Abstract
The hydrodynamic coefficients in the axial current are calculated on the basis of the equilibrium quantum statistical density operator in the third order of perturbation theory in thermal vorticity tensor both for the case of massive and massless fermions. The coefficients obtained describe third-order corrections to the Chiral Vortical Effect and include the contribution from local acceleration. We show that the methods of the Wigner function and the statistical density operator lead to the same result for an axial current in describing effects associated only with vorticity when the local acceleration is zero, but differ in describing mixed effects for which both acceleration and vorticity are significant simultaneously.
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References
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].
A.V. Sadofyev, V.I. Shevchenko and V.I. Zakharov, Notes on chiral hydrodynamics within effective theory approach, Phys. Rev. D 83 (2011) 105025 [arXiv:1012.1958] [INSPIRE].
V.I. Zakharov, Chiral Magnetic Effect in Hydrodynamic Approximation, Lect. Notes Phys. 871 (2013) 295 [arXiv:1210.2186] [INSPIRE].
D.E. Kharzeev, K. Landsteiner, A. Schmitt and H.U. Yee, ’Strongly interacting matter in magnetic fields’: an overview, Lect. Notes Phys. 871 (2013) 1 [arXiv:1211.6245] [INSPIRE].
A. Vilenkin, Quantum field theory at finite temperature in a rotating system, Phys. Rev. D 21 (1980) 2260 [INSPIRE].
A. Vilenkin, Macroscopic parity violating effects: neutrino fluxes from rotating black holes and in rotating thermal radiation, Phys. Rev. D 20 (1979) 1807 [INSPIRE].
J.-h. Gao, S. Pu and Q. Wang, Covariant chiral kinetic equation in the Wigner function approach, Phys. Rev. D 96 (2017) 016002 [arXiv:1704.00244] [INSPIRE].
K. Landsteiner, E. Megias and F. Pena-Benitez, Anomalous Transport from Kubo Formulae, Lect. Notes Phys. 871 (2013) 433 [arXiv:1207.5808] [INSPIRE].
M. Buzzegoli, E. Grossi and F. Becattini, General equilibrium second-order hydrodynamic coefficients for free quantum fields, JHEP 10 (2017) 091 [Erratum ibid. 1807 (2018) 119] [arXiv:1704.02808] [INSPIRE].
G. Prokhorov and O. Teryaev, Anomalous current from the covariant Wigner function, Phys. Rev. D 97 (2018) 076013 [arXiv:1707.02491] [INSPIRE].
G. Prokhorov, O. Teryaev and V. Zakharov, Axial current in rotating and accelerating medium, Phys. Rev. D 98 (2018) 071901 [arXiv:1805.12029] [INSPIRE].
D.E. Kharzeev, J. Liao, S.A. Voloshin and G. Wang, Chiral magnetic and vortical effects in high-energy nuclear collisions — A status report, Prog. Part. Nucl. Phys. 88 (2016) 1 [arXiv:1511.04050] [INSPIRE].
V. Koch et al., Status of the chiral magnetic effect and collisions of isobars, Chin. Phys. C 41 (2017) 072001 [arXiv:1608.00982] [INSPIRE].
M. Baznat, K. Gudima, A. Sorin and O. Teryaev, Hyperon polarization in heavy-ion collisions and holographic gravitational anomaly, Phys. Rev. C 97 (2018) 041902 [arXiv:1701.00923] [INSPIRE].
O. Rogachevsky, A. Sorin and O. Teryaev, Chiral vortaic effect and neutron asymmetries in heavy-ion collisions, Phys. Rev. C 82 (2010) 054910 [arXiv:1006.1331] [INSPIRE].
A. Sorin and O. Teryaev, Axial anomaly and energy dependence of hyperon polarization in Heavy-Ion Collisions, Phys. Rev. C 95 (2017) 011902 [arXiv:1606.08398] [INSPIRE].
M. Baznat, K. Gudima, A. Sorin and O. Teryaev, Helicity separation in Heavy-Ion Collisions, Phys. Rev. C 88 (2013) 061901 [arXiv:1301.7003] [INSPIRE].
F. Becattini and I. Karpenko, Collective Longitudinal Polarization in Relativistic Heavy-Ion Collisions at Very High Energy, Phys. Rev. Lett. 120 (2018) 012302 [arXiv:1707.07984] [INSPIRE].
F. Becattini, I. Karpenko, M. Lisa, I. Upsal and S. Voloshin, Global hyperon polarization at local thermodynamic equilibrium with vorticity, magnetic field and feed-down, Phys. Rev. C 95 (2017) 054902 [arXiv:1610.02506] [INSPIRE].
I. Karpenko and F. Becattini, Vorticity in the QGP liquid and Λ polarization at the RHIC Beam Energy Scan, Nucl. Phys. A 967 (2017) 764 [arXiv:1704.02142] [INSPIRE].
