Welcome

• Yi Yin (Institute of modern physics, Chinese Academy of Sciencessti)

Mixing, moats and modulations in dense QCD matter

• Fabian Rennecke (Justus Liebig University Giessen)

nteractions in the hot and dense QCD medium give rise to extensive mixing between hadronic and gluonic degrees of freedom. The resulting mass matrix is non-Hermitian, which can lead to moat regimes with spatial modulations and instabilities towards inhomogeneous phases. I will discuss the underlying physics, implications for the QCD phase diagram and experimental opportunities.

Perturbatively Confined Phase of QCD under Imaginary Rotation

• Kenji Fukushima (The University of Tokyo)

In this talk, I will report our recent achievements based on refs. [1,2]. Below are highlights from our results. **Perturbative Confinement under Imaginary Rotation** We perturbatively calculated the Polyakov loop potential at high $T$ with *imaginary* angular velocity. Under the rapid imaginary rotation, the potential favors zero Polyakov loop, i.e. confinement. In ref. [1], we found a phase transition to confinement around $\omega/T=i\pi/2$. Furthermore, we argued that this perturbatively confined phase can be smoothly connected to the hadronic phase. **Chiral Symmetry Breaking** In ref. [2], we introduced fermions and investigated the chiral phase transition. Our results show the spontaneous breaking of chiral symmetry in our previously found confined phase with imaginary angular velocity for any high $T$. **Inhomogeneity** In ref. [2], we also showed that the Polyakov loop potential exhibits an inhomogeneous distribution of the Polyakov loop. There should appear a spatial interface separating the confined phase and the deconfined phase in imaginary rotating systems. Although the analytical continuation to real rotation has some subtle points, the inhomogeneity can presumably persist in real rotating systems. [1] S. Chen, K. Fukushima, and Y. Shimada, Phys.Rev.Lett. 129 (2022) [2] S. Chen, K. Fukushima, and Y. Shimada, arXiv:2404.00965

Microscopic Encoding of Macroscopic Universality: Scaling properties of Dirac Eigenspectra near QCD Chiral Phase Transition

• Wei-Ping Huang

The core goal of heavy-ion collision experiments is to shed light on how the phases and properties of strong-interaction matter arise from the fundamental constituents and interactions of QCD. But even if macroscopic critical behaviors are finally established in experiments, how do they arise from the microscopic degrees of freedom, the quarks and gluons, remains to be solved. In this talk we will answer this question. We establish a connection between the cumulants of the chiral order parameter, i.e. the chiral condensate, and the correlations among the energy levels of quarks in the background of gluons, i.e. the eigenspectra of the massless QCD Dirac operator [1]. This relation elucidates how the fluctuations of the chiral condensate arise from the correlations within the infrared part of the energy spectra of quarks, and naturally leads to generalizations of the Banks–Casher relation for the cumulants of the chiral condensate. Then, through (2+1)-flavor lattice QCD calculations with varying light quark masses near the QCD chiral transition, we demonstrate the correlations among the infrared part of the Dirac eigenvalue spectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate [1]. Our study reveals how the hidden scaling features at the microscale give rise to the macroscopic universal properties of QCD. Furthermore, for higher temperatures away from the critical window we see dilute instanton gas picture goes from breakdown to restoration by investigating the correlation among Dirac eigenvalues at physical point [2], where a non-trivial region appears. **Reference:** [1] H.-T. Ding, W.-P. Huang, S. Mukherjee, and P. Petreczky, Phys. Rev. Lett. 131, 161903 (2023) [2] H.-T. Ding, W.-P. Huang, Y. Zhang, et al., work in progress.

Finite temperature QCD phase transition with 3 flavors of Mobius domain wall fermions

• Yu Zhang

We present an update on the study of the finite temperature QCD phase transition at zero baryon chemical potential with 3 degenerate flavors of Mobius domain wall fermions. The simulation is performed on lattice extent $N_t=12$ with lattice spacing $a=0.1361(20)$ fm, corresponding to temperature around 121(2) MeV. We investigate a range of quark masses and two different volumes with aspect ratios $N_{s}/N_{t}=2,3$. By analying the renormalzied chiral condensate, susceptibility and binder cumulant, we found the rapid transition at $m_q^{\mathrm{\overline {MS}}}(2\, \mathrm{GeV}) \simeq 3-4 \, \mathrm{MeV}$ for T=121(2) MeV is in the broad crossover transition region. Besides that, we will discuss the residual chiral symmetry breaking effect on chiral condensate and chiral susceptibilities between $L_s=16$ and 32.

