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

The present paper investigates the impact of pairing correlation on the nuclear level density (NLD) and radiative strength function (RSF) of an odd-odd and rare-earth $^{166}$Ho nucleus. By employing the exact thermal pairing (EP) solution in conjunction with both the temperature-dependent independent-particle model (EP+IPM) for the NLD and the phonon damping model (EP+PDM) for the RSF, we achieve good agreement with the experimental NLD and RSF data, which have been recently extracted by using the Oslo method. Notably, without adding any extra parameters, our calculations successfully reproduce the pygmy dipole resonances (PDR) and a portion of the strength around the region of scissor resonance (SR) in the RSF. This suggests that the SR in this nucleus may be less pronounced than that obtained in the previous analysis within the phenomenological model. These features are the consequences of the EP and the couplings of the PDM phonon to all the particle-hole (ph), particle-particle (pp), and hole-hole (hh) configurations within the EP+PDM, thus insisting on the importance of the underlying physics involved in this model. Utilizing the obtained NLD and RSF, we predict the $^{165}$Ho<math><msup><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>γ</mi><mo>)</mo></mrow><mrow><mn>166</mn></mrow></msup></math>Ho and Maxwellian-averaged cross sections, which exhibit remarkable agreement with all the available experimental data from the Experimental Nuclear Reaction Data and Karlsruhe Astrophysical Database of Nucleosynthesis in Stars. These results reflect the imprint of the pairing correlation on those quantities.

Vietnam

Le Tan Phuc

Tran Vu Dong

Nguyen Dinh Dang

Bui Minh Hue

Le Thi Quynh Huong

India

Balaram Dey

Nguyen Ngoc Anh

Nguyen Quang Hung

Imprint of pairing correlation in (n, ) and Maxwellian-averaged cross sections of an odd-odd Ho nucleus

We consider nonequilibrium evolution of non-Gaussian fluctuations within relativistic hydrodynamics relevant for the QCD critical point search in heavy-ion collision experiments. We rely on the hierarchy of relaxation timescales, which emerges in the hydrodynamic regime near the critical point, to focus on the slowest mode such as the fluctuations of specific entropy, whose equilibrium magnitude, non-Gaussianity, and typical relaxation time are increasing as the critical point is approached. We derive evolution equations for the non-Gaussian correlators of this diffusive mode in an arbitrary relativistic hydrodynamic flow. We compare with the simpler case of the stochastic diffusion on a static homogeneous background and identify terms which are specific to the case of the full hydrodynamics with pressure fluctuations and flow.

Poland

Xin An

Gökçe Başar

Mikhail Stephanov

Non-Gaussian fluctuation dynamics in relativistic fluids

Chiral anomaly implies the existence of nondissipative transport phenomena, such as the chiral magnetic effect. At second order in the derivative expansion, novel quantum transport phenomena emerge. In this paper, we focus on the anomalous transport driven by a combination of shear, vorticity, and magnetic field. We find that the corresponding transport phenomena—shear-induced chiral magnetic and chiral vortical effects—induce characteristic charge correlations among the hadrons produced in heavy ion collisions. We propose the charge asymmetry of triangular flow as a signature of the anomalous transport, and estimate the strength of the signal, as well as the background, using hydrodynamical model simulations. We find that the signal-to-background ratio for the proposed observable is favorable for experimental detection.

Matteo Buzzegoli

Dmitri E. Kharzeev

China

Yu-Chen Liu

Shuzhe Shi

Sergei A. Voloshin

Shear-induced anomalous transport and charge asymmetry of triangular flow in heavy-ion collisions

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.

