We incorporate the effective restoration of $U(1)_{\rm A}$ symmetry in the 2+1 flavor entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model by introducing a temperature-dependent strength $K(T)$ to the Kobayashi-Maskawa-'t Hooft (KMT) determinant interaction. $T$ dependence of $K(T)$ is well determined from pion and $a_0$-meson screening masses obtained by lattice QCD (LQCD) simulations with improved p4 staggered fermions. The strength is strongly suppressed in the vicinity of the pseudocritical temperature of chiral transition. The EPNJL model with the $K(T)$ well reproduces meson susceptibilities calculated by LQCD with domain-wall fermions. The model shows that the chiral transition is second order at the "light-quark chiral-limit" point where the light quark mass is zero and the strange quark mass is fixed at the physical value. This indicates that there exists a tricritical point. Hence the location is estimated.
This paper is devoted to the evaluation of the pionic scalar density at finite temperature and baryonic density. We express the latter effect in terms of the nuclear response evaluated in the random phase approxima- tion. We discuss the density and temperature evolution of the pionic density which governs the quark condensate evolution. Numerical evalua- tions are performed.
The effective intercept parameter of the two-pion Bose-Einstein correlation function, lambda_*, is found to be sensitive to the partial restoration of U_A(1) symmetry in ultra-relativistic nuclear collisions. An increase in the yield of the eta' meson, proposed earlier as a signal of partial U_A(1) restoration, is shown to create a ``hole'' in the low p_t region of lambda_*. A comparison with NA44 data from central S+Pb collisions at 200 AGeV is made and implications for future heavy ion experiments are discussed.
The partial restoration of chiral symmetry in nuclear medium is investigated in a model independent way by exploiting operator relations in QCD. An exact sum rule is derived for the quark condensate valid for all density. This sum rule is simplified at low density to a new relation with the in-medium quark condensate <bar{q}q>*, in-medium pion decay constant F_{pi}^t and in-medium pion wave-function renormalization Z_{pi}*. Calculating Z_{pi}*at low density from the iso-scalar pion-nucleon scattering data and relating F_{pi}^t to the isovector pion-nucleus scattering length b_1^*, it is conclu…
We study the effect of the chiral phase transition on pion production in hot hadronic matter. The phase of restored chiral symmetry is characterized by the appearance of the scalar $σ$-meson as a chiral partner of the pion as well as by the degeneracy of the vector and axial-vector mesons. We find rapid thermal and chemical equilibration of these degrees of freedom in the symmetric phase. Provided that the chiral transition temperature is not considerably high, the presence of a chirally symmetric phase will result in $\sim 1.6$ times more thermal pions in the final state.
We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the $η$-$η'$ sector and the $U_A(1)$ anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard $SU(3)$ framework for the octet case and combining the use of the $U(3)$ framework and the large-$N_c$ expansion of QCD to account properly for the nonet sector and anomalous contributions. The analysis is performed including finite temperature corrections as well as the calculation of $U(3)$ quark condensates a…
We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140 MeV to 800 MeV. The lattice computations were performed with 2+1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220 MeV and a kaon mass of 500 MeV. The lattices had temporal extents Nt = 4, 6 and 8 and aspect ratios of Ns / Nt \geq 4. At least up to a temperature of 140 MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pse…
We study the effects of Lorentz non-invariance on the physical pion velocity at the critical temperature $T_c$ in an effective theory of hidden local symmetry (HLS) with the "vector manifestation" fixed point. We match at a "matching scale" $Λ_M$ the axial-vector current correlator in the HLS with the one in the operator product expansion for QCD, and present the matching condition to determine the bare pion velocity. We find that the physical pion velocity, which is found to be one at $T=T_c$ when starting from the Lorentz invariant bare HLS, remains close to one with the Lorentz non-invarian…
Lattice QCD is used to calculate the potential between a static quark and anti-quark in the presence of a finite density of pi^+'s. Correlation functions of multiple pi^+'s are used in conjunction with Wilson-loop correlators to determine the difference between the Q\overline{Q}-potential in free-space and in the presence of a pion condensate. The modifications to the potential are found to have significant dependence on the Q\overline{Q} separation over the range r < 1 fm explored in this work. Our results are consistent with the pion-condensate behaving as a (nonlinear) chromo-dielectric.
