14 (2024) 011028 [arXiv:2304.03430] [INSPIRE].
X.-G. Huang, Electromagnetic fields and anomalous transports in heavy-ion collisions — A pedagogical review, Rept. Prog. Phys. 79 (2016) 076302 [arXiv:1509.04073] [INSPIRE].
K. Hattori, M. Hongo and X.-G. Huang, New Developments in Relativistic Magnetohydrodynamics, Symmetry 14 (2022) 1851 [arXiv:2207.12794] [INSPIRE].
J.-H. Gao, G.-L. Ma, S. Pu and Q. Wang, Recent developments in chiral and spin polarization effects in heavy-ion collisions, Nucl. Sci. Tech. 31 (2020) 90 [arXiv:2005.10432] [INSPIRE].
G.S. Bali et al., The QCD phase diagram for external magnetic fields, JHEP 02 (2012) 044 [arXiv:1111.4956] [INSPIRE].
T. Vachaspati, Magnetic fields from cosmological phase transitions, Phys. Lett. B 265 (1991) 258 [INSPIRE].
R.C. Duncan and C. Thompson, Formation of very strongly magnetized neutron stars - implications for gamma-ray bursts, Astrophys. J. Lett. 392 (1992) L9 [INSPIRE].
Y.-Q. Zhao and D. Hou, Vector meson spectral function in a dynamical AdS/QCD model, Eur. Phys. J. C 82 (2022) 1102 [arXiv:2108.08479] [INSPIRE].
Y.-Q. Zhao and D. Hou, J/Ψ suppression in a rotating magnetized holographic QGP matter, Eur. Phys. J. C 83 (2023) 1076 [arXiv:2306.04318] [INSPIRE].
N.R.F. Braga and Y.F. Ferreira, Bottomonium dissociation in a rotating plasma, Phys. Rev. D 108 (2023) 094017 [arXiv:2309.11643] [INSPIRE].
L.A.H. Mamani, D. Hou and N.R.F. Braga, Melting of heavy vector mesons and quasinormal modes in a finite density plasma from holography, Phys. Rev. D 105 (2022) 126020 [arXiv:2204.08068] [INSPIRE].
N.R.F. Braga and L.F. Ferreira, Heavy meson dissociation in a plasma with magnetic fields, Phys. Lett. B 783 (2018) 186 [arXiv:1802.02084] [INSPIRE].
N.R.F. Braga, L.F. Ferreira and A. Vega, Holographic model for charmonium dissociation, Phys. Lett. B 774 (2017) 476 [arXiv:1709.05326] [INSPIRE].
Z.-R. Zhu, M. Sun, R. Zhou and J. Han, R2 corrections to holographic heavy meson dissociation, arXiv:2401.05893 [INSPIRE].
X. Cao, S. Qiu, H. Liu and D. Li, Thermal properties of light mesons from holography, JHEP 08 (2021) 005 [arXiv:2102.10946] [INSPIRE].
Y.-Q. Zhao, Z.-R. Zhu and X. Chen, The effect of gluon condensate on imaginary potential and thermal width from holography, Eur. Phys. J. A 56 (2020) 57 [arXiv:1909.04994] [INSPIRE].
S.-Q. Feng, Y.-Q. Zhao and X. Chen, Systematical study of thermal width of heavy quarkonia in a finite temperature magnetized background from holography, Phys. Rev. D 101 (2020) 026023 [arXiv:1910.05668] [INSPIRE].
N.R.F. Braga and L.F. Ferreira, Thermal width of heavy quarkonia from an AdS/QCD model, Phys. Rev. D 94 (2016) 094019 [arXiv:1606.09535] [INSPIRE].
S.I. Finazzo and J. Noronha, Estimates for the Thermal Width of Heavy Quarkonia in Strongly Coupled Plasmas from Holography, JHEP 11 (2013) 042 [arXiv:1306.2613] [INSPIRE].
Y.-Q. Zhao and D. Hou, Configuration entropy of Υ(1S) state in strong coupling plasma, Phys. Lett. B 847 (2023) 138271 [arXiv:2305.07087] [INSPIRE].
N.R.F. Braga, L.F. Ferreira and O.C. Junqueira, Configuration entropy of a rotating quark-gluon plasma from holography, Phys. Lett. B 847 (2023) 138265 [arXiv:2301.01322] [INSPIRE].
N.R.F. Braga, Y.F. Ferreira and L.F. Ferreira, Configuration entropy and stability of bottomonium radial excitations in a plasma with magnetic fields, Phys. Rev. D 105 (2022) 114044 [arXiv:2110.04560] [INSPIRE].
