(2) Francesco Becattini,Matteo Buzzegoli,Takafumi Niida,Shi Pu, Ai-Hong Tang,Qun Wang, Spin polarization in relativistic heavy-ion collisions, arXiv: 2402.04540, Invited Review for QGP 6.

(1) Yi-Liang Yin, Wen-Bo Dong, Jin-Yi Pang, Shi Pu, Qun Wang, The spin alignment of rho mesons in a pion gas, arXiv: 2402.03672

2023年

(9) Shi Pu, Bo-Wen Xiao, Jian Zhou, Ya-Jin Zhou, Coherent photons induced high energy reactions in ultraperipheral heavy ion collisions, Acta Phys.Sin. 72 (2023) 7, 072503, 收录专题：高能重离子碰撞过程的自旋与手征效应

We review the recent progress in the studies of coherent photons induced high energy reactions in ultraperipheral heavy ion collisions. The strong electromagnetic field created by a fast moving charged heavy ion can be effectively viewed as a flux of quasi-real coherent photons. In this paper, we mainly discuss two different type processes that coherent photons take part in: lepton pair production via photon fusion and diffractive vector meson production in UPCs. We focus on investigating the impact parameter dependent effect and the final state soft radiation effect. On the other hand, a series of recent work have revealed that coherent photons are highly linearly polarized with its polarization vector being parallel to its transverse momentum. It has been shown that the linearly polarized photons can lead to cos 4\phicos⁡4ϕazimuthal asymmetries in di-lepton production. This theoretical predication soon has been confirmed by the STAR measurement. With this new development from both theory and experiment sides, the linearly polarized photons provide a new experimental avenue to explore novel QCD phenomenology. For example, the linearly polarized photons can give rise to various different azimuthal asymmetries in diffractive vector meson production. These observables provide us unique chance to study two source interference effect in high energy scatterings, Coulomb-Nuclear interference effect as well as extracting gluon Wigner distribution. We will discuss these novel phenomenology studies and the possible future developments.

(8) Shi Pu, Xu-guang Huang, Relativistic spin hydrodynamics, Acta Phys.Sin. 72 (2023) 7, 071202  (Invited review) 收录专题：高能重离子碰撞过程的自旋与手征效应

In recent years, due to the discoveries of hyperon spin polarization and vector meson spin alignment in relativistic heavy-ion collision experiments, the spin transports in quark-gluon matter has received intensive studies. The relativistic spin hydrodynamics is one of the important theoretical frameworks to describe the spin transports, which encodes the spin degree of freedom into a hydrodynamic theory. The relativistic spin hydrodynamics have the conservation equations for energy-momentum tensor, currents and total angular momentum. In this article, we give an overview of the recent progresses of the relativistic spin hydrodynamics. We focus on the following topics: 1) The derivation of the relativistic spin hydrodynamic equations, including the phenomenological approach, the effective theory method, and the kinetic approach, 2) Some special properties of spin hydrodynamics, especially the asymmetric energy-momentum tensor and the pseudogauge transformation, and 3) The analytical solutions to the relativistic spin hydrodynamics for systems under Bjorken and Gubser expansion.

(7) Xiang-Yu Wu, Cong Yi, Guang-You Qin, Shi Pu, Global and local polarization of  Λ Λ hyperons across RHIC-BES energies, QM proceedings. 

(6) Shuo Fang, Shi Pu, Di-Lun Yang, Spin polarization and spin alignment from quantum kinetic theory with self-energy corrections, Phys.Rev.D 109 (2024) 3, 034034, arXiv: 2311.15197 

We derive the quantum kinetic theory for massive fermions with collision terms and self-energy corrections based on quantum field theory. We adopt an effective power counting scheme with ℏℏ expansion to obtain the leading-order perturbative solutions of the vector and axial Wigner functions and the corresponding kinetic equations. We observe that both the onshell relation and the structure of Wigner functions, along with the kinetic equations, are modified due to the presence of self-energies and their space-time gradients. We further apply our formalism to investigate the spin polarization phenomena in relativistic heavy ion collisions and derive the modification to the spin polarization spectrum of massive quarks. We find that the gradient of vector self-energy plays a similar role to the background electromagnetic fields, which induces a more dominant contribution than the collisional effects by a naive power counting in the gradient expansion and weak coupling. Our findings could further modify the spin polarization of strange quarks and spin alignment of ϕϕ mesons beyond local thermal equilibrium.