Exploration of the Phase Diagram of (2+1)-Flavor QCD through the Study of Fluctuations of Conserved Charges with Domain Wall fermions

• Jishnu Goswami (RIKEN Center for Computational Science)

In this presentation, we explore the phase diagram of (2+1)-flavor Quantum Chromodynamics (QCD) through the study of fluctuations of conserved charges using Domain Wall Fermions (DWF). DWF are known for their better control over chiral symmetry, closely matching the symmetries of continuum QCD. This implies that studies of QCD phase transitions using DWF fall within the same universality class as those in continuum QCD, making DWF a natural choice for studying QCD phase transitions at finite temperature, chemical potential, and quark masses. We will present our ongoing calculations of chiral observables, quark number susceptibilities, and conserved charge fluctuations for two pion masses, approximately 220 MeV and 135 MeV, using Mobius Domain Wall fermions for aspect ratios of lattices $LT=2$ and $LT=3$, respectively. We will demonstrate that the second-order conserved charge fluctuations, while following expected features obtained using staggered fermion discretization schemes, can differ quantitatively at lower temperatures. Furthermore, we argue that these differences, particularly for the second-order electric charge fluctuations, are a consequence of the pion spectrum distortion in the staggered fermion formalism. We will also present the first calculations of the kurtosis ratio of electric charge cumulants as well as various fourth-order cumulants calculated using Mobius Domain Wall fermions.

Critical dynamics of phase transition in the QCD phase diagram within the real-time fRG approach

• Yong-rui Chen (Dalian University of Technology)

The Schwinger-Keldysh functional renormalization group (fRG) is employed to investigate critical dynamics of Model A and Model H that is related to second-order phase transition in the QCD phase diagram. The purely dissipative relaxation of a non-conserved field is described in Model A. The effective action of model A is expanded to the order of $O(\partial^2)$ in the derivative expansion for the $O(N)$ symmetry. A conserved order parameter coupled to transverse momentum density is contained in Model H which describes the gas-liquid and binary-fluid transitions. According to the dynamic scaling analysis, Model H and QCD critical end point belong to the same dynamic universality class in the critical region. The higher-order correction of the transport coefficient $\bar\lambda$ and shear viscosity $\bar\eta$ coming from the mode-couplings contribution are obtained by calculating the two-point correlation functions. Finally, the dynamical critical exponent $z$ are obtained as a function of the spatial dimension $d$.

Experimental Study of QCD Phase Structure at RHIC Beam Energy Scan

• Xiaofeng Luo

The shear viscosity of parton matter under two-body scatterings

• Zi-Wei Lin (East Carolina University)

The shear viscosity $\eta$ of a quark-gluon plasma in equilibrium can be calculated numerically using the Green-Kubo relation or analytically using several methods, including the Israel-Stewart, Navier-Stokes, relaxation time approximation, and Chapman-Enskog methods. In this study [1], we first examine these analytical methods for two-body isotropic and anisotropic scatterings and confirm that the Chapman-Enskog method is the most accurate as it agrees best with the Green-Kubo numerical results. We then apply the Chapman-Enskog method to study the shear viscosity of the parton matter in the center cell of Au+Au collisions at 200AGeV and Pb+Pb collisions at 2.76ATeV from a multi-phase transport (AMPT) model. At the parton scattering cross section of 3 mb that enables the transport model to reproduce bulk observables including the elliptic flow, the average eta/s of the parton matter is found to be very small, between one to three times 1/(4$\pi$). We further find that as a result of using a constant Debye mass or cross section for parton scatterings, the $\eta/s$ ratio from the AMPT model increases with time (as the effective temperature decreases), contrary to the pQCD results that use temperature-dependent Debye masses [2]. This is one direction to improve the AMPT model. Here we also plan to show some results on extending the analytical calculation of shear viscosity to a parton matter that consists of multiple parton species under their corresponding temperature-dependent pQCD cross sections. They will lay the foundation for directly linking the parton cross sections in the model to the actual/extracted QCD shear viscosity. [1] N. MacKay and Z.W. Lin. Eur. Phys. J. C 82, 918 (2022). [2] P.B. Arnold, G.D. Moore, and L.G. Yaffe, JHEP 11, 001 (2000); JHEP 05, 051 (2003).