The intercept parameter of the two-pion Bose-Einstein correlation functions at low transverse momentum is shown to play the role of an experimentally accessible measure of the (partial) restoration of U_A(1) symmetry in ultra-relativistic nuclear collisions.
Exploring $U_A(1)$ symmetry restoration in a magnetic field by meson screening masses in the NJL model
College of Physics, Jilin University（吉林大学物理学院）；School of Physical Science and Technology, Inner Mongolia University（内蒙古大学物理科学与技术学院）；Center for Fundamental Physics, School of Mechanics and Optoelectronic Physics, Anhui University of Science and Technology（安徽理工大学力学与光电物理学院基础物理中心）；Department of Physics and Siyuan Laboratory, Jinan University（暨南大学物理系思言实验室）
We investigate the shear viscosity of a pion gas in relativistic kinetic theory, using the Nambu-Jona-Lasinio model to construct the pion mass and the pi-pi interaction at finite temperature. Whereas at low temperatures the scattering properties and, hence, the viscosity are in agreement with lowest-order chiral perturbation theory, we find strong medium modifications in the crossover region. Here the system is strongly coupled and the scattering lengths diverge, similarly as for ultra-cold Fermi gases at a Feshbach resonance. As a consequence, the ratio eta/s is found to be strongly reduced a…
We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.
The imposition of Dirichlet boundary conditions in lattice computations obstructs the formation of a chiral condensate. We use chiral perturbation theory and meson models to address the effect of a Dirichlet boundary on chiral symmetry breaking. While pions are the longest-range modes in QCD, the restoration of chiral symmetry due to a boundary is shown not to depend upon the pion Compton wavelength but rather on that of the sigma meson. Power-law finite size corrections are exposed, and require prohibitively large lattices to overcome. We further speculate on the frustration of the chiral con…
A possible effective restoration of the anomalous $U_A(1)$ symmetry would have a non-trivial effect on the global phase diagram of QCD. In this work we investigate the effective restoration of the $U_A(1)$ through the calculation of scalar and pseudo-scalar screening masses and corresponding susceptibilities, for physical and lower than physical pion masses. Calculations have been performed in (2+1)-flavor HISQ discretization scheme with a physical value of the strange quark mass. Preliminary calculations of the continuum extrapolated scalar and pseudo-scalar masses are presented, based on lat…
We study chiral symmetry restoration by analyzing thermal properties of QCD's (pseudo-)Goldstone bosons, especially the pion. The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions. To obtain the correlation functions, we solve the Dyson-Schwinger equations and the inhomogeneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation. In the chiral limit, the pion and its partner sigma degenerate at the critical temperature $T_c$. At $T \gtrsim T_c$, it is found that the pion rapidly dissociates, which sign…
The soft pion correction at high energy may play a crucial role in non-perturbative parts of sea quark distributions. In this paper, we show that, while the soft pion correction for the strange sea qaurk distribution is suppressed in the large and the medium $x$ region compared with that for the up and the down sea quark one, it can become large and SU(3) flavor symmetric in the very small $x$ region. This gives us a good reason for the symmetry restoration of light sea quark distributions required by the mean charge sum rule for the light sea quarks. Then, by estimating this sum rule with the…
We investigate the screening masses of neutral pions and sigma mesons in hot and magnetized quark matter in the framework of a two-flavor lattice-improved Nambu-Jona-Lasinio (NJL) model with a magnetic field dependent coupling constant, which is determined by utilizing the results from lattice QCD simulations. Since such model can well reproduce inverse magnetic catalysis (IMC), by comparing with the standard NJL model, we systemically analyze the impacts of IMC on the temperature and magnetic field dependences of the longitudinal and transverse screening masses of the chiral partners, i.e. π^…
We analyze chiral restoration within the $O(N+1)/O(N)$ Non-Linear Sigma Model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$. The free energy is constructed diagramatically to ${\cal O}(TM^3)$ in the pion mass expansion, which allows to derive the quark condensate and the scalar susceptibility in the chiral limit. At this order, we do not have to deal with renormalization, neither from divergences from mass tadpoles nor from those of higher order loop contributions. Our results for the critical behaviour are consistent with expectations from lattice analysis …
We study thermal properties of a large-N massless pion gas using a low-energy QCD approach given by an $O(N +1)/O(N)$ Nonlinear Sigma Model. We build diagrammatically the associated finite free energy to $O(TM^{3})$ in the pion mass expansion through an effective vertex that considers all the contributions coming from closed diagrams. Subsequently, we calculate finite order parameters such as the quark condensate and its respective derivative, i.e., the scalar susceptibility, in the chiral limit, along with their associated critical exponents. These results are compared with our previous unita…
