arXiv subjects

Xin-Li Sheng

Publications and source records attributed to Xin-Li Sheng.

34 records · Page 2Linked to original sources

arXiv2023

Momentum dependence of $ϕ$ meson's spin alignment

We study the rapidity and azimuthal angle dependences of the global spin alignment $ρ_{00}$ for $ϕ$ mesons 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 $ρ_{00}<1/3$ at the rapidity $Y=0$, and then it increases with rapidity and becomes $ρ_{00}>1/3$ 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 $ρ_{00}$ at different rapidities.

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arXiv2023

Electric and magnetic conductivities in magnetized fermion systems

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 $\hbar$ 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.

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arXiv2023

Spin alignment of vector mesons in heavy-ion collisions

Polarized quarks and antiquarks in high-energy heavy-ion collisions can lead to the spin alignment of vector mesons formed by quark coalescence. Using the relativistic spin Boltzmann equation for vector mesons derived from Kadanoff-Baym equations with an effective quark-meson model for strong interaction and quark coalescence model for hadronizaton, we calculate the spin density matrix element $ρ_{00}$ for $ϕ$ mesons and show that anisotropies of local field correlations or fluctuations with respect to the spin quantization direction lead to $ϕ$ meson's spin alignment. We propose that the local correlation or fluctuation of $ϕ$ fields is the dominant mechanism for the observed the $ϕ$ meson's spin alignment and its strength can be extracted from experimental data as functions of collision energies. The calculated transverse momentum dependence of $ρ_{00}$ agrees with STAR's data. We further predict the azimuthal angle dependence of $ρ_{00}$ which can be tested in future experiments.

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arXiv2023

Relativistic spin dynamics for vector mesons

We propose a relativistic theory for spin density matrices of vector mesons based on Kadanoff-Baym equations in the closed-time-path formalism. The theory puts the calculation of spin observables such as the spin density matrix element $ρ_{00}$ for vector mesons on a solid ground. Within the theory we formulate $ρ_{00}$ for $ϕ$ mesons into a factorization form in separation of momentum and space-time variables. We argue that the main contribution to $ρ_{00}$ at lower energies should be from the $ϕ$ fields that can polarize the strange quark and antiquark in the same way as electromagnetic fields. The key observation is that there is correlation inside the $ϕ$ meson wave function between the $ϕ$ field that polarizes the strange quark and that polarizes the strange antiquark. This is reflected by the fact that the contributions to $ρ_{00}$ are all in squares of fields which are nonvanishing even if the fields may strongly fluctuate in space-time. The fluctuation of strong force fields can be extracted from $ρ_{00}$ of quarkonium vector mesons as links to fundamental properties of quantum chromodynamics.

hep-ph↗

arXiv2022

Lorentz-covariant kinetic theory for massive spin-1/2 particles

We construct a matrix-valued spin-dependent distribution function (MVSD) for massive spin-1/2 fermions and study its properties under Lorentz transformations. Such transformations result in a Wigner rotation in spin space and in a nontrivial matrix-valued shift in space-time, which corresponds to the side jump in the massless case. We express the vector and axial-vector components of the Wigner function in terms of the MVSD and show that they transform in a Lorentz-covariant manner. We then construct a manifestly Lorentz-covariant Boltzmann equation which contains a nonlocal collision term encoding spin-orbit coupling. Finally, we obtain the spin-dependent distribution function in local equilibrium by demanding detailed balance.

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arXiv2022

Charge-dependent directed flows in heavy-ion collisions by Boltzmann-Maxwell equations

We have calculated the directed flow $v_{1}$ and charge-dependent directed flow $Δv_{1}$ 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 $Δv_{1}$ for pions and protons. The difference lies in that $Δv_{1}$ for protons mainly comes from pressure gradients of the medium, while the dominant contribution to $Δv_{1}$ 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 $Δv_{1}$ for pions

hep-ph↗

arXiv2022

What can we learn from global spin alignment of $ϕ$ meson in heavy-ion collisions?