(5) Dong-Lin Wang, Shi Pu, Stability and causality criteria in linear mode analysis: stability means causality, Phys. Rev. D (Letter 109 (2024) 3, L031504

Causality and stability are fundamental requirements for the differential equations describing predictable relativistic many-body systems. In this work, we investigate the stability and causality criteria in linear mode analysis. We discuss the updated stability criterion in 3+1 dimensional systems and introduce the improved sufficient criterion for causality. Our findings clearly demonstrate that stability implies causality in linear mode analysis. Furthermore, based on the theorems present in this work, we conclude that if updated stability criterion and improved causality criterion are fulfilled in one inertial frame of reference (IFR), they hold for all IFR.

(4) Xin-li Sheng, Shi Pu, Qun Wang, Momentum dependence of the spin alignment of the phi meson, Phys.Rev.C 108 (2023) 5, 054902, arXiv: 2308.14038

We study the rapidity and azimuthal angle dependences of the global spin alignment ρ00 for ϕmesons with respect to the reaction plane in Au+Au collisions at RHIC by the relativistic coalescence model in the spin transport theory. The global spin alignment of ϕ mesons arises from local fluctuations of strong force fields whose values are extracted from the STAR's data. The calculated results show that ρ00<1/3 at the rapidity Y=0, and then it increases with rapidity and becomes ρ00>1/3 at Y=1. Such a rapidity dependence is dominated by the relative motion of the ϕ meson in the bulk matter. We also give prediction for the azimuthal angle dependence of ρ00 at different rapidities.

(3) Xin-Qing Xie, Dong-Lin Wang, Chen Yang, Shi Pu, Causality and stability analysis for the minimal causal spin hydrodynamics, Phys.Rev.D 108 (2023) 9, 094031, arXiv:2306.13880  

We perform the linear analysis of causality and stability for a minimal extended canonical spin hydrodynamics up to second order of the gradient expansion. The first order canonical spin hydrodynamics is proved to be acausal and unstable. To remove the unstable and acausal modes, we then formulate the minimal causal spin hydrodynamics up to second order of the gradient expansion. We derive that causality and stability conditions for this minimal causal spin hydrodynamics. Interestingly, the satisfaction of the stability condition relies on the equations of state for the spin density and chemical potentials. Moreover, different with the conventional relativistic dissipative hydrodynamics, the stability of the theory seems to be broken at the finite wave-vector when the stability conditions are fulfilled at small and large wave-vector limits. It implies that the linear stability conditions are necessary but may be insufficient.

(2) Cong Yi, Xiang-Yu Wu, Di-Lun Yang, Jian-Hua Gao, Shi Pu, Probing vortical structures in heavy-ion collisions at RHIC-BES energies through helicity polarization, Phys.Rev.C (Letter) 109, (2024)1, L011901

 

We investigate the hydrodynamic helicity polarization of Λ hyperons, defined as the projection of the spin polarization vector along the directions of particle momenta, at RHIC-BES energies by utilizing the relativistic (3+1)D CLVisc hydrodynamics framework with SMASH initial conditions. As opposed to local spin polarization at high energy collisions, our hydrodynamic simulations demonstrate that the helicity polarization induced by the kinetic vorticity dominates over other contributions at intermediate and low collision energies. Our findings provide an opportunity to probe the fine structure of local kinetic vorticity as a function of azimuthal angle at intermediate and low collision energies by mapping our predictions to the future measurements in experiments.

(1) Hao-Hao Peng, Xin-Li Sheng, Shi Pu, Qun Wang, Electric and magnetic conductivities in magnetized fermion systems, Phys.Rev.D 107 (2023) 11, 116006, arXiv: 2304.00519 

 

In Wigner function approach with relaxation time approximation, we calculate electric and magnetic conductivities of a fermion system in the strong magnetic field. The linear response has been calculated to the perturbation of electromagnetic fields on the background constant magnetic field. The Wigner function is separated into an equilibrium part in the background magnetic field and an off-equilibrium part induced by perturbative fields. The analytical expression for the equilibrium part and the corresponding equilibrium conditions are given. For the off-equilibrium part, we obtain the kinetic equation at the leading order in ħ from the master equation of the Wigner function. When perturbative fields only depend on the proper time, the off-equilibrium part can be analytically solved from which the vector and axial vector currents are obtained. We obtain the longitudinal and transverse Ohm conductivities as well as Hall conductivity as the linear response of the vector current to the perturbative electric field. The behaviors of these conductivities as functions of the evolving time, relaxation time, particle mass, and strength of the background magnetic field are investigated both analytically and numerically.