In case of chiral U_A(1) symmetry restoration the mass of the eta' boson (the ninth, would-be Goldstone boson) is decreased, thus its production cross section is heavily enhanced. The eta' decays (through one of its decay channels) into five pions. These pions will not be correlated in terms of Bose-Einsten correlations, thus the production enhancement changes the strength of two-pion correlation functions at low momentum. Preliminary results strongly support the mass decrease of the eta' boson. In this paper we propose a method to select pions coming from eta' decays. We investigate the effic…
In this work, we review how the mass and the width of the $f_{0}(500)$ pole behave in a regime where temperature is below the critical chiral transition value. This is attained by considering a large-$N$ $O(N + 1)/O(N)$ invariant Non-Linear Sigma Model (NLSM) such that we can study the dynamical generation of a $f_{0}(500)$ resonance. Introducing thermal effects via the imaginary time formalism allows us to study the behavior of the pole and relate it to chiral restoration.
Chiral symmetry imposes some constrains on hadron correlation functions in dense medium. These constraints imply a certain general structure of the two- and three-point correlation functions of chiral partners and lead to the effect of mixing arising from the interaction of the long-ranged nuclear pions with corresponding interpolating currents. It reflects the phenomena of partial restoration of chiral symmetry. We consider soft pion corrections for quark condensates and several possible pairs of chiral partners for both mesons and nucleons and analyse their mixing patterns. We explored both …
Using unitarized Chiral Perturbation Theory methods, we perform a detailed analysis of the $ππ$ scattering poles $f_0(600)$ and $ρ(770)$ behaviour when medium effects such as temperature or density drive the system towards Chiral Symmetry Restoration. In the analysis of real poles below threshold, we show that it is crucial to extend properly the unitarized amplitudes so that they match the perturbative Adler zeros. Our results do not show threshold enhancement effects at finite temperature in the $f_0(600)$ channel, which remains as a pole of broad nature. We also implement T=0 finite density…
We derive the expressions of the vector and axial current from a chiral Lagrangian restricted to nucleons and pions. They display mixing terms between the axial and vector currents. We study the modifications in the nuclear medium of the coupling constants of the axial current, namely the pion decay constant and the nucleonic axial one due to the requirements of chiral symmetry. We express the renormalizations in terms of the local scalar pion density. The latter also governs the quark condensate evolu- tion and we discuss the link between this evolution and the renormaliza- tions. In the case…
In case of chiral U_A(1) symmetry restoration the mass of the eta' boson (the ninth, would-be Goldstone boson) is decreased, thus its production cross section is heavily enhanced. The eta' decays (through one of its decay channels) into five pions. These pions will not be correlated in terms of Bose-Einsten correlations, thus the production enhancement changes the strength of two-pion correlation functions at low momentum. Preliminary results strongly support the mass decrease of the eta' boson. In this paper we propose a method to select pions coming from eta' decays. We investigate the effic…
Temperature dependence of pion and sigma-meson screening masses is evaluated by the Polyakov-loop extended Nambu--Jona-Lasinio model with the entanglement vertex (EPNJL model). We propose a practical way of calculating meson screening masses in the NJL-type effective models. The method based on the Pauli-Villars regularization solves the well-known difficulty that the evaluation of screening masses is not easy in the NJL-type effective models. The method is applied to analyze temperature dependence of pion screening masses calculated with state-of-the-art lattice simulations with success in re…
The role of effective degrees of freedom on the vector and axial-vector susceptibilities and the pion velocity at chiral restoration is analyzed. We consider two possible scenarios, one in which pions are considered to be the only low-lying degrees of freedom -- that we shall refer to as "standard" -- and the other in which pions, vector mesons and constituent quarks (or quasiquarks in short) are the relevant low-lying degrees of freedom -- that we shall refer to as "vector manifestation (VM)." We show at one-loop order in chiral perturbation theory with hidden local symmetry Lagrangian that w…
We calculate the meson screening mass in a pion superfluid in the framework of Nambu--Jona-Lasinio model. The minimum of the attractive quark potential is always located at the phase boundary of pion superfluid. Different from the temperature and baryon density effect, the potential at finite isospin density can not be efficiently suppressed and the matter is always in a strongly coupled phase due to the Goldstone mode in the pion superfluid.