Carving out the landscape of relativistic transport

• Michal P. Heller (Max Planck Institute for Gravitational Physics (Albert Einstein Institute))

I will discuss constraints posed by relativistic causality on transport properties of quantum field theories when stochastic fluctuations can be ignored. Based on 2212.07434 and 2305.07703

Polarization and Spin Alignment in Heavy-Ion Collisions

• Shinichi Esumi (University of Tsukuba (JP))

QCD topology with extreme electromagnetic fields

• José Javier Hernández Hernández (University of Bielefeld)

We present the first non-perturbative determination of the magnetic field dependence of the QCD topological susceptibility for temperatures in the crossover region from Lattice QCD. At low temperatures we observe that the sum rule that relates the magnetic field dependence of the susceptibility and the chiral condensate is maintained well beyond the weak magnetic field limit. Furthermore we will also discuss our recent progress regarding the non-perturbative determination of the QCD contributions to the axion-photon coupling.

Baryon electric charge correlation as a magnetometer of QCD

• Jin-Biao Gu (Central China Normal University)

We present the first lattice QCD results of quadratic fluctuations and correlations of conserved charges in (2+1)-flavor lattice QCD in the presence of a background magnetic field. The simulations were performed using the Highly Improved Staggered Quarks with physical pion mass $m_\pi$ = 135 MeV on $N_\tau=8$ and 12 lattices. We find that the correlation between net baryon number and electric charge, denoted as $\chi^{\rm BQ}_{11} $, can serve as a magnetometer of QCD. At pseudocritical temperatures the $\chi^{\rm BQ}_{11}$ starts to increase rapidly with magnetic field strength $eB \gtrsim 2M^2_{\pi}$ and by a factor 2 at $eB\simeq 8 M^2_{\pi}$. By comparing with the hadron resonance gas model, we find that the $eB$ dependence of $\chi^{\rm BQ}_{11}$ is mainly due to the doubly charged $\Delta$(1232) baryon. Although the doubly charged $\Delta$(1232) could not be detected experimentally, its decay products, protons and pions, retain the $eB$ dependence of $\Delta$(1232)’s contribution to $\chi^{\rm BQ}_{11}$. Furthermore, the ratio of electric charge chemical potential to baryon chemical potential, $\mu_{\rm Q}/\mu_{\rm B}$, shows significant dependence on the magnetic field strength and varies with the ratio of electric charge to baryon number in the colliding nuclei in heavy ion collisions. These results provide baselines for effective theory and model studies, and both $\chi^{\rm BQ}_{11}$ and $\mu_{\rm Q}/\mu_{\rm B}$ could be useful probes for the detection of magnetic fields in relativistic heavy ion collision experiments as compared with corresponding results from the hadron resonance gas model.

Yang-Lee Edge singularity and the analytical structure of QCD phase diagram

• Vladimir Skokov

Charm degrees of freedom in the vicinity of $T_{pc}$ from lattice QCD

• Sipaz Sharma

We study the nature of charm degrees of freedom in hot strong interaction matter by performing lattice QCD calculations of the second and fourth-order cumulants of charm fluctuations, and their correlations with net baryon number, electric charge and strangeness fluctuations. We show that below the chiral crossover temperature, the thermodynamics of charm can be very well understood in terms of charmed hadrons. Above the chiral transition charm quarks show up as new degrees of freedom contributing to the partial charm pressure. However, up to temperatures as high as 175 MeV charmed hadron-like excitations provide a significant contribution to the partial charm pressure.