2022年

(9) Hao-Hao Peng, Sihao Wu, Ren-jie Wang, Duan She, Shi Pu, Anomalous magnetohydrodynamics with temperature-dependent electric conductivity and application to the global polarization, Phys. Rev. D 107 (2023) 9, 096010, arXiv: 2211.11286.

 

We have derived the solutions of the relativistic anomalous magnetohydrodynamics with longitudinal Bjorken boost invariance and transverse electromagnetic fields in the presence of temperature or energy density dependent electric conductivity. We consider the equations of states in a high temperature limit or in a high chiral chemical potential limit. We obtain both perturbative analytic solutions up to the order of ℏ and numerical solutions in our configurations of initial electromagnetic fields and Bjorken flow velocity. Our results show that the temperature or energy density dependent electric conductivity play an important role to the decaying of the energy density and electromagnetic fields. We also implement our results to the splitting of global polarization for Λ and`Λ hyperons induced by the magnetic fields. Our results for the splitting of global polarization disagree with the experimental data in low energy collisions, which implies that the contribution from electromagnetic fields may be insufficient to explain the global polarization of Λ and`Λ hyperons in the low energy collisions.

 

(8) Shuo Lin, Ren-Jie Wang, Jian-Fei Wang, Hao-Jie Xu, Shi Pu, Qun Wang, Photoproduction of e⁺ e^-  in peripheral isobar collisions, Phys. Rev. D 107 (2023) 5, 054004, arXiv: 2210.05106.

We investigate the photoproduction of dielectrons in peripheral collisions of Ru+Ru and Zr+Zr at 200 GeV. With the charge and mass density distributions given by the calculation of the density functional theory, we calculate the spectra of transverse momentum, invariant mass, and azimuthal angle for dielectrons at 40–80% centrality. The ratios of these spectra in Ru+Ru collisions over to Zr+Zr collisions are shown to be smaller than (44/40)⁴ (the ratio of Z⁴ for Ru and Zr) at low transverse momentum. The deviation arises from the different mass and charge density distributions in Ru and Zr. So the photoproduction of dileptons in isobar collisions may provide a new way to probe the nuclear structure.

 

(7) Shuo Fang, Shi Pu, Di-Lun Yang, Quantum kinetic theory for dynamical spin polarization from QED-type interaction, Phys. Rev. D 106 (2022) 1, 016002, arXiv: 2204.11519.

 

We investigate the dynamical spin polarization of a massless electron probing an electron plasma in locally thermal equilibrium via the Moller scattering from the quantum kinetic theory. We derive an axial kinetic equation delineating the dynamical spin evolution in the presence of the collision term with quantum corrections up to O(ℏ) and the leading-logarithmic order in coupling by using the hard-thermal-loop approximation, from which we extract the spin-polarization rate induced by the spacetime gradients of the medium. When the electron probe approaches local equilibrium, we further simplify the collision term into a relaxation-time expression. Our kinetic equation may be implemented in the future numerical simulations for dynamical spin polarization.

 

(6) Ren-jie Wang, Shuo Lin, Shi Pu, Yi-fei Zhang, Qun Wang, Lepton pair photoproduction in peripheral relativistic heavy-ion collisions, Phys. Rev. D 106 (2022) 3, 034025, arXiv:  2204.02761.

 

We study the lepton pair photoproduction in peripheral heavy-ion collisions based on the formalism in our previous work [R.-j. Wang, S. Pu, and Q. Wang, Phys. Rev. D 104, 056011 (2021)]. We present the numerical results for the distributions of the transverse momentum, azimuthal angle and invariant mass for e⁺ e^- and  μ⁺ μ^-  pairs as functions of the impact parameter and other kinematic variables in Au+Au collisions. Our calculation incorporates the information on the transverse momentum and polarization of photons which is essential to describe the experimental data. We observe a broadening effect in the transverse momentum for lepton pairs with and without smear effects. We also observe a significant enhancement in the distribution of cos(2φ) for μ⁺ μ^- pairs. Our results provide a baseline for future studies of other higher order corrections beyond Born approximation and medium effects in the lepton pair production.