Temperature dependence of pion and sigma-meson screening masses is evaluated by the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model with the entanglement vertex. We propose a practical way of calculating meson screening masses in the NJL-type effective models. The method based on the Pauli-Villars regularization solves the well-known difficulty that the evaluaton of screening masses is not easy in the NJL-type effective models.The PNJL model with the entanglement vertex and the Pauli-Villars regularization well reproduces lattice QCD results on temperature dependence of the chiral cond…
We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U(1)_A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N_τ= 8 and spatial extent N_σ= 16 in a temperature range of T = 139 - 195 MeV, corresponding to lattice spacings of a \approx 0.12 - 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m_π= 200 MeV. The strange quark mass is set near its phy…
We study the pion velocity near the critical temperature $T_c$ of chiral symmetry restoration in QCD. Using chiral perturbation theory based on hidden local symmetry (HLS) as an effective field theory, where the chiral symmetry restoration is realized as the vector manifestation (VM), we show that the pion velocity for $T \to T_c$ is close to the speed of light, $v_π(T) = 0.83 - 0.99$ which is at variance with the sigma model result which predicts $v_π(T_c) = 0$. Our prediction on $v_π(T_c)$ is compared with the value extracted from the recent RHIC data.
We consider the $O(N+1)/O(N)$ Non-Linear Sigma Model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$, in the chiral limit. At $T=0$ this formulation provides a good description of scattering data in the scalar channel and generates dynamically the $f_0(500)$ pole, the pole position lying within experimental determinations. Previous $T=0$ results with this model are updated using newer analysis of pion scattering data. We calculate the pion scattering amplitude at finite $T$ and show that it satisfies exactly thermal unitarity, which had been assumed but not fo…
We study possible restoration patterns of chiral symmetry in a generalized hidden local symmetry model, which is a low energy effective theory of QCD including pseudo-scalar, vector and axial-vector mesons. We derive Wilsonian renormalization group equations and analyze the running couplings and their fixed points at the chiral restoration point. We find three types of the chiral restoration, which are classified as the standard, vector manifestation and intermediate scenarios, respectively. It turns out that the rho and A_1 meson become massless and their decay into pion is suppressed in all …
In the framework of Coulomb Gauge QCD we explore dynamical breaking of chiral symmetry and screening of the confinement potential at finite density. The screened potential is applied in study of charmonium dissociation.