Quantum critical point from competition between Dirac Kondo effect and chiral symmetry breaking

• Koichi Hattori (Zhejiang University)

We discuss the QCD phase diagram in strong magnetic fields, where the chiral condensate is enhanced by the magnetic catalysis mechanism. In contrast to the conventional discussions, we include heavy-quark impurities that have been known to induce the Kondo effect. We propose a quantum critical point that arises as a consequence of the Kondo effect and the chiral symmetry breaking. Our phase diagram is obtained from a self-consistent determination of the magnitudes of the chiral condensate and the Kondo condensate, which is a particle pairing composed of conducting Dirac fermions and localized impurities. We also discuss finite-temperature effects and implications for condensed matter physics including bilayer graphene. Koichi Hattori, Daiki Suenaga, Kei Suzuki, Shigehiro Yasui, "Dirac Kondo effect under magnetic catalysis," Phys.Rev.B 108 (2023) 24, 245110. 2211.16150 [hep-ph]

Exploring Dense QCD through Hamiltonian Lattice Simulations　in (1+1) Dimensions

• Kentaro Nishimura

We study one-flavor $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ lattice QCD in ($1+1$) dimensions at zero temperature and finite density using matrix product states and the density matrix renormalization group. We compute physical observables such as the equation of state, chiral condensate, and quark distribution function as functions of the baryon number density. As a physical implication, we discuss the inhomogeneous phase at nonzero baryon density, where the chiral condensate is inhomogeneous, and baryons form a crystal. We also discuss how the dynamical degrees of freedom change from hadrons to quarks through the formation of quark Fermi seas.

Baryonic Vortex and Magnetic Field Generation

• Zebin Qiu (Keio University)

We propose a vortex carrying baryon number in low energy dense QCD with finite baryon and isospin chemical potentials. The isospin chemical potential is responsible for the charged pion condensate, among which Abrikosov vortex could arise with quantized magnetic flux. Our discovery is that when the winding of neutral pion is added, such a vortex carries a baryon number conserved by the homotopy of Skyrmion. Then the energy is reduced by a finite baryon chemical potential through the gauged Wess-Zumino-Witten term. As a result, we reveal a baryonic vortex state above critical baryon density featuring energy lower than homogeneous pion condensates. Our vortex bears a self-generated magnetic field, which indicates applicable scenarios for Magnetar cores.

Thermalization of the Wigner function — a real time, non-perturbative quantum simulation based on the Schwinger Model

• Shile Chen

Thermalization of the quark gluon plasma (QGP) created in relativistic heavy-ion collisions is a crucial theoretical question in understanding the onset of hydrodynamics, and in a broad sense, a key step to the exploration of thermalization in quantum systems. Addressing this problem theoretically, in a first principle manner, requires a real-time, non-perturbative method. To this end, we carry out a fully quantum simulation on a classical hardware, of a massive Schwinger model, which well mimics QCD as it shares the important properties such as confinement and chiral symmetry breaking. We focus on the real-time evolution of the Wigner function, namely, the two-point correlation function, which approximates quark momentum distribution, etc. Starting from a non-equilibrium initial state, the real time evolution of the Wigner functions, as well as the entanglement entropy, both demonstrate that thermalization of the quantum system is approachable. In particular, relaxation to the thermalized state depends on coupling strength, in the presence of quantum fluctuations. We also study the connection of the Wigner function thermalization to the well-known Eigenstate Thermalization.

Probing dense QCD matter with neutron stars

• Sophia Han

A quarkyonic matter model

• Toru Kojo (Tohoku University)

Pressure and speed of sound in two-flavor color-superconducting quark matter at next-to-leading order

• Andreas Geissel (TU Darmstadt)

We investigate the thermodynamic properties of color-superconducting two-flavor quark matter at high densities and zero temperature at next-to-leading order (NLO) in the strong coupling and the gap. Assuming that the ground state of dense quark matter is a color superconductor, we calculate the pressure and the speed of sound for two massless quark flavors. Our results show that the NLO correction is comparable to the leading-order effects of the gap. In particular, we find that gap-induced corrections become increasingly relevant for both the pressure and the speed of sound. Finally, we provide a parameterization of the speed of sound and discuss generalizations of our results to three-flavor quark matter relevant to neutron stars.

