We investigate the high-temperature phase of QCD using lattice QCD simulations with $N_f = 2$ dynamical Möbius domain-wall fermions. On generated configurations, we study the axial $U(1)$ symmetry, overlap-Dirac spectra, screening masses from mesonic correlators, and topological susceptibility. We find that some of the observables are quite sensitive to lattice artifacts due to a small violation of the chiral symmetry. For those observables, we reweight the Möbius domain-wall fermion determinant by that of the overlap fermion. We also check the volume dependence of observables. Our data near the chiral limit indicates a strong suppression of the axial $U(1)$ anomaly at temperatures $\geq$ 220 MeV.
In order to study the fate of mesons in thermal QCD at finite baryon chemical potential, we consider light mesonic correlation functions using the Taylor expansion to ${\cal O}((μ/T)^2)$, in both the hadronic and quark-gluon plasma phases. We use the FASTSUM anisotropic fixed-scale lattices with $N_f = 2+1$ flavours of Wilson fermion. We find that mesonic correlators are sensitive to finite-density corrections and that the second-order terms indicate the chiral crossover in the vector and axial-vector channels.
We present NLO results for thermal imaginary-time correlators in the vector and scalar channels as a function of the quark mass. The range of quark masses for which a non-relativistic approximation works in the temperature range considered is estimated, and charm quarks turn out to be a borderline case. Comparing with simulation data from fine lattices, we find good agreement in the vector channel but a substantial discrepancy in the scalar one. An explanation for the discrepancy is suggested in terms of physics of the quark-antiquark threshold region. Perturbative predictions for the bottom s…
We investigate the distance and temperatures scale for which the string in baryonic quark configuration approaches the limiting behavior of mesonic strings in pure Yang-Mills SU(3) lattice gauge theory. We calculate and compare the numerical values of the Polyakov loop correlators and the width profile of both diquark-quark $(QQ)Q$ and mesonic $Q\bar{Q}$ strings. We find the diquark-quark configuration to exhibit an identical behavior to the mesonic string for the potential and energy-density width profile for temperature near the end of QCD plateau. In the vicinity of the deconfinement point;…
We review recent progress in studying spectral functions for mesonic observables at finite temperatures, by analysis of imaginary time correlators directly calculated on isotropic lattices. Special attention is paid to the lattice artifacts present in such calculations.
We analyze temporal and spatial meson correlators in quenched lattice QCD at T>0. Below T_c we observe little change in the meson properties as compared with T=0. Above T_c we observe new features: chiral symmetry restoration and signals of plasma formation, but also indication of persisting mesonic (metastable) states and different temporal and spatial masses in the mesonic channels. This suggests a complex picture of QGP in the region 1 - 1.5 T_c.
The analytic form of the lattice quark propagator is used to derive the functional form for short distance mesonic correlators. These are then used to calculate ``Continuum Model'' Ansatze which comprise of a pole, representing the ground state, plus a contribution for the excited states, coming from the short distance behaviour. These are compared to Monte Carlo data.
We discuss the behavior of charmonia and bottomonia correlators and spectral functions above the deconfinement temperature and determine melting temperatures for different mesonic states.
Lattice NRQCD with leading finite lattice spacing errors removed is used to calculate decay constants of mesons made up of heavy quarks. Quenched simulations are done with a tadpole improved gauge action containing plaquette and six-link rectangular terms. The tadpole factor is estimated using the Landau link. For each of the three values of the coupling constant considered, quarkonia are calculated for five masses spanning the range from charmonium through bottomonium, and one set of quark masses is tuned to the B(c). "Perturbative" and nonperturbative meson masses are compared. One-loop pert…
We present results for lattice QCD in the limit of infinite gauge coupling on a discrete spatial but continuous Euclidean time lattice. A worm type Monte Carlo algorithm is applied in order to sample two-point functions which gives access to the measurement of mesonic temporal correlators. The continuous time limit, based on sending $N_τ\rightarrow \infty$ and the bare anistotropy to infinity while fixing the temperature in a non-perturbative setup, has various advantages: the algorithm is sign problem free, fast, and accumulates high statistics for correlation functions. Even though the measu…
Using quenched chiral perturbation theory, we compute the long-distance behaviour of two-point functions of flavour non-singlet axial and vector currents in a finite volume, for small quark masses, and at a fixed gauge-field topology. We also present the corresponding predictions for the unquenched theory at fixed topology. These results can in principle be used to measure the low-energy constants of the chiral Lagrangian, from lattice simulations in volumes much smaller than one pion Compton wavelength. We show that quenching has a dramatic effect on the vector correlator, which is argued to …
We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures $T=220-380$ MeV. We measure the correlators of spin-one ($J=1$) operators including vector, axial-vector, tensor and axial-tensor. Restoration of chiral $U(1)_A$ and $SU(2)_L \times SU(2)_R$ symmetries of QCD implies degeneracies in vector--axial-vector ($SU(2)_L \times SU(2)_R$) and tensor--axial-tensor ($U(1)_A$) pairs, which are indeed observed at temperatures above $T_c$. Moreover, we observe an approximate degeneracy of all $J=1$ correlators with incre…
We study multi-particle state contributions to the QCD two-point functions of the axial-vector and pseudo-scalar quark bilinears in a finite spatial volume. For sufficiently small quark masses one expects three-meson states with two additional pions at rest to have the lowest total energy after the ground state. We calculate this three-meson state contribution using chiral perturbation theory. We find it to be strongly suppressed and too small to be seen in present-day lattice simulations.
