<p>Recent theoretical analyses show that spin current can be induced by the baryon chemical potential gradient <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math> which becomes sizable in the fireballs created in heavy-ion collisions (HIC) at a beam energy of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>10</mn><mo>)</mo></mrow></math> GeV. This spin transport phenomenon can be considered as the cousin effect of the spin-Hall effect (SHE) in condensed matter systems with <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math> playing the role of the analogous electric field. In this letter, we study this important mechanism, which we call “baryonic SHE” or <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math>-induced polarization (<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>∇</mi><msub><mi>μ</mi><mi>B</mi></msub></mrow></math>-IP), for differential spin polarization generation that has not been systematically explored before. We predict the signature of the baryonic SHE in HIC using a <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo><mi mathvariant="normal">D</mi></mrow></math> viscous hydrodynamic model MUSIC with a multiphase transport initial condition. We propose to use the second Fourier coefficients of the net spin polarization of Λ hyperon as sensitive probes for the baryonic SHE. Those baryonic SHE observables show a qualitative difference in sign and beam energy dependence for the situations with and without the baryonic SHE. Future experimental observation of these distinct qualitative features would provide strong evidence for the existence of this “baryonic SHE” in the hot and dense quantum chromodynamics matter.</p>

China

Baochi Fu

Long-Gang Pang

Huichao Song

Yi Yin

Signatures of a baryonic spin-Hall effect in dense QCD matter

Quark-gluon plasma’s (QGP) properties at non-hydrodynamic and non-perturbative regimes remain largely unexplored. Here, we examine the response functions describing how a QGP-like plasma responds to initial energy-momentum disturbance in both static and Bjorken-expanding plasma at non-hydrodynamic gradient using the Boltzmann equation in the relaxation-time approximation (RTA). We show that the resulting response functions are remarkably similar in both static and expanding backgrounds at non-hydrodynamic gradients. While non-hydrodynamic response can not be described by the conventional first-order and second-order theories, its behavior is reasonably captured by the extended version of hydrodynamics proposed by us [1]. The potential sensitivity of the Euclidean correlator to non-hydrodynamic response is also illustrated.

Weiyao Ke

Non-hydrodynamic response in QCD-like plasma

We introduce a freeze-out procedure to convert the critical fluctuations in a droplet of quark-gluon plasma (QGP) that has, as it expanded and cooled, passed close to a posited critical point on the phase diagram into cumulants of hadron multiplicities that can subsequently be measured. The procedure connects the out-of-equilibrium critical fluctuations described in concert with the hydrodynamic evolution of the droplet of QGP by extended hydrodynamics, known as <math><mrow><mtext>Hydro</mtext><mo>+</mo></mrow></math>, with the subsequent kinetic description in terms of observable hadrons. We introduce a critical scalar isoscalar field sigma whose fluctuations cause correlations between observed hadrons due to the couplings of the sigma field to the hadrons via their masses. We match the QGP fluctuations obtained by solving the <math><mrow><mtext>Hydro</mtext><mo>+</mo></mrow></math> equations describing the evolution of critical fluctuations before freeze-out to the correlations of the sigma field. In turn, these are imprinted onto correlations and fluctuations in the multiplicity of hadrons, most importantly protons, after freeze-out via the generalization of the familiar half-century-old Cooper-Frye freeze-out prescription which we introduce. The proposed framework allows us to study the effects of critical slowing down and the consequent deviation of the observable predictions from equilibrium expectations quantitatively. We also quantify the suppression of cumulants due to conservation of baryon number. We demonstrate the procedure in practice by freezing out a <math><mrow><mtext>Hydro</mtext><mo>+</mo></mrow></math> simulation in an azimuthally symmetric and boost invariant background that includes radial flow discussed in Rajagopal et al. [Phys. Rev. D 102, 094025 (2020)].