Discussion

Chiral Effects and Astrophysics

• Naoki Yamamoto

Chiral Kinetic Theory in Curved Space Revisited and Radiative Corrections

• Shu Lin

It is usually believed that physics in off-equilibrium state can be equivalently studied using equilibrium state with suitable metric perturbation. We point out it is not the case for spin polarization phenomena: the exisiting chiral kinetic theory in curved space fails to recover all the couplings between spin and hydrodynamic gradients [1]. We present a new form of chiral kinetic theory in curved space, in which the equivalence is established [2]. The equivalence allows us to formulate spin polarization in hydrodynamic medium as a scattering problem, which is then studied using in-medium form factors [3,4]. We find radiative corrections to all couplings between spin and hydrodynamic gradients. Implications for local spin polarization of Lambda hyperon will be discussed. [1] Y.-C. Liu, L.-L. Gao, K. Mameda and X.-G. Huang, Phys.Rev.D 99 (2019) 8, 085014 [2] J. Tian and S. Lin, to appear [3] S. Lin and J. Tian, Acta Phys.Sin. 72 (2023) 7, 071201 [4] S. Lin and J. Tian, Eur.Phys.J.Plus 139 (2024) 2, 109

A novel quark pairing in sQGP induced by the non-Abelian feature of the interaction

• Fei Gao (Beijing Institute of Technology)

In this talk I will show you our recent results on the quark pairing gap in sQGP by solving the coupled Dyson-Schwinger equations for quark propagator and quark gluon vertex in the Nambu-Gorkov basis which is widely applied to study the color superconductivity. We acquire a quark pairing gap in chiral limit above the chiral phase transition temperature $T_c$. The gap persists up to $2-3\,T_c$ and vanishes at higher temperature. Such a quark pairing characterizes the strongly coupled quark gluon plasma phase as a new phase and distinct from the phase with quasi quarks and gluons.

Mass spectra of neutral mesons (K0, π0, η, η’) and the related QCD phase transitions under strong magnetic fields

• mao shijun (Xi'an Jiaotong University)

Mass spectra of light mesons (K0, π0, η, η’) under external magnetic fields are investigated in temperature-baryon chemical potential plane by using quark model. We observe that there appear mass jumps for mesons at their Mott transitions, which are induced by the Landau levels of their constituent quarks. The critical temperature of the Mott transition shows different behaviors, which first decreases and then increases with magnetic fields for π0 meson, decreases monotonically for K0 meson, but increases monotonically for η meson. We will also discuss the chiral symmetry restoration and UA(1) symmetry restoration phase transition in terms of mesons.

Gauge invariance and thermodynamic stability of rotating magnetized systems

• Kazuya Mameda (Tokyo University of Science)

In this presentation, I revisit the Dirac theory under an external magnetic field and rotation. Motivated by experimental observations of significant vorticities in heavy ion collisions, there has been active exploration into the thermodynamics of rotating QCD matter. While the pure rotational effect has received attention, the interplay between rotation and magnetic fields remains insufficiently elucidated. In this talk, I address two significant issues present in previous formulations of rotating magnetized systems: gauge invariance and thermodynamic stability. I demonstrate that resolving both issues necessitates considering the kinetic angular momentum coupled with angular momentum. The reformulated Dirac theory presented here reproduces a well-known charged density first discovered by Hattori and Yin. Moreover, it indicates that higher-order contributions of angular velocity do not affect the charge density, providing evidence of its anomalous nature. Lastly, I offer insights into the rotational response of QCD vacuum from the perspective of the Savvidy vacuum.

Towards a “bottom-up” construction of qunatum kinetic theory with spin

• Zonglin Mo

Quantum Kinetic Theory (QKT) is a versatile tool for studying quantum effects in various many-body systems, including Quark-Gluon Plasma in a weakly coupled regime. Such a theory is commonly obtained from a "top-down" approach, starting from a microscopic theory and deriving the equation of motion for the distribution function. In this talk, we propose a "bottom-up" effective theory approach to formulate kinetic theory with spin. The low-energy effective degrees of freedom in SKT are identified as the spin averaged and spin-dependent distribution function. In the spirit of effective theory, the kinetic theory includes the equation of motion for those distribution functions as well as the constitutive relation connection them to observables. We compare the resulting quantum kinetic theory with those constructed from the "top-down" approach. We also demonstrate the matching between our kinetic theory's description and that from the real-time field theory calculations.