We study the pion velocity near the critical temperature $T_c$ of chiral symmetry restoration in QCD. Using the hidden local symmetry (HLS) model as the effective field theory, where the chiral symmetry restoration is realized as the vector manifestation (VM), we show that the pion velocity for $T \to T_c$ receives neither quantum nor (thermal) hadronic corrections at the critical temperature even when we start from the bare theory with Lorentz symmetry breaking. We show that this is related to a new fixed point structure originated in the VM. Further we match at a matching scale the axial-vec…
In this work, we investigate not only the pole masses but also the screening masses of neutral pions at finite temperature and magnetic field by utilizing the random phase approximation (RPA) approach in the framework of the two-flavor Nambu--Jona-Lasinio (NJL) model. And two equivalent formalisms in the presence of a magnetic field, i.e. the Landau level representation (LLR) and the proper-time representation (PTR), are applied to obtain the corresponding analytical expressions of the polarization functions (except the expressions for the pole masses in the PTR). In order to evaluate the appl…
We investigate the (partial) chiral restoration at finite temperature (T) under the strong external magnetic field B_0 of the SU(2) light-flavor QCD matter. To this end, we employ the instanton-liquid QCD vacuum configuration accompanied with the linear Schwinger method for inducing the magnetic field. The Harrington-Shepard caloron solution is used to modify the instanton parameters, i.e. the average instanton size (rho) and inter-instanton distance (R), as functions of T. In addition, we include the meson-loop corrections (MLC) as the large-N_c corrections because they are critical for repro…
We present results for screening masses of light and strange mesons in 2+1 flavour QCD using improved (p4fat3) staggered fermions on 6x24^3 lattices. We have studied the screening masses of scalar, pseudo-scalar, vector and axial-vector mesons along the line of constant physics, determined by a pion mass ~220 MeV and a kaon mass ~500 MeV. In order to investigate the cut-off and volume dependencies we have also performed studies of the meson screening correlators in the non-interacting theory using the p4 and the standard staggered discretizations.
Soft-pion theorems are used to show how chiral symmetry constrains the contributions of low-momentum pions to the quark condensate, the pion decay constant and hadron masses, all of which have been proposed as signals of partial restoration of chiral symmetry in matter. These have contributions of order T^2 for a pion gas or of order m_pi for cold nuclear matter, which have different coefficients in all three cases, showing that there are no simple relations between the changes to these quantities in matter. In particular, such contributions are absent from the masses of vector mesons and nucl…
We present lattice QCD results for the screening masses of light mesons and charmonia. The lattice computations were performed with 2+1 flavors of improved staggered quarks using quark masses which correspond to realistic pion and kaon masses at zero temperature. For the light quark sector we have found that the screening masses in the pseudo-scalar and the isovector scalar channels do not become degenerate at the chiral crossover temperature indicating an effective non-restoration of the axial symmetry. Also the splitting between the vector and the pseudo-scalar screening masses persists even…
Screening correlators and masses were studied at finite temperature in QCD with two flavours of dynamical staggered quarks on a lattice. The spectrum of screening masses show a hierarchical approach to chiral symmetry restoration. Control of explicit chiral symmetry breaking through the quark mass was shown to be an important step to understanding this phenomenon. No sign of decays was found in the finite temperature scalar meson-like correlators in the confined phase.
In this work we study the chiral phase transition as observed by an accelerating observer taking into account the Unruh effect. We use Chiral Perturbation Theory at leading order and the large $N$ limit ($N$ being the number of pions) as an effective description of low-energy QCD, and the Thermalization Theorem to compute the relevant partition function for the accelerating observer. As a result, we obtain that chiral symmetry is restored for uniformly accelerated observers with acceleration $a$ larger than the critical value $a_c=4πf_π$, with $f_π$ being the pion decay constant.