 

(5) Xiang-Yu Wu, Cong Yi, Guang-You Qin, Shi Pu,  Local and global polarization of Λ hyperons across RHIC-BES energies: The roles of spin hall effect, initial condition, and baryon diffusion Phys. Rev. C 105 (2022) 6, 064909, arXiv: 2204.02218.

 

We perform a systematic study on the local and global spin polarization of Λ and Λ¯ hyperons in relativistic heavy-ion collisions at beam energy scan energies via the (3+1)-dimensional CLVisc hydrodynamics model with a multiphase transport (AMPT) and simulating many accelerated strongly interacting hadron (SMASH) initial conditions. Following the quantum kinetic theory, we decompose the polarization vector as the parts induced by thermal vorticity, shear tensor and the spin Hall effect (SHE). We find that the polarization induced by the SHE and the total polarization strongly depends on the initial conditions. At 7.7GeV, the SHE gives a sizable contribution and even flips the sign of the local polarization along the beam direction for the AMPT initial condition, which is not observed for the SMASH initial condition. Meanwhile, the local polarization along the out-of-plane direction induced by the SHE with the AMPT initial condition does not always increase with decreasing collision energies. Next, we find that the polarization along the beam direction is sensitive to the baryon diffusion coefficient, but the local polarization along the out-of-plane direction is not. Our results for the global polarization of Λ and Λ¯ agree well with the data of the STAR Collaboration. Interestingly, the global polarization of Λ¯ is not always larger than that of Λ due to various competing effects. Our findings are helpful for understanding the polarization phenomenon and the detailed structure of quark-gluon plasma in relativistic heavy-ion collisions.

(4) Patrick Copinger, Shi Pu, Berry phase in the phase space worldline representation: The axial anomaly and classical kinetic theory, Phys.Rev.D 105 (2022) 11, 116014, arXiv: 2203.00847

 

The Berry phase is analyzed for Weyl and Dirac fermions in a phase space representation of the worldline formalism. Kinetic theories are constructed for both at a classical level. Whereas the Weyl fermion case reduces in dimension, resembling a theory in quantum mechanics, the Dirac fermion case takes on a manifestly Lorentz covariant form. To achieve a classical kinetic theory for the non-Abelian Dirac fermion Berry phase a spinor construction of Barut and Zanghi is utilized. The axial anomaly is also studied at a quantum level. It is found that under an adiabatic approximation, which is necessary for facilitating a classical kinetic theory, the index of the Dirac operator for massless fermions vanishes. Even so, similarities of an axial rotation to an exact noncovariant Berry phase transform are drawn by application of the Fujikawa method to the Barut and Zanghi spinors on the worldline.

 

(3) Xin-Li Sheng, Yang Li, Shi Pu, Qun Wang, Lorentz Transformation in Maxwell Equations for Slowly Moving Media, Symmetry 14 (2022) 1641, arXiv: 2202.03122

 

We use the method of field decomposition, a widely used technique in relativistic magnetohydrodynamics, to study the small velocity approximation (SVA) of the Lorentz transformation in Maxwell equations for slowly moving media. The “deformed” Maxwell equations derived using SVA in the lab frame can be put into the conventional form of Maxwell equations in the medium’s co-moving frame. Our results show that the Lorentz transformation in the SVA of up to (v is the speed of the medium and c is the speed of light in a vacuum) is essential to derive these equations: the time and charge density must also change when transforming to a different frame, even in the SVA, not just the position and current density, as in the Galilean transformation. This marks the essential difference between the Lorentz transformation and the Galilean one. We show that the integral forms of Faraday and Ampere equations for slowly moving surfaces are consistent with Maxwell equations. We also present Faraday equation in the covariant integral form, in which the electromotive force can be defined as a Lorentz scalar that is independent of the observer’s frame. No evidence exists to support an extension or modification of Maxwell equations.

 

(2) Yoshimasa Hidaka, Shi Pu, Qun Wang, Foundations and applications of quantum kinetic theory, Prog. Part. Nucl. Phys. 127 (2022) 103989, arXiv: 2201.07644  (Invited Review)

 

Many novel quantum phenomena emerge in non-equilibrium relativistic quantum matter under extreme conditions such as strong magnetic fields and rotations. The quantum kinetic theory based on Wigner functions in quantum field theory provides a powerful and effective microscopic description of these quantum phenomena. In this article we review some of recent advances in the quantum kinetic theory and its applications in describing these quantum phenomena.

