We point out that chiral condensates at nonzero temperature and magnetic fields are in strict connection to the space-time integral of corresponding two-point neutral meson correlation functions in the pseudoscalar channel via the Ward-Takahashi identity. Screening masses of neutral pseudoscalar mesons, which are defined as the exponential decay of the corresponding spatial correlation functions in the long distance, thus are intrinsically connected to (inverse) magnetic catalysis of chiral condensates. To study this we performed lattice simulations of $(2+1)$-flavor QCD on $32^3\times N_t$ lattices with pion mass $M_π\simeq 220$ MeV in a fixed scale approach having temperature $T\in[17, 281]$ MeV and magnetic field strength $eB\in[0, 2.5]$ GeV$^2$. We find that screening lengths, i.e. inverses of screening masses of $π^0$, $K^0$ and $η^0_{s\bar{s}}$, turn out to have the similar complex $eB$ and $T$ dependences of the corresponding chiral condensates. Although the transition temperature is found to always decrease as $eB$ grows, we show that the suppression due to magnetic fields becomes less significant for hadron screening length and chiral condensates with heavier quarks involved, and ceases to occur for $η^0_{s\bar{s}}$ and strange quark chiral condensate. The complex $eB$ and $T$ dependences of both screening masses and chiral condensates, reflecting the crossover nature of the QCD transition, are attributed to the competition between sea and valence quark effects. These findings could be useful to guide low-energy models and effective theories of QCD.
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 compute flavor non-singlet meson screening masses in the chiral limit of QCD with $N_f=3$ quarks. The calculation is carried out at 12 temperatures from $T\approx 1$ GeV up to the electroweak scale. For each temperature we simulated several lattice spacings, so as to be able to perform the continuum limit extrapolation with confidence at a few permille accuracy. In the entire range of temperatures explored, the meson screening masses deviate from the free theory result $2πT$ by at most a few percent. Their values, however, cannot be explained by one-loop perturbation theory up to the electr…
We propose a practical effective model by introducing temperature ($T$) dependence to the coupling strengths of four-quark and six-quark Kobayashi-Maskawa-'t Hooft interactions in the 2+1 flavor Polyakov-loop extended Nambu-Jona-Lasinio model. The $T$ dependence is determined from LQCD data on the renormalized chiral condensate around the pseudocritical temperature $T_c^χ$ of chiral crossover and the screening-mass difference between $π$ and $a_0$ mesons in $T > 1.1T_c^χ$ where only the $U(1)_{\rm A}$-symmetry breaking survives. The model well reproduces LQCD data on screening masses $M_ξ^{\rm…
We present a strategy to study QCD non-perturbatively on the lattice at very high temperatures. This strategy exploits a non-perturbative, finite-volume, definition of the strong coupling constant to renormalize the theory. As a first application we compute the flavor non-singlet mesonic screening masses in a wide range of temperature, from $T\sim 1 $ GeV up to $\sim 160 $ GeV with three flavors in the chiral limit of QCD. Our results show very interesting features of the screening spectrum at very high temperatures. On one hand the mass splitting between the vector and the pseudoscalar screen…
Study of the scalar and pseudoscalar meson mass spectrum above the QCD chiral phase transition, using an effective Lagrangian approach
Dipartimento di Fisica, “Sapienza” Università di Roma（罗马大学物理系）；INFN, Sezione di Roma（罗马INFN分部）；Dipartimento di Fisica, Università di Pisa（比萨大学物理系）；INFN, Sezione di Pisa（比萨INFN分部）
We discuss the interpretation of Euclidean correlation functions at finite temperature ($T$) and their relationship with the corresponding real-time Green's functions. The soluble 2+1 dimensional Gross-Neveu model in the large-$N$ limit is used throughout as a working example. First, the real-time bound state, identified as an elementary excitation at finite $T$, is solved. The bound state mass, the dispersion relation at low momenta, the coupling constant and decay constant are calculated. To characterize the structure of the bound state the on-shell form factor is carefully introduced and ca…
We discuss a strategy to study non-perturbatively QCD up to very high temperatures by Monte Carlo simulations on the lattice. It allows not only the thermodynamic properties of the theory but also other interesting thermal features to be investigated. As a first concrete application, we compute the flavour non-singlet mesonic screening masses and we present the results of Monte Carlo simulations at 12 temperatures covering the range from T $\sim$ 1 GeV up to $\sim$ 160 GeV in the theory with three massless quarks. On the one side, chiral symmetry restoration manifests itself in our results thr…
We present a strategy based on the step-scaling technique to study non-perturbatively thermal QCD up to very high temperatures. As a first concrete application, we compute the flavour non-singlet meson screening masses at 12 temperatures covering the range from $T \sim 1$ GeV up to $\sim 160$ GeV in the theory with three massless quarks. The calculation is carried out by Monte Carlo simulations on the lattice by considering large spatial extensions in order to have negligible finite volume effects. For each temperature we have simulated 3 or 4 values of the lattice spacing, so as to perform th…
Responses to chemical potential of the pseudoscalar meson screening mass and the chiral condensate in lattice QCD are investigated. On a $16 \times 8^2 \times \4$ lattice with two flavors of staggered quarks the first and second responses below and above $T_c$ are evaluated. Different behavior in the low and the high temperature phases are observed, which may be explained as a consequence of the chiral symmetry breaking and restoration.
