Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD.

We present the first study of the quark mass dependence of the heavy quark momentum and spatial diffusion coefficients using lattice QCD with light dynamical quarks corresponding to a pion mass of 320 MeV. We find that, for the temperature range 195 MeV

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

Macroscopic properties of the strong interaction near its chiral phase transition exhibit scaling behaviors, which are the same as those observed close to the magnetic transition in a three-dimensional classical spin system with O(4) symmetry. We show that the universal scaling properties of the chiral phase transition in quantum chromodynamics (QCD) at the macroscale are, in fact, encoded within the microscopic energy levels of its fundamental constituents, the quarks. 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, i.e., the eigenspectra of the massless QCD Dirac operator. 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 a generalization 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 that 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. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses. Our study reveals how the hidden scaling features at the microscale give rise to the macroscopic universal properties of QCD.

Heavy Quark Diffusion from 2+1 Flavor Lattice QCD with 320 MeV Pion Mass.

We present the first calculations of the heavy flavor diffusion coefficient using lattice QCD with light dynamical quarks corresponding to a pion mass of around 320 MeV. For temperatures 195 MeV

Lattice QCD Determination of the Bjorken-x Dependence of Parton Distribution Functions at Next-to-Next-to-Leading Order.

We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices with spacings a=0.04 and 0.06 fm and valence pion mass m_{π}=300 MeV, at boost momentum as large as 2.42 GeV. As a crucial step to control the systematics, we renormalize the pion valence quasidistribution in the recently proposed hybrid scheme, which features a Wilson-line mass subtraction at large distances in coordinate space, and develop a procedure to match it to the MS[over ¯] scheme. We demonstrate that the renormalization and the perturbative matching in Bjorken-x space yield a reliable determination of the valence quark distribution for 0.03≲x≲0.80 with 5%-20% uncertainties.

Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansions.

Taylor expansion in powers of baryon chemical potential (µ_{B}) is an oft-used method in lattice QCD to compute QCD thermodynamics for µ_{B}>0. Based only upon the few known lowest order Taylor coefficients, it is difficult to discern the range of µ_{B} where such an expansion around µ_{B}=0 can be trusted. We introduce a resummation scheme for the Taylor expansion of the QCD equation of state in µ_{B} that is based on the n-point correlation functions of the conserved current (D_{n}). The method resums the contributions of the first N correlation function D_{1},…,D_{N} to the Taylor expansion of the QCD partition function to all orders in µ_{B}. We show that the resummed partition function is an approximation to the reweighted partition function at µ_{B}≠0. We apply the proposed approach to high-statistics lattice QCD calculations using 2+1 flavors of Highly Improved Staggered Quarks with physical quark masses on 32^{3}×8 lattices and for temperatures T≈145-176 MeV. We demonstrate that, as opposed to the Taylor expansion, the resummed version not only leads to improved convergence but also reflects the zeros of the resummed partition function and severity of the sign problem, leading to its eventual breakdown. We also provide a generalization of scheme to include resummation of powers of temperature and quark masses in addition to µ_{B}, and show that the alternative expansion scheme of [S. Borsányi et al., Phys. Rev. Lett. 126, 232001 (2021).PRLTAO0031-900710.1103/PhysRevLett.126.232001] is a special case of this generalized resummation.

Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD.

We introduce novel relations between the derivatives [∂^{n}ρ(λ,m_{l})/∂m_{l}^{n}] of the Dirac eigenvalue spectrum [ρ(λ,m_{l})] with respect to the light sea quark mass (m_{l}) and the (n+1)-point correlations among the eigenvalues (λ) of the massless Dirac operator. Using these relations we present lattice QCD results for ∂^{n}ρ(λ,m_{l})/∂m_{l}^{n} (n=1, 2, 3) for m_{l} corresponding to pion masses m_{π}=160-55 MeV and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using (2+1) flavors of highly improved staggered quarks with the physical value of strange quark mass, three lattice spacings a=0.12, 0.08, 0.06 fm, and lattices having aspect ratios 4-9. We find that ρ(λ→0,m_{l}) develops a peaked structure. This peaked structure arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper as a→0, and its amplitude is proportional to m_{l}^{2}. We demonstrate that this ρ(λ→0,m_{l}) is responsible for the manifestations of axial anomaly in two-point correlation functions of light scalar and pseudoscalar mesons. After continuum and chiral extrapolations we find that axial anomaly remains manifested in two-point correlation functions of scalar and pseudoscalar mesons in the chiral limit.

Chiral Phase Transition Temperature in (2+1)-Flavor QCD.