We study the vector and axial-vector current correlators in perturbative and non-perturbative regimes of QCD. The correlators in Euclidean coordinate space are calculated on the lattice using the Möbius domain-wall fermion formulation at three lattice spacings covering 0.044--0.080~fm. The dynamical quark effects of $2+1$ light flavors are included. The sum $V+A$ and the difference $V-A$ of the vector ($V$) and axial-vector ($A$) current correlators calculated on the lattice after extrapolating to the physical point agree with those converted from the ALEPH experimental data of hadronic $τ$ de…
We present results for mesonic propagators in temporal and spatial directions at T below and above the deconfining transition in quenched QCD. Anisotropic lattices are used to get enough information in the temporal direction. We use the Wilson fermion action for light quarks and Fermilab action for heavy quarks.
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…
Point to point vacuum correlators containing diquarks in the color anti-triplet representation are computed both in the quenched approximation and dynamical overlap simulations with two flavors. The scalar, pseudoscalar and axial vector diquarks are combined with light quarks to form color singlets. The scalar ("good") diquark channel shows a stronger attraction than the axial vector ("bad") channel in the quenched data set. The pseudoscalar diquark channel shows a finite volume zero mode artifact: the correlator becomes negative at large distance when the quark mass is small. By separating co…
We calculate temporal correlators and their spectral functions with meson quantum numbers in the deconfined phase of QCD using the hard thermal loop (HTL) approximation for the quark propagator. Although this approach does not result in a complete next-to-leading order perturbative calculation it takes into account important medium effects such as thermal quark masses and Landau damping in the quark-gluon plasma. We show that both effects lead to competing modifications of the free mesonic correlation functions. We find that correlators in scalar channels are only moderately influenced by the …
We examine the axial U(1) symmetry near and above the finite temperature phase transition in two-flavor QCD using lattice QCD simulations. Although the axial U(1) symmetry is always violated by quantization, (i.e.) the chiral anomaly, the correlation functions may manifest effective restoration of the symmetry in the high temperature phase. We explicitly study this possibility by calculating the meson correlators as well as the Dirac operator spectral density near the critical point. Our numerical simulations are performed on a $16^3\times 8$ lattice with two flavors of dynamical quarks repres…
We investigate point-to-point correlation functions for various mesonic and baryonic channels using the ${\cal O}(a)$-improved Wilson action due to Sheikholeslami and Wohlert. We consider propagators to both time slices 0 and 1. We find that discretisation effects are more pronounced than those reported with unimproved Wilson fermions, but that the same procedure for removing finite size effects is successful. Extrapolating to the chiral limit, we see the notable features predicted phenomenologically: the ratio of interacting to free correlators in the vector channel is roughly constant to abo…
Point to point correlators of currents are computed in quenched QCD using a chiral lattice fermion action, the overlap action. I compare correlators made of exact quark propagators with correlators restricted to low (less than 500 MeV) eigenvalue eigenmodes of the Dirac operator. In many cases they show qualitative resemblence (typically at small values of the quark mass and distances larger than 0.4 fm) and they differ qualitatively at larger quark masses or at very short distance. Lattice results are in qualitative agreement (and in the difference of vector and axial vector channels, quantit…
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…
We study the role of diquarks in light baryons through point to point baryon correlators. We contrast results from quenched simulations with ones with two flavors of dynamical overlap fermions. The scalar, pseudoscalar and axial vector diquarks are combined with light quarks to form color singlets. The quenched simulation shows large zero mode effects in correlators containing the scalar and pseudoscalar diquark. The two scalar diquarks created by gamma_5 and gamma_0gamma_5 lead to different behavior in baryon correlators, showing that the interaction of diquarks with the third light quark mat…
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 study spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures up to 380 MeV with various quark masses. We measure the correlators of spin-one isovector operators including vector, axial-vector, tensor and axial-tensor. At temperatures above $T_c$ we observe an approximate degeneracy of the correlators in these channels, which is unexpected because some of them are not related under $SU(2)_L \times SU(2)_R$ nor $U(1)_A$ symmetries. The observed approximate degeneracy suggests emergent $SU(2)_{CS}$ (chiral-spin) and $SU…
The isovector axial form factor of the nucleon plays a key role in interpreting data from long-baseline neutrino oscillation experiments. We present a lattice QCD calculation of this form factor, introducing a new method to directly extract its z-expansion from lattice correlators. Our final parameterization of the form factor, which extends up to spacelike virtualities of 0.7 GeV^2 with fully quantified uncertainties, agrees with previous lattice calculations but is significantly less steep than neutrino-deuterium scattering data suggests.