Xu-Guang Huang

Matthias Kaminski

Spin relaxation rate for heavy quarks in weakly coupled QCD plasma

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

The electron capture in  $$^{163}\mathrm {Ho}$$  <math> <mrow> <msup> <mrow></mrow> <mn>163</mn> </msup> <mi>Ho</mi> </mrow> </math>   experiment (ECHo) is designed to directly measure the effective electron neutrino mass by analysing the endpoint region of the  $$^{163}\mathrm {Ho}$$  <math> <mrow> <msup> <mrow></mrow> <mn>163</mn> </msup> <mi>Ho</mi> </mrow> </math>   electron capture spectrum. We present a data reduction scheme for the analysis of high statistics data acquired with the first phase of the ECHo experiment, ECHo-1k, to reliably infer the energy of  $$^{163}\mathrm {Ho}$$  <math> <mrow> <msup> <mrow></mrow> <mn>163</mn> </msup> <mi>Ho</mi> </mrow> </math>   events and discard triggered noise or pile-up events. On a first level, the raw data is filtered purely based on the trigger time information of the acquired signals. On a second level, the time profile of each triggered event is analysed to identify the signals corresponding to a single energy deposition in the detector. We demonstrate that events not belonging to this category are discarded with an efficiency above 99.8%, with a minimal loss of  $$^{163}\mathrm {Ho}$$  <math> <mrow> <msup> <mrow></mrow> <mn>163</mn> </msup> <mi>Ho</mi> </mrow> </math>   events of about 0.7%. While the filter using the trigger time information is completely energy independent, a slight energy dependence of the filter based on the time profile is precisely characterised. This data reduction protocol will be important to minimise systematic errors in the analysis of the  $$^{163}\mathrm {Ho}$$  <math> <mrow> <msup> <mrow></mrow> <mn>163</mn> </msup> <mi>Ho</mi> </mrow> </math>   spectrum for the determination of the effective electron neutrino mass.

Germany

Robert Hammann

Arnulf Barth

Andreas Fleischmann

Dennis Schulz

Loredana Gastaldo

Data reduction for a calorimetrically measured  $$^{163}\mathrm {Ho}$$  <math> <mrow> <msup> <mrow></mrow> <mn>163</mn> </msup> <mi>Ho</mi> </mrow> </math>   spectrum of the ECHo-1k experiment

We derive a set of nontrivial relations between second-order transport coefficients which follow from the second law of thermodynamics upon considering a regime close to uniform rotation of the fluid. We demonstrate that an extension of hydrodynamics by spin variable is equivalent to modifying conventional hydrodynamics by a set of second-order terms satisfying the relations we derived. We point out that a novel contribution to the heat current orthogonal to vorticity and temperature gradient reminiscent of the thermal Hall effect is constrained by the second law.

Shiyong Li

Nondissipative Second-Order Transport, Spin, and Pseudogauge Transformations in Hydrodynamics

In the context of the search for the QCD critical point using non-Gaussian fluctuations, we obtain the evolution equations for non-Gaussian cumulants to the leading order of the systematic expansion in the magnitude of thermal fluctuations. We develop a diagrammatic technique in which the leading order contributions are given by tree diagrams. We introduce a Wigner transform for multipoint correlators and derive the evolution equations for three- and four-point Wigner functions for the problem of nonlinear stochastic diffusion with multiplicative noise.

Evolution of Non-Gaussian Hydrodynamic Fluctuations

To describe dynamics of bulk and fluctuations near the QCD critical point we develop general relativistic fluctuation formalism for a fluid carrying baryon charge. Feedback of fluctuations modifies hydrodynamic coefficients including bulk viscosity and conductivity and introduces nonlocal and noninstantaneous terms in constitutive equations. We perform necessary ultraviolet (short-distance) renormalization to obtain cutoff-independent deterministic equations suitable for numerical implementation. We use the equations to calculate the universal nonanalytic small-frequency dependence of transport coefficients due to fluctuations (long-time tails). Focusing on the critical mode we show how this general formalism matches existing <math><mtext>Hydro+</mtext></math> description of fluctuations near the QCD critical point and nontrivially extends it inside and outside of the critical region.

Fluctuation dynamics in a relativistic fluid with a critical point