We present a lattice-QCD-based determination of the chiral phase transition temperature in QCD with two degenerate, massless quarks and a physical strange quark mass using lattice QCD calculations with the highly improved staggered quarks action. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of 58 MeV≲m_{π}≲163 MeV. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling analysis. Finite-volume effects are controlled by extrapolating to the thermodynamic limit using spatial lattice extents in the range of 2.8-4.5 times the inverse of the pion mass. Continuum extrapolations are carried out by using three different values of the lattice cutoff, corresponding to lattices with temporal extents N_{τ}=6, 8, and 12. After thermodynamic, continuum, and chiral extrapolations, we find the chiral phase transition temperature T_{c}^{0}=132_{-6}^{+3} MeV.

Universal Off-Equilibrium Scaling of Critical Cumulants in the QCD Phase Diagram.

Exploiting the universality between the QCD critical point and the three-dimensional Ising model, closed form expressions derived for nonequilibrium critical cumulants on the crossover side of the critical point reveal that they can differ in both magnitude and sign from equilibrium expectations. We demonstrate here that key elements of the Kibble-Zurek framework of nonequilibrium phase transitions can be employed to describe the dynamics of these critical cumulants. Our results suggest that observables sensitive to critical dynamics in heavy-ion collisions should be expressible as universal scaling functions, thereby providing powerful model-independent guidance in searches for the QCD critical point.

QCD phase transition with chiral quarks and physical quark masses.

We report on the first lattice calculation of the QCD phase transition using chiral fermions with physical quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm)(3) and (11 fm)(3) and temperatures between 139 and 196 MeV. Each temperature is calculated at a single lattice spacing corresponding to a temporal Euclidean extent of N(t) = 8. The disconnected chiral susceptibility, χ(disc) shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability near the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD "phase transition" is not first order but a continuous crossover for m(π) = 135 MeV. The peak location determines a pseudocritical temperature T(c) = 155(1)(8) MeV, in agreement with earlier staggered fermion results. However, the peak height is 50% greater than that suggested by previous staggered results. Chiral SU(2)(L) × SU(2)(R) symmetry is fully restored above 164 MeV, but anomalous U(1)(A) symmetry breaking is nonzero above T(c) and vanishes as T is increased to 196 MeV.

Additional strange hadrons from QCD thermodynamics and strangeness freezeout in heavy ion collisions.

We compare lattice QCD results for appropriate combinations of net strangeness fluctuations and their correlations with net baryon number fluctuations with predictions from two hadron resonance gas (HRG) models having different strange hadron content. The conventionally used HRG model based on experimentally established strange hadrons fails to describe the lattice QCD results in the hadronic phase close to the QCD crossover. Supplementing the conventional HRG with additional, experimentally uncharted strange hadrons predicted by quark model calculations and observed in lattice QCD spectrum calculations leads to good descriptions of strange hadron thermodynamics below the QCD crossover. We show that the thermodynamic presence of these additional states gets imprinted in the yields of the ground-state strange hadrons leading to a systematic 5-8 MeV decrease of the chemical freeze-out temperatures of ground-state strange baryons.

Strangeness at high temperatures: from hadrons to quarks.

Appropriate combinations of up to fourth order cumulants of net strangeness fluctuations and their correlations with net baryon number and electric charge fluctuations, obtained from lattice QCD calculations, have been used to probe the strangeness carrying degrees of freedom at high temperatures. For temperatures up to the chiral crossover, separate contributions of strange mesons and baryons can be well described by an uncorrelated gas of hadrons. Such a description breaks down in the chiral crossover region, suggesting that the deconfinement of strangeness takes place at the chiral crossover. On the other hand, the strangeness carrying degrees of freedom inside the quark gluon plasma can be described by a weakly interacting gas of quarks only for temperatures larger than twice the chiral crossover temperature. In the intermediate temperature window, these observables show considerably richer structures, indicative of the strongly interacting nature of the quark gluon plasma.

Freeze-out conditions in heavy ion collisions from QCD thermodynamics.

We present a determination of freeze-out conditions in heavy ion collisions based on ratios of cumulants of net electric charge fluctuations. These ratios can reliably be calculated in lattice QCD for a wide range of chemical potential values by using a next-to-leading order Taylor series expansion around the limit of vanishing baryon, electric charge and strangeness chemical potentials. From a computation of up to fourth order cumulants and charge correlations we first determine the strangeness and electric charge chemical potentials that characterize freeze-out conditions in a heavy ion collision and confirm that in the temperature range 150 MeV ≤ T ≤ 170 MeV the hadron resonance gas model provides good approximations for these parameters that agree with QCD calculations on the 5%-15% level. We then show that a comparison of lattice QCD results for ratios of up to third order cumulants of electric charge fluctuations with experimental results allows us to extract the freeze-out baryon chemical potential and the freeze-out temperature.