Complex poles of the unitarized pi-pi scattering amplitude in nuclear matter are studied. Partial restoration of chiral symmetry is modeled by the decrease of in-medium pion decay constant f*_{pi}. For large chiral restoration (f*_{pi}/f_{pi} << 1), 2nd sheet poles in the scalar (sigma) and the vector (rho) mesons are both dictated by the Lambert W function and show universal softening as f*_{pi} decreases. In-medium pi-pi cross section receives substantial contribution from the soft mode and exhibits a large enhancement in low-energy region. Fate of this universality for small chiral restorat…
We discuss recent advances on QCD chiral symmetry restoration at finite temperature, within the theoretical framework of Effective Theories. $U(3)$ Ward Identities are derived between pseudoscalar susceptibilities and quark condensates, allowing to explain the behaviour of lattice meson screening masses. Unitarized interactions and the generated $f_0(500)$ thermal state are showed to play an essential role in the description of the transition through the scalar susceptibility
The question as to what the relevant effective degrees of freedom at the chiral phase transition are remains largely unanswered and must be addressed in confronting both terrestrial and space laboratory observations purporting to probe matter under extreme conditions. We address this question in terms of the vector susceptibility χ_V (VSUS in short) and the axial-vector susceptibility χ_A (ASUS in short) at the temperature-induced chiral transition. We consider two possible, albeit simplified, cases that are contrasting, one that is given by the standard chiral theory where only the pions figu…
In the framework of nonlocal SU(2) chiral quark models with Polyakov loop, we analyze the dependence of the deconfinement and chiral restoration critical temperatures on the explicit chiral symmetry breaking driven by the current quark mass. Our results are compared with those obtained within the standard local Polyakov-Nambu-Jona-Lasinio (PNJL) model and with lattice QCD calculations. For a wide range of pion masses, it is found that both deconfinement and chiral restoration critical temperatures turn out to be strongly entangled, in contrast with the corresponding results within the PNJL mod…
We investigate the effect of composite pions on the behaviour of the chiral condensate at finite temperature within the Polyakov-loop improved NJL model. To this end we treat quark-antiquark correlations in the pion channel (bound states and scattering continuum) within a Beth-Uhlenbeck approach that uses medium-dependent phase shifts. A striking medium effect is the Mott transition which occurs when the binding energy vanishes and the discrete pion bound state merges the continuum. This transition is triggered by the lowering of the continuum edge due to the chiral restoration transition. Thi…
We use the linear sigma model with quarks to study the QCD phase diagram from the point of view of chiral symmetry restoration. We compute the leading order effective potential for high and low temperatures and finite quark chemical potential, up to the contribution of the ring diagrams to account for the plasma screening effects. We fix the values of the model couplings using physical values for the input parameters such as the vacuum pion and sigma masses, the critical temperature at vanishing quark chemical potential and the conjectured end point value of the baryon chemical potential of th…
Using non-perturbative lattice method we studied hadronic screening correlators above and immediately below the deconfinement transition temperature, Tc, in the quenched approximation with lattice spacing of 1/(8T) using clover improved Wilson fermions. Simulations were performed at temperatures T /Tc = 0, 0.95 and 1.5. Mesonic screening correlators show no statistically significant thermal effects below Tc, and clear evidence for weakly interacting quarks above Tc . Baryon screening correlators yield similar physics above Tc, but show precursor effects for chiral symmetry restoration below Tc…
We point out that, in analogy with spin waves in antiferromagnets, all parameters describing the real-time propagation of soft pions at temperatures below the QCD chiral phase transition can be expressed in terms of static correlators. This allows, in principle, the determination of the soft pion dispersion relation on the lattice. Using scaling and universality arguments, we determine the critical behavior of the parameters of pion propagation. We predict that when the critical temperature is approached from below, the pole mass of the pion drops despite the growth of the pion screening mass.…
We present lattice QCD results for mesonic screening masses in the temperature range 140 MeV $\lesssim T \lesssim$ 2500 MeV. Our calculations were carried out using (2+1)-flavors of the Highly Improved Staggered Quark (HISQ) action, with a physical value for the strange quark mass and two values of the light quark mass corresponding to pion masses of 160 MeV and 140 MeV. Continuum-extrapolated results were obtained using calculations with a variety of lattice spacings corresponding to temporal lattice extents $N_τ= 6 - 16$. We discuss the implications of these results for the effective restora…
We report on recent work relating the medium effects observed in dilepton spectra in heavy-ion collisions to potential signals of chiral symmetry restoration. The key connection remains the approach to spectral function degeneracy between the vector-isovector channel with its chiral partner, the axialvector-isovector channel. Several approaches are discussed to elaborate this connection, namely QCD and Weinberg sum rules with input for chiral order parameters from lattice QCD, and chiral hadronic theory to directly evaluate the medium effects of the axialvector channel and the pertinent pion d…