United States

Maneesha Pradeep

Krishna Rajagopal

Mikhail Stephanov

Freezing out fluctuations in <math><mrow><mtext>Hydro</mtext><mo>+</mo></mrow></math> near the QCD critical point

In this work we aim to gain qualitative insight on the far-from-equilibrium behavior of the gluon plasma produced in the early stages of a heavy-ion collision. It was recently discovered [1] that the distribution functions of quarks and gluons in QCD effective kinetic theory (EKT) exhibit self-similar “scaling” evolution with time-dependent scaling exponents long before those exponents reach their pre-hydrodynamic fixed-point values. In this work we shed light on the origin of this time-dependent scaling phenomenon in the small-angle approximation to the Boltzmann equation. We first solve the Boltzmann equation numerically and find that time-dependent scaling is a feature of this kinetic theory, and that it captures key qualitative features of the scaling of hard gluons in QCD EKT. We then proceed to study scaling analytically and semi-analytically in this equation. We find that an appropriate momentum rescaling allows the scaling distribution to be identified as the instantaneous ground state of the operator describing the evolution of the distribution function, and the approach to the scaling function is described by the decay of the excited states. That is to say, there is a frame in which the system evolves adiabatically. Furthermore, from the conditions for adiabaticity we can derive evolution equations for the time-dependent scaling exponents. In addition to the known free-streaming and BMSS fixed points, we identify a new “dilute” fixed point when the number density becomes small before hydrodynamization. Corrections to the fixed point exponents in the small-angle approximation agree quantitatively with those found previously in QCD EKT and arise from the evolution of the ratio between hard and soft scales.

CERN

Jasmine Brewer

Bruno Scheihing-Hitschfeld

Scaling and adiabaticity in a rapidly expanding gluon plasma

The non-Gaussian fluctuations of baryon density are sensitive to the presence of the conjectured QCD critical point. Their observational consequences are crucial for the ongoing experimental search for this critical point through the beam energy scan program at Relativistic Heavy Ion Collider (RHIC). In the expanding fireball created in a heavy-ion collision, critical fluctuations would inescapably fall out of equilibrium and require a systematic description within a dynamical framework. In this paper, we employ newly developed effective field theory (EFT) for fluctuating hydrodynamics to study the real-time critical non-Gaussian fluctuations of a conserved charge density. In particular, we derive the evolution equations for multi-point correlators of density fluctuations and obtain the closed-form solutions with arbitrary initial conditions that can readily be implemented in realistic simulations for heavy-ion collisions. We find that non-linear interactions among noise fields, which are missing in traditional stochastic hydrodynamics, could potentially contribute to the quartic (fourth-order) fluctuations in the scaling regime even at tree level in off-equilibrium situations.

Noriyuki Sogabe

Off-equilibrium non-Gaussian fluctuations near the QCD critical point: an effective field theory perspective

We study the spin polarization generated by the hydrodynamic gradients. In addition to the widely studied thermal vorticity effects, we identify an undiscovered contribution from the fluid shear. This shear-induced polarization (SIP) can be viewed as the fluid analog of strain-induced polarization observed in elastic and nematic materials. We obtain the explicit expression for SIP using the quantum kinetic equation and linear response theory. Based on a realistic hydrodynamic model, we compute the differential spin polarization along both the beam direction <math><mover><mi>z</mi><mo>^</mo></mover></math> and the out-plane direction <math><mover><mi>y</mi><mo>^</mo></mover></math> in noncentral heavy-ion collisions at <math><mrow><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>, including both SIP and thermal vorticity effects. We find that SIP contribution always shows the same azimuthal angle dependence as experimental data and competes with thermal vorticity effects. In the scenario that <math><mi>Λ</mi></math> inherits and memorizes the spin polarization of a strange quark, SIP wins the competition, and the resulting azimuthal angle dependent spin polarization <math><msub><mi>P</mi><mi>y</mi></msub></math> and <math><msub><mi>P</mi><mi>z</mi></msub></math> agree qualitatively with the experimental data.

Shuai Y. F. Liu

Longgang Pang

Shear-Induced Spin Polarization in Heavy-Ion Collisions

We analyze the combined effects of hydrodynamic fluctuations and chiral magnetic effect (CME) for a chiral medium in the presence of a background magnetic field. Based on the recently developed non-equilibrium effective field theory, we show fluctuations give rise to a CME-related positive contribution to magnetoresistance, while the early studies without accounting for the fluctuations find a CME-related negative magnetoresistance. At zero axial relaxation rate, the fluctuations contribute to the transverse conductivity in addition to the longitudinal one.