(1) Jun-Jie Zhang, Xin-Li Sheng, Shi Pu, Jian-Nan Chen, Guo-Liang Peng, Phys.Rev.Res. 4 (2022) 3, 033138, arXiv: 2201.06171

 

We have calculated the directed flow $v_{1}$ and charge-dependent directed flow $\Delta v_{1}$ for pions and protons in Au+Au collisions at $\sqrt{s_{NN}}=200$GeV by solving the coupled Boltzmann-Maxwell equations self-consistently. Our numerical results show that $v_{1}$ for pions and protons are all negative in the positive mid rapidity region and have similar behavior  and magnitude. In contrast we find a quite different behavior in $\Delta v_{1}$ for pions and protons. The difference lies in that $\Delta v_{1}$ for protons mainly comes from pressure gradients of the medium, while the dominant contribution to $\Delta v_{1}$ for pions is from electromagnetic fields. Our results indicate that the effect of the electric field will slightly exceed that of the magnetic and lead to a small negative slope of $\Delta v_{1}$ for pions.

2021年

(5) Dong-Lin Wang, Xin-Qing Xie, Shuo Fang, Shi Pu, Analytic solutions of relativistic dissipative spin hydrodynamics with radial expansion in Gubser flow, Phys.Rev.D 105 (2022) 11, 114050, arXiv: 2112.15535

 

We have derived the analytic solutions of dissipative relativistic spin hydrodynamics with Gubser expansion. Following the standard strategy of deriving the solutions in a Gubser flow, we take the Weyl rescaling and obtain the energy-momentum and angular momentum conservation equations in the space-time. We then derive the analytic solutions of spin density, spin potential and other thermodynamic in space-time and transform them back into Minkowski space-time . In the Minkowski space-time, the spin density and spin potential including the information of radial expansion decay as ∼tau and ∼tau in large limit, with being proper time and  being the characteristic length of the system, respectively. Moreover, we observe the nonvanishing spin corrections to the energy density and other dissipative terms in the Belinfante form of dissipative spin hydrodynamics. Our results can also be used as test beds for future simulations of relativistic dissipative spin hydrodynamics.

 

(4) Cong Yi, Shi Pu, Jian-Hua Gao, Di-Lun Yang, Hydrodynamic helicity polarization in relativistic heavy ion collisions, Phys.Rev.C 105 (2022) 4, 044911, arXiv: 2112.15531

 

We study helicity polarization through the (3+1) dimensional relativistic viscous hydrodynamic models at  200GeV Au+Au collisions. Similar to the local spin polarization, we consider the helicity polarization beyond global equilibrium and investigate the contributions induced by thermal vorticity, shear viscous tensor, and the fluid acceleration. We find that the local helicity polarization induced by thermal vorticity dominates over other contributions. It also implies that in the low-energy collisions, the the fluid vorticity as part of thermal vorticity may play the crucial role to the total helicity polarization. Such a finding could be useful for probing the local strength of vorticity in rotational quark gluon plasmas by measuring helicity polarization. Our simulation confirms the strict space reversal symmetry, whereas we also compare our numerical results with approximated relations derived from ideal Bjorken flow. Our studies also provide a baseline for the future investigation on local parity violation through the correlations of helicity polarization.

(3) Dong-Lin Wang, Shuo Fang, Shi Pu. Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion. Phys.Rev.D 104 (2021) 11, 114043. arXiv:2107.11726.

We have studied analytically the longitudinally boost-invariant motion of a relativistic dissipative fluid with spin. We have derived the analytic solutions of spin density and spin chemical potential as a function of proper time \tau in the presence of the viscous tensor and the second order relaxation time corrections for spin. Interestingly, analogous to the ordinary particle number density and chemical potential, we find that the spin density and spin chemical potential decay as \tau^-1 and \tau^-{1/3}, respectively. These solutions can serve both to gain insight on the dynamics of spin polarization in relativistic heavy-ion collisions and as test beds for further numerical codes.

(2) Ren-jie Wang, Shi Pu, Qun Wang. Lepton pair production in ultraperipheral collisions. Phys.Rev.D 104 (2021) 5, 056011. arXiv:2106.05462.