Q. Li et al., Observation of the chiral magnetic effect in ZrTe5, Nature Phys. 12 (2016) 550 [arXiv:1412.6543] [INSPIRE].
S.P. Robinson and F. Wilczek, A Relationship between Hawking radiation and gravitational anomalies, Phys. Rev. Lett. 95 (2005) 011303 [gr-qc/0502074] [INSPIRE].
M. Stone and J. Kim, Mixed Anomalies: Chiral Vortical Effect and the Sommerfeld Expansion, Phys. Rev. D 98 (2018) 025012 [arXiv:1804.08668] [INSPIRE].
V.I. Zakharov, Notes on conservation laws in chiral hydrodynamics, arXiv:1611.09113 [INSPIRE].
F. Becattini and E. Grossi, Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration, Phys. Rev. D 92 (2015) 045037 [arXiv:1505.07760] [INSPIRE].
F. Becattini, Thermodynamic equilibrium with acceleration and the Unruh effect, Phys. Rev. D 97 (2018) 085013 [arXiv:1712.08031] [INSPIRE].
W. Florkowski, E. Speranza and F. Becattini, Perfect-fluid hydrodynamics with constant acceleration along the stream lines and spin polarization, Acta Phys. Polon. B 49 (2018) 1409 [arXiv:1803.11098] [INSPIRE].
F. Becattini, V. Chandra, L. Del Zanna and E. Grossi, Relativistic distribution function for particles with spin at local thermodynamical equilibrium, Annals Phys. 338 (2013) 32 [arXiv:1303.3431] [INSPIRE].
W. Florkowski, A. Kumar and R. Ryblewski, Thermodynamic versus kinetic approach to polarization-vorticity coupling, Phys. Rev. C 98 (2018) 044906 [arXiv:1806.02616] [INSPIRE].
F. Becattini, L. Bucciantini, E. Grossi and L. Tinti, Local thermodynamical equilibrium and the beta frame for a quantum relativistic fluid, Eur. Phys. J. C 75 (2015) 191 [arXiv:1403.6265] [INSPIRE].
T. Hayata, Y. Hidaka, T. Noumi and M. Hongo, Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method, Phys. Rev. D 92 (2015) 065008 [arXiv:1503.04535] [INSPIRE].
F. Becattini, Covariant statistical mechanics and the stress-energy tensor, Phys. Rev. Lett. 108 (2012) 244502 [arXiv:1201.5278] [INSPIRE].
M. Hongo, Path-integral formula for local thermal equilibrium, Annals Phys. 383 (2017) 1 [arXiv:1611.07074] [INSPIRE].
D.N. Zubarev, A.V. Prozorkevich and S.A. Smolyanskii, Derivation of nonlinear generalized equations of quantum relativistic hydrodynamics, Teor. Mat. Fiz. 40 (1979) 394 Theor. Math. Phys. 40 (1979) 821.
C.G. Van Weert, Maximum entropy principle and relativistic hydrodynamics, Annals Phys. 140 (1982) 133.
W. Florkowski, B. Friman, A. Jaiswal and E. Speranza, Relativistic fluid dynamics with spin, Phys. Rev. C 97 (2018) 041901 [arXiv:1705.00587] [INSPIRE].
J.I. Korsbakken and J.M. Leinaas, The Fulling-Unruh effect in general stationary accelerated frames, Phys. Rev. D 70 (2004) 084016 [hep-th/0406080] [INSPIRE].
M. Buzzegoli and F. Becattini, General thermodynamic equilibrium with axial chemical potential for the free Dirac field, JHEP 12 (2018) 002 [arXiv:1807.02071] [INSPIRE].
S.R. De Groot, W.A. Van Leeuwen and C.G. Van Weert, Relativistic Kinetic Theory. Principles and Applications, North-Holland, Amsterdam, The Netherlands (1980).
M. Laine and A. Vuorinen, Basics of Thermal Field Theory, Lect. Notes Phys. 925 (2016) 1 [arXiv:1701.01554] [INSPIRE].
J.I. Kapusta and C. Gale, Finite-temperature field theory: Principles and applications, emphCambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2011).
P. Castorina, D. Kharzeev and H. Satz, Thermal Hadronization and Hawking-Unruh Radiation in QCD, Eur. Phys. J. C 52 (2007) 187 [arXiv:0704.1426] [INSPIRE].
F. Becattini, P. Castorina, J. Manninen and H. Satz, The Thermal Production of Strange and Non-Strange Hadrons in e + e − Collisions, Eur. Phys. J. C 56 (2008) 493 [arXiv:0805.0964] [INSPIRE].
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Prokhorov, G.Y., Teryaev, O.V. & Zakharov, V.I. Effects of rotation and acceleration in the axial current: density operator vs Wigner function. J. High Energ. Phys. 2019, 146 (2019). https://doi.org/10.1007/JHEP02(2019)146
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DOI: https://doi.org/10.1007/JHEP02(2019)146