We propose that a significant positive deviation from 1/3 for the spin density matrix element $ρ_{00}$ of the $ϕ$ meson may indicate the existence of a mean field of the $ϕ$ meson generated in heavy-ion collisions. This explains why STAR preliminary data for the $ϕ$ meson's $ρ_{00}$ are much larger than 1/3 while the data of $Λ$ and $\barΛ$ polarization seem not to allow such a significant and positive deviation. The contribution may be from the polarization of the strange quark and antiquark through the $ϕ$ field, an effective mode of the gluon field in strong interaction. We show that $ρ_{00}$ for the $ϕ$ meson is a good analyzer for fields even if they may strongly fluctuate in space-time.

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arXiv2022

Lorentz transformation in Maxwell equations for slowly moving media

We use the method of field decomposition, a technique widely used 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 under the SVA in the lab frame can be put into the conventional form of Maxwell equations in the medium's comoving frame. Our results show that the Lorentz transformation in the SVA up to $O(v/c)$ ($v$ is the speed of the medium and $c$ is the speed of light in 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 of the Lorentz transformation from 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 the covariant integral form in which the electromotive force can be defined as a Lorentz scalar independent of the observer's frame. No evidences exist to support an extension or modification of Maxwell equations.

physics.class-ph↗

arXiv2021

Ideal spin hydrodynamics from Wigner function approach

Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Comparing with ideal hydrodynamics without spin, additional terms at first and second order in the Knudsen number $\text{Kn}$ and the average spin polarization $χ_s$ have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motions for these parameters are derived by conservation laws at the leading and next-to-leading order $\text{Kn}$ and $χ_s$.

hep-th↗

arXiv2021

Space-average electromagnetic fields and EM anomaly weighted by energy density in heavy-ion collisions

We study the space-average electromagnetic (EM) fields weighted by the energy density in the central regions of heavy ion collisions. These average quantities can serve as a barometer for the magnetic-field induced effects such as the magnetic effect, the chiral separation effect and the chiral magnetic wave. Comparing with the magnetic fields at the geometric center of the collision, the space-average fields weighted by the energy density are smaller in the early stage but damp slower in the later stage. The space average of squared fields as well as the EM anomaly $\mathbf{E}\cdot\mathbf{B}$ weighted by the energy density are also calculated. We give parameterized analytical formula for these average quantities as functions of time by fitting numerical results for collisions in the collision energy range $7.7-200$ GeV with different impact parameters.

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arXiv2021

Improved quark coalescence model for spin alignments of vector mesons

We propose an improved quark coalescence model for spin alignment of vector mesons by spin density matrix with phase space dependence. Within this model we propose an understanding of spin alignments of vector mesons $ϕ$ and $K^{*0}$ in the static limit: a large positive deviation of $ρ_{00}$ for $ϕ$ mesons from $1/3$ may come from the electric part of the vector $ϕ$ field, while a negative deviation of $ρ_{00}$ for $K^{*0}$ mesons may come from the electric part of vorticity fields. In the low-$p_T$ region, $ρ_{00}$ for $K^{*0}$ mesons is proportional to $p_T^2$, which is qualitatively agree with experimental results.

hep-ph↗

arXiv2021

Electromagnetic fields from the extended Kharzeev-McLerran-Warringa model in relativistic heavy-ion collisions

Based on the Kharzeev-McLerran-Warringa (KMW) model that estimates strong electromagnetic (EM) fields generated in relativistic heavy-ion collisions, we generalize the formulas of EM fields in the vacuum by incorporating the longitudinal position dependence, the generalized charge distributions and retardation correction. We further generalize the formulas of EM fields in the pure quark-gluon plasma (QGP) medium by incorporating a constant Ohm electric conductivity and also during the realistic early-time stages QGP evolution by using a time-dependent electric conductivity. Using the extended KMW model, we observe a slower time evolution and a more reasonable impact parameter $b$ dependence of the magnetic field strength than those from the original KMW model in the vacuum. The inclusion of medium effects by using the lattice data helps to further prolong the time evolution of magnetic field, such that the magnetic field strength during the realistic QGP evolution at thermal freeze-out time can meet the $1σ$ bound constrained from experimentally measured difference in global polarizations of $Λ$ and $\barΛ$ hyperons in Au+Au collisions at top RHIC energy. These generalized formulations in the extended KMW model will be potentially useful for many EM fields relevant studies in heavy-ion collisions, especially at lower colliding energies and for various species of colliding nuclei.