We investigate mesonic screening correlators at T=2T_c using the overlap Fermions in the quenched approximation, where T_c is the QCD phase transition temperature. Using lattices with temporal extent up to 8, we found that both pseudoscalar and vector correlators exhibit a nice $cosh$ behaviour, leading to a plateau behaviour in the local screening masses as a function of distance. The rho and pi masses so determined show very little variation with the lattice spacing a. This augurs well for the use of chiral Fermions, and further suggests the small deviations of these masses from the ideal ga…
Knowledge of the screening masses at finite chemical potential can provide insight into the nature of the QCD phase diagram. However, lattice studies at finite chemical potential suffer from the well-known issue of the sign problem, which has made the calculation of observables such as screening correlators and screening masses at finite chemical potential quite challenging. One way to proceed is by expanding the observable in a Taylor series in the chemical potential and hence calculating the finite-density corrections to the observable. In this talk, we will use this approach to calculate th…
We study the thermal transition of QCD with two degenerate light flavours by lattice simulations using $\mathcal{O}(a)$-improved Wilson quarks. Particular emphasis lies on the pattern of chiral symmetry restoration, which we probe via the static screening correlators. On $32^3$ volumes we observe that the screening masses in transverse iso-vector vector and axial-vector channels become degenerate at the transition temperature. The splitting between the screening masses in iso-vector scalar and pseudoscalar channels is strongly reduced compared to the splitting at zero temperature and is actual…
We study physics at temperatures just above the QCD phase transition (Tc) using chiral (overlap) Fermions in the quenched approximation of lattice QCD. Exact zero modes of the overlap Dirac operator are localized and their frequency of occurrence drops with temperature. This is closely related to axial U(1) symmetry, which remains broken up to 2Tc. After subtracting the effects of these zero modes, chiral symmetry is restored, as indicated by the behavior of the chiral condensate. The pseudoscalar and vector screening masses are close to ideal gas values.
Screening masses of positive- and negative-parity hadron ground-states, including those with strangeness
Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学理论交叉研究中心）；Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）；School of Physics, Beijing Institute of Technology（北京理工大学物理学院）；Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University（重庆大学物理系及强耦合物理重庆市重点实验室）
We study the thermal transition of QCD with two degenerate light flavours by lattice simulations using $O(a)$-improved Wilson quarks. Temperature scans are performed at a fixed value of $N_t = (aT)^{-1}=16$, where $a$ is the lattice spacing and $T$ the temperature, at three fixed zero-temperature pion masses between 200 MeV and 540 MeV. In this range we find that the transition is consistent with a broad crossover. As a probe of the restoration of chiral symmetry, we study the static screening spectrum. We observe a degeneracy between the transverse isovector vector and axial-vector channels s…
I present a numerical study of the crossover between the low temperature chirally broken phase and the high temperature chirally restored phase in $SU(N_c)$ gauge theory with $N_c=3-5$ colors and $N_f=2$ degenerate fermion flavors. Fermion masses span a range of intermediate values (represented by the squared ratio of pseudoscalar to vector meson masses $(m_{PS}/m_V)^2\sim 0.25$ to 0.63). Observables include the temperature dependent chiral condensate and screening masses. At each fermion mass these quantities show nearly identical temperature dependence across $N_c$.
We present an update of our study of the phase diagram of two-flavour QCD at zero baryon density with dynamical $O(a)$ improved Wilson quarks. All simulations are done on lattices with a temporal extent of $N_t=16$ and spatial extent $L=32,48$ and 64, ensuring that discretisation effects are small and finite size effects can be controlled. In the approach to the chiral limit we currently have three scans with pion masses between 540 and 200 MeV. In this proceedings article the focus is on the new scan at $m_π=200$ MeV and the measurement of screening masses. We also present first results conce…
We explore the idea that the chiral phase transition in QCD can be described as a transition from a disordered instanton liquid to a strongly correlated phase of polarized instanton anti-instanton molecules. We find a number of non perturbative effects caused by the presence of instantons above T_c, among them the fact that instantons contribute to the euquation of state. We also study how instantons affect the propagation of light quarks at high temperature and determine the spacelike screening masses for mesons and baryons. We derive the corresponding effective interaction and find that the …
We study the chiral properties of domain-wall quarks at high temperatures on an ensemble of quenched configurations. Low lying eigenmodes of the Dirac operator are calculated and used to check the extent to which the Atiyah-Singer index theorem is obeyed on lattices with finite $N_5$. We calculate the connected and disconnected screening propagators for the lowest mass scalar and pseudoscalar mesons in the sectors of different topological charge and note that they behave as expected. Separating out the would-be zero eigenmodes enables us to accurately estimate the disconnected propagators with…
Chiral symmetry breaking for large "Nf" and the properties of the "rho" meson near the conformal window
Institute of Physics, Gomal University（哥马尔大学物理研究所）；Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma ed Chiapas（恰帕斯自治优秀大学物理数学科学学院）；Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo（米乔阿肯圣尼古拉斯德伊达尔戈大学电气工程学院）；Centro de Ciencias Exactas, Universidad del Bío-Bío（比奥比奥大学精确科学中心）；Department of Physics, University of Science and Technology, Bannu（班努科技大学物理系）