The lepton pair production in ultraperipheral collisions is studied in the classical field approximation. We derive a general form of the cross section in terms of photon distributions that depend on the transverse momentum and coordinate based on the wave packet form of nuclear wave functions. Such a general form of the cross section in the classical field approximation contains the results of the generalized equivalent photon approximation (EPA) as well as the corrections beyond EPA in the Born approximation. By rewriting the general form of the cross section in light-cone coordinates, we find a good connection with the transverse momentum dependent distribution factorization formalism in the Born approximation. Our numerical results are consistent with current experimental data.

(1) Cong Yi, Shi Pu, Di-Lun Yang. Reexamination of local spin polarization beyond global equilibrium in relativistic heavy ion collisions. Phys.Rev.C 104 (2021) 6, 064901. arXiv:2106.00238.

We study local spin polarization in the relativistic hydrodynamic model. Generalizing the Wigner functions previously obtained from chiral kinetic theory by Y. Hidaka et al. [Phys. Rev. D 97, 016004 (2018)] to the massive case, we present the possible contributions up to the order of hbar from thermal vorticity, shear viscous tensor, other terms associated with the temperature and chemical-potential gradients, and electromagnetic fields to the local spin polarization. We then implement the (3+1)-dimensional viscous hydrodynamic model to study the spin polarizations from these sources with a small chemical potential and ignorance of electromagnetic fields by adopting an equation of state different from those in other recent studies. Although the shear correction alone upon the local polarization results in a sign and azimuthal-angle dependence more consistent with experimental observations, as also discovered in other recent studies, it is mostly suppressed by the contributions from thermal vorticity and other terms that yield an opposite trend. It is found that the total local spin polarization can be very sensitive to the equation of states, the ratio of shear viscosity to entropy density, and the freeze-out temperature.

2020年

(7) Kenji Fukushima, Shi Pu. Spin hydrodynamics and symmetric energy-momentum tensors - A current induced by the spin vorticity -.  Phys.Lett.B 817 (2021) 136346. arXiv:2010.01608.

We discuss a puzzle in relativistic spin hydrodynamics; in the previous formulation the spin source from the antisymmetric part of the canonical energy-momentum tensor (EMT) is crucial. The Belinfante improved EMT is pseudo-gauge transformed from the canonical EMT and is usually a physically sensible choice especially when gauge fields are coupled as in magnetohydrodynamics, but the Belinfante EMT has no antisymmetric part. We find that pseudo-transformed entropy currents are physically inequivalent in nonequilibrium situations. We also identify a current induced by the spin vorticity read from the Belinfante symmetric EMT.

(6) Jianfei Wang, Shi Pu. Relativistic Kelvin Circulation Theorem for Ideal Magnetohydrodynamics. Nucl.Phys.Rev. 37 (2020) 3, 679-683. arXiv:2008.07789.

We have studied the relativistic Kelvin circulation theorem for ideal Magnetohydrodynamics. The relativistic Kelvin circulation theorem is a conservation equation for the called T-vorticity, We have briefly reviewed the ideal magnetohydrodynamics in relativistic heavy ion collisions. The highlight of this work is that we have obtained the general expression of relativistic Kelvin circulation theorem for ideal Magnetohydrodynamics. We have also applied the analytic solutions of ideal magnetohydrodynamics in Bjorken flow to check our results. Our main results can also be implemented to relativistic magnetohydrodynamics in relativistic heavy ion collisions.

(5) Patrick Copinger, Shi Pu. Chirality production with mass effects -- Schwinger pair production and the axial Ward identity. Int.J.Mod.Phys.A 35 (2020) 28, 2030015. arXiv: 2008.03635. (Invited review) 

The anomalous generation of chirality with mass effects via the axial Ward identity and its dependence on the Schwinger mechanism is reviewed, utilizing parity violating homogeneous electromagnetic background fields. The role vacuum asymptotic states play on the interpretation of expectation values is examined. It is discussed that observables calculated with an in–out scattering matrix element predict a scenario under Euclidean equilibrium. A notable ramification of which is a vanishing of the chiral anomaly. In contrast, it is discussed observables calculated under an in–in, or real-time, formalism predict a scenario out-of equilibrium, and capture effects of mean produced particle–antiparticle pairs due to the Schwinger mechanism. The out-of equilibrium chiral anomaly is supplemented with exponential quadratic mass suppression as anticipated for the Schwinger mechanism. Similar behavior in and out-of equilibrium is reviewed for applications including the chiral magnetic effect and chiral condensate.

