We study the relaxation dynamics of the spin polarization of baryons (nucleon and <math><mi>Λ</mi></math> baryon), in a thermal pion gas as a simple model of the hadronic phase of the QCD plasma produced in relativistic heavy-ion collisions. For this purpose, we formulate the quantum kinetic theory for the spin density matrix of baryons in the leading order of the gradient expansion. Considering the baryon-pion elastic scattering processes as the dominant interaction between baryons and thermal pions, we compute the spin relaxation rate of nucleons and <math><mi>Λ</mi></math> baryons in a pion gas up to temperature 200 MeV. In the case of nucleons, we evaluate the spin relaxation rate in the <math><mi>s</mi></math>-channel resonance approximation, based on the known experimental data on <math><mi>Δ</mi></math> resonances. We also estimate the spin relaxation rate for <math><mi>Λ</mi></math> baryons, based on experimental inputs and theoretical models for the low-energy <math><mrow><mi>Λ</mi><mi>π</mi></mrow></math> scattering, including the chiral perturbation theory.

Japan

Yoshimasa Hidaka

Masaru Hongo

United States

Mikhail A. Stephanov

Ho-Ung Yee

Spin relaxation rate for baryons in a thermal pion gas

We compute the relaxation rate of the spin density of heavy quarks in a perturbative QCD plasma to leading-log order in the coupling constant g. The spin relaxation rate Γ s  in spin hydrodynamics is shown to be Γ s  ~ g 4 log(1/g)T(T/M)2 in the heavy-quark limit T/M ≪ 1, which is smaller than the relaxation rate of other non- hydrodynamic modes by additional powers of T/M. We demonstrate three different methods to evaluate the spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamic regime, 2) the spin density correlation function in the strict hydrodynamic limit, and 3) quantum kinetic theory of the spin distribution function in momentum space. We highlight the interesting differences between these methods, while they are ultimately connected to each other by the underlying Ward-Takahashi identity for the non-conserved spin density.

China

Xu-Guang Huang

Matthias Kaminski

Mikhail Stephanov

Spin relaxation rate for heavy quarks in weakly coupled QCD plasma

Abstract We develop a relativistic (quasi-)hydrodynamic framework, dubbed gyrohydrodynamics, to describe the fluid dynamics of many-body systems with spin under strong vorticity based on entropy-current analysis. This framework generalizes the recently developed spin hydrodynamics to the regime where the spin density is at the leading order in derivatives but suppressed by another small parameter, the Planck constant ℏ, due to its quantum nature. Our analysis shows that the complete first-order constitutive relations of gyrohydrodynamics involve 17 transport coefficients and are highly anisotropic.

Zheng Cao

Koichi Hattori

Hidetoshi Taya

Gyrohydrodynamics: Relativistic spinful fluid with strong vorticity

Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.

Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation

We develop the effective field theory of diffusive Nambu-Goldstone (NG) modes associated with spontaneous internal symmetry breaking taking place in nonequilibrium open systems. The effective Lagrangian describing semiclassical dynamics of the NG modes is derived and matching conditions for low-energy coefficients are also investigated. Due to new terms peculiar to open systems, the associated NG modes show diffusive gapless behaviors in contrast to the propagating NG mode in closed systems. We demonstrate two typical situations relevant to the condensed matter physics and high-energy physics, where diffusive type-A or type-B NG modes appear.

Suro Kim

Toshifumi Noumi

United Kingdom

Atsuhisa Ota

Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems

We provide a statistical mechanical derivation of relativistic magnetohydrodynamics on the basis of (3 + 1)-dimensional quantum electrodynamics; the system endowed with a magnetic one-form symmetry. The conservation laws and constitutive relations are presented in a manifestly covariant way with respect to the general coordinate transformation. The method of the local Gibbs ensemble (or nonequilibrium statistical operator) combined with the path-integral formula for a thermodynamic functional enables us to obtain exact forms of constitutive relations. Applying the derivative expansion to exact formulas, we derive the first-order constitutive relations for nonlinear relativistic magnetohydrodynamics. Our results for the QED plasma preserving parity and charge-conjugation symmetries are equipped with two electrical resistivities and five (three bulk and two shear) viscosities. We also show that those transport coefficients satisfy the Onsager’s reciprocal relation and a set of inequalities, indicating semi-positivity of the entropy production rate consistent with the local second law of thermodynamics.