N.R.F. Braga and O.C. Junqueira, Configuration entropy in the soft wall AdS/QCD model and the Wien law, Phys. Lett. B 820 (2021) 136485 [arXiv:2105.12347] [INSPIRE].
N.R.F. Braga and O.C. Junqueira, Configuration entropy and confinement/deconfinement transiton in holographic QCD, Phys. Lett. B 814 (2021) 136082 [arXiv:2010.00714] [INSPIRE].
J.-X. Chen, D.-F. Hou and H.-C. Ren, Drag force and heavy quark potential in a rotating background, JHEP 03 (2024) 171 [arXiv:2308.08126] [INSPIRE].
J. Zhou, X. Chen, Y.-Q. Zhao and J. Ping, Thermodynamics of heavy quarkonium in rotating matter from holography, Phys. Rev. D 102 (2021) 126029 [INSPIRE].
J. Zhou, X. Chen, Y.-Q. Zhao and J. Ping, Thermodynamics of heavy quarkonium in a magnetic field background, Phys. Rev. D 102 (2020) 086020 [arXiv:2006.09062] [INSPIRE].
Z.-Q. Zhang, X. Zhu and D.-F. Hou, Imaginary potential of heavy quarkonia from thermal fluctuations in rotating matter from holography, Nucl. Phys. B 989 (2023) 116149 [INSPIRE].
S. Tahery, X. Chen and Z.-Q. Zhang, Holographic imaginary potential of a quark antiquark pair in the presence of gluon condensation, JHEP 03 (2023) 207 [arXiv:2208.01233] [INSPIRE].
Z.-Q. Zhang, D. Hou, H.-C. Ren and L. Yin, The Subleading Term of the Strong Coupling Expansion of the Heavy-Quark Potential in a \( \mathcal{N} \) = 4 Super Yang-Mills Plasma, JHEP 07 (2011) 035 [arXiv:1104.1344] [INSPIRE].
S.-X. Chu, D. Hou and H.-C. Ren, The Subleading Term of the Strong Coupling Expansion of the Heavy-Quark Potential in a N = 4 Super Yang-Mills Vacuum, JHEP 08 (2009) 004 [arXiv:0905.1874] [INSPIRE].
D. Hou and H.-C. Ren, Heavy Quarkonium States with the Holographic Potential, JHEP 01 (2008) 029 [arXiv:0710.2639] [INSPIRE].
D. Hou, M. Atashi, K. Bitaghsir Fadafan and Z.-Q. Zhang, Holographic energy loss of a rotating heavy quark at finite chemical potential, Phys. Lett. B 817 (2021) 136279 [INSPIRE].
X. Chen, S.-Q. Feng, Y.-F. Shi and Y. Zhong, Moving heavy quarkonium entropy, effective string tension, and the QCD phase diagram, Phys. Rev. D 97 (2018) 066015 [arXiv:1710.00465] [INSPIRE].
J.-X. Chen and D.-F. Hou, Heavy quark potential and jet quenching parameter in a rotating D-instanton background, Eur. Phys. J. C 84 (2024) 447 [arXiv:2202.00888] [INSPIRE].
Z.-R. Zhu, D.-F. Hou and X. Chen, Potential analysis of holographic Schwinger effect in the magnetized background, Eur. Phys. J. C 80 (2020) 550 [arXiv:1912.05806] [INSPIRE].
X. Chen, L. Zhang and D. Hou, Running coupling constant at finite chemical potential and magnetic field from holography, Chin. Phys. C 46 (2022) 073101 [arXiv:2108.03840] [INSPIRE].
P.-P. Wu, Z.-Q. Zhang and X. Zhu, Entropic destruction of heavy quarkonium in a rotating hot and dense medium from holography, Chin. Phys. C 46 (2022) 113103 [arXiv:2207.06122] [INSPIRE].
A. Li and Z.-Q. Zhang, Entropic destruction of heavy quarkonium with hyperscaling violation, Chin. Phys. C 45 (2021) 103105 [arXiv:2108.00174] [INSPIRE].
Z.-R. Zhu and D. Hou, Inverse magnetic catalysis and energy loss in holographic QCD model, arXiv:2305.12375 [INSPIRE].
F. Sun et al., Chiral phase transition and spin alignment of vector mesons in the polarized-Polyakov-loop Nambu–Jona-Lasinio model under rotation, Phys. Rev. D 109 (2024) 116017 [arXiv:2402.16595] [INSPIRE].
M. Wei and M. Huang, Spin alignment of vector mesons from quark dynamics in a rotating medium, Chin. Phys. C 47 (2023) 104105 [arXiv:2303.01897] [INSPIRE].