Japan

Naoki Yamamoto

Positive magnetoresistance induced by hydrodynamic fluctuations in chiral media

We propose a new scenario characterizing the transition of the quark–gluon plasma (QGP) produced in heavy-ion collisions from a highly non-equilibrium state at early times toward a fluid described by hydrodynamics at late times. We develop an analogy to the evolution of a quantum mechanical system that is governed by the instantaneous ground states. In the simplest case, these slow modes are “pre-hydrodynamic” in the sense that they are initially distinct from, but evolve continuously into, hydrodynamic modes. For a class of collision integrals, the pre-hydrodynamic mode represents the angular distribution (in momentum space) of those gluons that carry most of the energy. We illustrate this scenario using a kinetic description of weakly-coupled Bjorken expanding plasma. Rapid longitudinal expansion drives a reduction in the degrees of freedom at early times. In the relaxation time approximation for the collision integral, we show quantitatively that the full kinetic theory evolution is dominated by the pre-hydrodynamic mode. We elaborate on the criterion for the dominance of pre-hydrodynamic slow modes and speculate that adiabatic hydrodynamization may describe the pre-equilibrium behavior of the QGP produced in heavy-ion collisions.

Li Yan

Adiabatic hydrodynamization in rapidly-expanding quark–gluon plasma

We systematically analyze the effects of the derivatives of the hydrodynamic fields on axial Wigner function that describes the spin polarization vector in phase space. We have included all possible first-order derivative contributions that are allowed by symmetry and compute the associated transport functions at one-loop using the linear response theory. In addition to reproducing known effects due to the temperature gradient and vorticity, we have identified a number of potentially significant contributions that are overlooked previously. In particular, we find that the shear strength, the symmetric and traceless part of the flow gradient, will induce a quadrupole for spin polarization in the phase space. Our results, together with hydrodynamic gradients obtained from hydrodynamic simulations, can be employed as a basis for the interpretation of the Λ (anti-Λ) spin polarization measurement in heavy-ion collisions.

Shuai Liu

Spin polarization induced by the hydrodynamic gradients

Upcoming experimental programs, including the Beam Energy Scan at RHIC, will look for signatures of a possible critical point in the QCD phase diagram in fluctuation observables. To understand and predict these signatures, one must account for the fact that the dynamics of any critical fluctuations must be out-of-equilibrium: because of critical slowing down, the fluctuations cannot stay in equilibrium as the droplet of quark gluon plasma produced in a collision expands and cools. Furthermore, their out-of-equilibrium dynamics must also influence the hydrodynamic evolution of the cooling droplet. The recently developed Hydro+ formalism allows for a consistent description of both the hydrodynamics and the out-of-equilibrium fluctuations, including the feedback between them. We shall provide an explicit demonstration of how this works, setting up a Hydro+ simulation in a simplified setting: a rapidity-independent fireball undergoing radial flow with an equation of state in which we imagine a critical point close to the <math><msub><mi>μ</mi><mi>B</mi></msub><mo>=</mo><mn>0</mn></math> axis of the phase diagram. Within this setup, we show that we can quantitatively capture nonequilibrium phenomena, including critical fluctuations over a range of scales and memory effects. Furthermore, we illustrate the interplay between the dynamics of the fluctuations and the hydrodynamic flow of the fireball: as the fluid cools and flows, the dynamical fluctuations lag relative to how they would evolve if they stayed in equilibrium; there is then a backreaction on the flow itself due to the out-of-equilibrium fluctuations; and, in addition, the radial flow transports fluctuations outwards by advection. Within our model, we find that the backreaction from the out-of-equilibrium fluctuations does not yield dramatically large effects in the hydrodynamic variables. Further work will be needed in order to check this quantitative conclusion in other settings but, if it persists, this will considerably simplify future modeling.