(4) Rajesh Biswas, Ashutosh Dash, Najmul Haque, Shi Pu, Victor Roy, Causality and stability in relativistic viscous non-resistive magneto-fluid dynamics, JHEP 10 (2020) 171, arXiv: 2007.05431 [nucl-th]

We investigate the causality and the stability of the relativistic viscous non-resistive magneto-hydrodynamics in the framework of the Israel-Stewart (IS) second-order theory, and also within a modified IS theory which incorporates the effect of magnetic fields in the relaxation equations of the viscous stress. We compute the dispersion relation by perturbing the fluid variables around their equilibrium values. In the ideal magnetohydrodynamics limit, the linear dispersion relation yields the well-known propagating modes: the Alfvén and the magneto-sonic modes. In the presence of bulk viscous pressure, the causality bound is found to be independent of the magnitude of the magnetic field. The same bound also remains true, when we take the full non-linear form of the equation using the method of characteristics. In the presence of shear viscous pressure, the causality bound is independent of the magnitude of the magnetic field for the two magneto-sonic modes. The causality bound for the shear-Alfvén modes, however, depends both on the magnitude and the direction of the propagation. For modified IS theory in the presence of shear viscosity, new non-hydrodynamic modes emerge but the asymptotic causality condition is the same as that of IS. In summary, although the magnetic field does influence the wave propagation in the fluid, the study of the stability and asymptotic causality conditions in the fluid rest frame shows that the fluid remains stable and causal given that they obey certain asymptotic causality condition.

  

(3) Jian-Hua Gao, Guo-Liang Ma, Shi Pu, Qun Wang, Recent developments in chiral and spin polarization effects in heavy-ion collisions, Nucl. Sci. Tech. 31 (2020) 9, 90, arXiv: 2005.10432 [hep-ph] (Invited review) 

We give a brief overview of recent theoretical and experimental results on the chiral magnetic effect and spin polarization effect in heavy-ion collisions. We present updated experimental results for the chiral magnetic effect and related phenomena. The time evolution of the magnetic fields in different models is discussed. The newly developed quantum kinetic theory for massive fermions is reviewed. We present theoretical and experimental results for the polarization of Λ hyperons and the ρ00 value of vector mesons.

 

(2) Ren-jie Wang, Patrick Copinger, Shi Pu, Anomalous magnetohydrodynamics with constant anisotropic electric conductivities, Nucl. Phys. A 1005 (2021) 121869, arXiv: 2004.06408 [hep-ph] 

We study anomalous magnetohydrodynamics in a longitudinal boost invariant Bjorken flow with constant anisotropic electric conductivities as outlined in Ref. [I. Siddique, R.-j. Wang, S. Pu, Q. Wang, Anomalous magnetohydrodynamics with longitudinal boost invariance and chiral magnetic effect, Phys. Rev. D 99 (11) (2019) 114029. arXiv: 1904.01807, doi: 10.1103/Phys. Rev. D.99.114029.]. For simplicity, we consider a neutral fluid and a force-free magnetic field in the transverse direction. We derived analytic solutions of the electromagnetic fields in the laboratory frame, the chiral density, and the energy density as functions of proper time.

 

(1) Kenji Fukushima, Shi Pu, Relativistic decomposition of the orbital and the spin angular momentum in chiral physics and Feynman's angular momentum paradox, Lect. Notes Phys. 987 (2021) 381-396, arXiv: 2001.00359 [hep-ph] (Invited review) 

 

Over recent years we have witnessed tremendous progresses in our understanding on the angular momentum decomposition. In the context of the proton spin problem in high energy processes the angular momentum decomposition by Jaffe and Manohar, which is based on the canonical definition, and the alternative by Ji, which is based on the Belinfante improved one, have been revisited under light shed by Chen et al. leading to seminal works by Hatta, Wakamatsu, Leader, etc. In chiral physics as exemplified by the chiral vortical effect and applications to the relativistic nucleus-nucleus collisions, sometimes referred to as a relativistic extension of the Barnett and the Einstein--de Haas effects, such arguments of the angular momentum decomposition would be of crucial importance. We pay our special attention to the fermionic part in the canonical and the Belinfante conventions and discuss a difference between them, which is reminiscent of a classical example of Feynman's angular momentum paradox. We point out its possible relevance to early-time dynamics in the nucleus-nucleus collisions, resulting in excess by the electromagnetic angular momentum.