STAR collaboration, Pattern of global spin alignment of ϕ and K*0 mesons in heavy-ion collisions, Nature 614 (2023) 244 [arXiv:2204.02302] [INSPIRE].
ALICE collaboration, Measurement of the J/ψ Polarization with Respect to the Event Plane in Pb-Pb Collisions at the LHC, Phys. Rev. Lett. 131 (2023) 042303 [arXiv:2204.10171] [INSPIRE].
P. Braun-Munzinger and J. Stachel, (Non)thermal aspects of charmonium production and a new look at J / psi suppression, Phys. Lett. B 490 (2000) 196 [nucl-th/0007059] [INSPIRE].
ALICE collaboration, Physics Preliminary Summary: Measurement of the J/ψ polarization with respect to the event plane in Pb–Pb collisions at the LHC, ALICE-PUBLIC-2022-005 (2022).
P. Faccioli, C. Lourenco, J. Seixas and H.K. Wohri, Towards the experimental clarification of quarkonium polarization, Eur. Phys. J. C 69 (2010) 657 [arXiv:1006.2738] [INSPIRE].
K. Schilling, P. Seyboth and G.E. Wolf, On the Analysis of Vector Meson Production by Polarized Photons, Nucl. Phys. B 15 (1970) 397 [Erratum ibid. 18 (1970) 332] [INSPIRE].
X.-L. Sheng, S.-Y. Yang, Y.-L. Zou and D. Hou, Mass splitting and spin alignment for ϕ mesons in a magnetic field in NJL model, Eur. Phys. J. C 84 (2024) 299 [arXiv:2209.01872] [INSPIRE].
X.-L. Sheng et al., Spin Alignment of Vector Mesons in Heavy-Ion Collisions, Phys. Rev. Lett. 131 (2023) 042304 [arXiv:2205.15689] [INSPIRE].
X.-L. Sheng, Q. Wang and X.-N. Wang, Improved quark coalescence model for spin alignment and polarization of hadrons, Phys. Rev. D 102 (2020) 056013 [arXiv:2007.05106] [INSPIRE].
X.-L. Sheng, L. Oliva and Q. Wang, What can we learn from the global spin alignment of ϕ mesons in heavy-ion collisions?, Phys. Rev. D 101 (2020) 096005 [Erratum ibid. 105 (2022) 099903] [arXiv:1910.13684] [INSPIRE].
ALICE collaboration, First measurement of quarkonium polarization in nuclear collisions at the LHC, Phys. Lett. B 815 (2021) 136146 [arXiv:2005.11128] [INSPIRE].
D. Dudal, D.R. Granado and T.G. Mertens, No inverse magnetic catalysis in the QCD hard and soft wall models, Phys. Rev. D 93 (2016) 125004 [arXiv:1511.04042] [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].
E. D’Hoker and P. Kraus, Magnetic Brane Solutions in AdS, JHEP 10 (2009) 088 [arXiv:0908.3875] [INSPIRE].
E. D’Hoker and P. Kraus, Charged Magnetic Brane Solutions in AdS (5) and the fate of the third law of thermodynamics, JHEP 03 (2010) 095 [arXiv:0911.4518] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [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].
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].
C. Gale and J.I. Kapusta, Vector dominance model at finite temperature, Nucl. Phys. B 357 (1991) 65 [INSPIRE].
X.-L. Sheng et al., Holographic spin alignment for vector mesons, arXiv:2403.07522 [INSPIRE].
G.S. Bali et al., QCD quark condensate in external magnetic fields, Phys. Rev. D 86 (2012) 071502 [arXiv:1206.4205] [INSPIRE].
E.-M. Ilgenfritz, M. Muller-Preussker, B. Petersson and A. Schreiber, Magnetic catalysis (and inverse catalysis) at finite temperature in two-color lattice QCD, Phys. Rev. D 89 (2014) 054512 [arXiv:1310.7876] [INSPIRE].
Acknowledgments
We would like to thank Francesco Becattini and Hai-cang Ren for the encouraging discussions. This work is supported in part by the National Key Research and Development Program of China under Contract No. 2022YFA1604900. This work is also partly supported by the National Natural Science Foundation of China (NSFC) under Grants No. 12275104, and No. 11735007. Si-wen Li is supported by the National Natural Science Foundation of China (NSFC) under Grant No. 12005033 and the Fundamental Research Funds for the Central Universities under Grant No. 3132024192.
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Zhao, YQ., Sheng, XL., Li, SW. et al. Holographic spin alignment of J/ψ meson in magnetized plasma. J. High Energ. Phys. 2024, 70 (2024). https://doi.org/10.1007/JHEP08(2024)070
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DOI: https://doi.org/10.1007/JHEP08(2024)070