Recent results on the far-from-equilibrium phase of quark-gluon matter

• Kirill Boguslavski (TU Wien (AT))

The interplay of hydrodynamics and fluctuations

• Xin An (National Center for Nuclear Research)

Fluctuations are ubiquitous phenomena emerging across all physical length scales and play a crucial role in determining properties and dynamics when the system's degrees of freedom are notably finite. Such extreme conditions can be achieved in heavy-ion collision experiments, where fluctuations are important measures of collectivity and criticality. We focus on non-equilibrium fluctuations integrated into hydrodynamics — an interplay of long-wavelength effective theory and additional non-hydrodynamic modes. This integration leads to a deterministic and covariant description of fluctuation dynamics through a closed set of nonlinear differential equations for n-point correlation functions involving full hydrodynamic degrees of freedom. I will discuss recent progress and future challenges within this general formalism.

Real-time dynamics of pseudo-Goldstone and critical mode in QCD

• Yang-yang Tan (Dalian University of Technology)

The low energy QCD matter can be effectively desicrbed by O(4) model. the spontaneous breaking of approximate symmetries gives rise to emergent pseudo-Goldstone modes and a radial $\sigma$ mode. It has been proposed that the damping of pseudo-Goldstone modes at finite temperatures is universally constrained in the way that $\Omega_{\varphi}/m_{\varphi}^2\simeq D_{\varphi}$ in the broken phase, where $\Omega_{\varphi}$ and $m_{\varphi} $ are the relaxation rate at zero wavenumber and the mass of pseudo-Goldstones, $D_{\varphi}$ is the Goldstone diffusivity in the limit of purely spontaneous breaking. We find that, away from the critical temperature, the proposed relation is always valid. When the temperature is very close to the critical value the pseudo-Goldstone damping displays a novel scaling behavior that follows $\Omega_\varphi/m_\varphi^2\propto m_{\varphi}^{\Delta_\eta}$ with a correction $\Delta_\eta$ controlled by the critical fluctuations and obeying the critical universalities. Near the critical temperature the radial mode emerges as the critical mode. We analyze the relaxation dynamics by incorporating the effective potential and transport coefficients derived from first-principles fRG-QCD calculations. Our results indicate that once away from the critical point, the relaxation time of the critical mode decreases dramatically. Specifically, along the freeze-out line, the relaxation time remains mild. Consequently, the non-equilibrium dynamics have limited effects on observables along the freeze-out line.

Spin alignment of $K^\ast$ induced by strange-baryonic inhomogeneity

• Feng Li (Lanzhou University)

The difference between the spin alignments of $K^\ast$ and those of $\phi$ at the low collision energies is a puzzle raised by the recent experiments. Unlike $\phi$ meson, $K^\ast$, carrying a unit strange charge, should react to strange chemical potential $\mu_S$. In this talk, I shall first convince you that $\mu_S$ is not small in a brayon-rich medium for keeping strange neutrality, and then derive the spin alignment induced by the gradient of $\mu_S$, and hence of baryon chemical potential $\mu_B$, using linear response theory, with the transport coefficients expressed, without any approximation, in terms of the $K^\ast$'s in-medium spectral properties by employing Ward-Takahashi identity. It turns out that such an effect applies mainly to the particles whose longitudinal and transverse modes diverge, and induces only the local spin alignment in a static medium. The magnitudes of these coefficients will be further estimated under the quasi-particle approximation.

Spin Alignment Induced by Curvature of Freezeout Hypersurface

• Zhong-Hua Zhang (Fudan University)

We derive a Cooper-Frye-type formula for the spin alignment of spin-1 bosons at local thermal equilibrium described by a grand canonical ensemble specified by temperature, fluid velocity, and spin potential. We develop a set of Feynman rules to evaluate the Wigner function order by order in space-time gradient. We assume that the vector mesons freeze out on a space-like hypersurface in the Minkowski space-time that is close to a hyperplane. We find that the leading order of the spin alignment is proportional to the curvature of the hypersurface and the hydrodynamic fields at first-order space-time gradient, such as thermal shear. It is a non-dissipate mechanism that induces spin alignment proportional to the hydrodynamic fields with the first-order space-time gradient.

Closing Remark and announcing XQCD2025