Revisiting relativistic magnetohydrodynamics from quantum electrodynamics

We derive relativistic hydrodynamic equations with a dynamical spin degree of freedom on the basis of an entropy-current analysis. The first and second laws of local thermodynamics constrain possible structures of the constitutive relations including a spin current and the antisymmetric part of the (canonical) energy-momentum tensor. Solving the obtained hydrodynamic equations within the linear-mode analysis, we find spin-diffusion modes, indicating that spin density is damped out after a characteristic time scale controlled by transport coefficients introduced in the antisymmetric part of the energy-momentum tensor in the entropy-current analysis. This is a consequence of mutual convertibility between spin and orbital angular momentum.

Mamoru Matsuo

Fate of spin polarization in a relativistic fluid: An entropy-current analysis

We develop the effective field theoretical (EFT) approach to time-translational symmetry breaking of nonequilibrium open systems based on the Schwinger-Keldysh formalism. In the Schwinger-Keldysh formalism, all the symmetries of the microscopic Lagrangian are doubled essentially because the dynamical fields are doubled to describe the time-evolution along the closed-time-path. The effective Lagrangian for open systems are then obtained by coarse-graining the microscopic Schwinger-Keldysh Lagrangian. As a consequence of coarse-graining procedure, there appear the noise and dissipation effects, which explicitly break the doubled time-translational symmetries into a diagonal one. We therefore need to incorporate this symmetry structure to construct the EFT for Nambu-Goldstone bosons in symmetry broken phases of open systems. Based on this observation together with the consistency of the Schwinger-Keldysh action, we construct and study the general EFT for time-translational symmetry breaking in particular, having in mind applications to synchronization, time crystal, and cosmic inflation.

Netherlands

Effective field theory of time-translational symmetry breaking in nonequilibrium open system

We investigate the phase structure of the compactified 2-dimensional nonlinear SU(3)/U(1)2 flag sigma model with respect to two θ-terms. Based on the circle compactification with the ℤ3-twisted boundary condition, which preserves an ’t Hooft anomaly of the original uncompactified theory, we perform the semiclassical analysis based on the dilute instanton gas approximation (DIGA). We clarify classical vacua of the theory and derive fractional instanton solutions connecting these vacua. The resulting phase structure based on DIGA exhibits the quantum phase transitions and triple degeneracy at special points in the (θ 1, θ 2)-plane, which is consistent with the phase diagram obtained from the anomaly matching and global inconsistency conditions. This result indicates the adiabatic continuity between the flag sigma models on ℝ2 and ℝ × S 1 with small compactification radius. We further estimate contributions from instanton-anti-instanton configuration (bion) and show the existence of the imaginary ambiguity, which is expected to be cancelled by that of the perturbative Borel resummation.

Tatsuhiro Misumi

Yuya Tanizaki

Phase structure of the twisted SU(3)/U(1)2 flag sigma model on ℝ × S 1

In QCD matter under an external magnetic field, the chiral magnetic effect (CME) leads to the collective gapless mode called the chiral magnetic wave (CMW). Since dynamic universality class generally depends on low-energy gapless modes, it is nontrivial whether the CME and the resulting CMW change that of the second-order chiral phase transition in QCD. To address this question, we study the critical dynamics near the chiral phase transition in massless two-flavor QCD under an external magnetic field. By performing the dynamic renormalization-group analysis within the ϵ expansion, we find that the presence of the CME changes the dynamic universality class to that of model A. We also show that the transport coefficient of the CME is not renormalized by the critical fluctuations of the order parameter.