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arXiv2021

From Kadanoff--Baym to Boltzmann equations for massive spin-1/2 fermions

We derive Boltzmann equations for massive spin-1/2 fermions with local and nonlocal collision terms from the Kadanoff--Baym equation in the Schwinger--Keldysh formalism, properly accounting for the spin degrees of freedom. The Boltzmann equations are expressed in terms of matrix-valued spin distribution functions, which are the building blocks for the quasi-classical parts of the Wigner functions. Nonlocal collision terms appear at next-to-leading order in $\hbar$ and are sources for the polarization part of the matrix-valued spin distribution functions. The Boltzmann equations for the matrix-valued spin distribution functions pave the way for simulating spin-transport processes involving spin-vorticity couplings from first principles.

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arXiv2020

Improved quark coalescence model for spin alignment and polarization of hadrons

We propose an improved quark coalescence model for spin alignment of vector mesons and polarization of baryons by spin density matrix with phase space dependence. The spin density matrix is defined through Wigner functions. Within the model we propose an understanding of spin alignments of vector mesons $ϕ$ and $K^{*0}$ (including $\bar{K}^{*0}$) in the static limit: a large positive deviation of $ρ_{00}$ for $ϕ$ mesons from 1/3 may come from the electric part of the vector $ϕ$ field, while a negative deviation of $ρ_{00}$ for $K^{*0}$ may come from the electric part of vorticity tensor fields. Such a negative contribution to $ρ_{00}$ for $K^{*0}$ mesons, in comparison with the same contribution to $ρ_{00}$ for $ϕ$ mesons which is less important, is amplified by a factor of the mass ratio of strange to light quark times the ratio of $\left\langle \mathbf{p}_{b}^{2}\right\rangle $ on the wave function of $K^{*0}$ to $ϕ$ ($\mathbf{p}_{b}$ is the relative momentum of two constituent quarks of $K^{*0}$ and $ϕ$). These results should be tested by a detailed and comprehensive simulation of vorticity tensor fields and vector meson fields in heavy ion collisions.

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arXiv2020

Kinetic theory with spin: From massive to massless fermions

We find that the recently developed kinetic theories with spin for massive and massless fermions are smoothly connected. By introducing a reference-frame vector, we decompose the dipole-moment tensor into electric and magnetic dipole moments. We show that the axial-vector component of the Wigner function contains a contribution from the transverse magnetic dipole moment which accounts for the transverse spin degree of freedom (DOF) and vanishes smoothly in the massless limit. As a result, the kinetic equations, describing four DOF for massive fermions, becomes smoothly the chiral kinetic equations describing two DOF in the massless limit. We also confirm the small-mass behavior of the Wigner function by explicit calculation using a Gaussian wave packet.

hep-ph↗

arXiv2019

Wigner Function for Spin-1/2 Fermions in Electromagnetic Fields

We study the Wigner function for massive spin-1/2 fermions in electromagnetic fields. Dirac form kinetic equation and Klein-Gordon form kinetic equation are obtained for the Wigner function, which are derived from the Dirac equation. The Wigner function and its kinetic equations are expanded in terms of the generators of Clifford algebra and a complicated system of partial differential equations is obtained. We prove that some component equations are automattically satisfied if the rest ones are fulfilled. In this thesis two methods are proposed for calculating the Wigner function, which are proved to be equivalent. The Wigner function is analytically calculated following the standard second-quantization procedure in the following cases: free fermions with or without spin imbalance, in constant magnetic field, in constant electric field, and in constant parallel electromagnetic field. Strong-field effects, such as the Landau levels and Schwinger pair-production are reproduced using the Wigner function approach. For an arbitrary space-time dependent field configuration, a semi-classical expansion with respect to the reduced Planck's constant $\hbar$ is performed. We derive general expressions for the Wigner function components at linear order in $\hbar$, in which order the spin corrections start playing a role. A generalized Bargmann-Michel-Telegdi (BMT) equation and a generalized Boltzmann equation are obtained for the undetermined polarization density and net fermion number density, which can be used to construct spin-hydrodynamics in the future. We also make a comparison between analytical results and the ones from semi-classical expansion, which shows coincidence for weak electromagnetic fields and small spin imbalance.

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