The isovector axial form factor of the nucleon plays a key role in interpreting data from long-baseline neutrino oscillation experiments. We perform a lattice-QCD based calculation of this form factor, introducing a new method to directly extract its $z$-expansion from lattice correlators. Our final parametrization of the form factor, which extends up to spacelike virtualities of $0.7\,{\rm GeV}^2$ with fully quantified uncertainties, agrees with previous lattice calculations but is significantly less steep than neutrino-deuterium scattering data suggests.
We analyze temporal and spatial meson correlators in quenched lattice QCD at T>0. Above T_c we find different masses and (spatial) screening masses, signals of plasma formation, and indication of persisting mesonic excitations.
The QCD-coupling is a necessary input in the computation of many observables, and the parametric error on input parameters can be a dominant source of uncertainty. The coupling can be extracted by comparing high order perturbative computations and lattice evaluated moments of mesonic two-point functions with heavy quarks, which provide a high energy scale for perturbation theory. The truncation of the perturbative series is an important systematic uncertainty. We report on our attempt to study this issue by measuring pseudo-scalar two-point functions in volumes of $L=2\, \text{fm}$ with twiste…
We consider corrections to nucleon correlation functions arising from times that are far from the asymptotic limit. For such times, the single nucleon state is contaminated by the pion-nucleon and pion-delta continuum. We use heavy baryon chiral perturbation theory to derive the spectral representation of the nucleon two-point function. Finite time corrections to the axial current correlation function are also derived. Pion-nucleon excited state contributions drive the axial correlator upward, while contributions from the interference of pion-delta and pion-nucleon states drive the axial corre…
Techniques to compute hadron properties from lattice QCD rely upon the limit of long time separation. For baryons, the signal-to-noise problem often restricts one to time separations that are not ideally long, and for which couplings to excited states can obstruct the isolation of ground-state baryon properties. We consider excited-state contamination in nucleon two- and three-point functions. Using chiral perturbation theory, we determine couplings to pion-nucleon and pion-delta excited states. In two-point functions, these contributions are small, in accordance with general properties of the…
We discuss the calculations of quarkonium spectral functions in potential models and their implications for the interpretation of the lattice data on quarkonium correlators. In particular, we find that melting of different quarkonium states does not lead to significant change in the Euclidean time correlators. The large change of the quarkonium correlators above deconfinement observed in the scalar and axial-vector channels appears to be due to the zero mode contribution.
We calculate mesonic two-point functions in the epsilon-regime of two-flavor QCD on the lattice with exact chiral symmetry. We use gauge configurations of size 16^3 32 at the lattice spacing a \sim 0.11 fm generated with dynamical overlap fermions. The sea quark mass is fixed at \sim 3 MeV and the valence quark mass is varied in the range 1-4 MeV, both of which are in the epsilon-regime. We find a good consistency with the expectations from the next-to-leading order calculation in the epsilon-expansion of (partially quenched) chiral perturbation theory. From a fit we obtain the pion decay cons…
We present results for the isovector axial, induced pseudoscalar, electric, and magnetic form factors of the nucleon. The calculations were done using $2+1+1$-flavor HISQ ensembles generated by the MILC collaboration with lattice spacings $a \approx$ 0.12, 0.09, 0.06$\mathrm{fm}$ and pion masses $M_π\approx$ 310, 220, 130$\mathrm{MeV}$. Excited-states contamination is controlled by using four-state fits to two-point correlators and by comparing two- versus three-states in three-point correlators. The $Q^2$ behavior is analyzed using the model independent z-expansion and the dipole ansatz. Fina…
We study the bottomonium screening masses in a 2+1 flavor QCD medium on the lattice using the Highly Improved Staggered Quark(HISQ) discretization for the quarks. We focus on a wide temperature range in the region $350~{\rm MeV}\le T < 1000 ~{\rm MeV}$, and perform our calculations on three different lattice spacings to control the lattice cut-off effects, corresponding to temporal lattice extent of $N_τ=8,10,12$. From a detailed study of the temperature dependence of screening masses we conclude that while the $η_b(1S)$ and $Υ(1S)$ states melt at $T>500$ MeV, the scalar and axial-vector state…
I compute the difference of vector and axial vector current correlators in the weak coupling phase of (lattice-regulated) SU(3) gauge theory with two flavors of symmetric-representation dynamical fermions. This is a walking theory at the bare parameter values chosen for the simulation. Otherwise, it is not a conventional technicolor candidate. The correlator difference shows scaling behavior in the fermion mass, and vanishes in the fermion zero mass limit. Consequences for the phenomenology of similar systems which might be candidates for beyond Standard Model physics are discussed. I check my…
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…
Anomalous correlators of vector and axial currents which enter the Kubo formulae for the chiral magnetic and the chiral separation conductivities are explicitly calculated for free overlap fermions on the lattice. The results are confronted with continuum calculations in the finite-temperature regularization, and a subtle point of such regularization for chiral magnetic conductivity related to the correct counting of the chiral states is highlighted. In agreement with some previous claims in the literature, we find that in a lattice regularization which respects gauge invariance, the chiral ma…
We calculate the vector and axial-vector current correlators in the coordinate space and compare them with the experimental information obtained through the spectral functions of hadronic tau decays measured by ALEPH. Lattice data are obtained with 2+1 Mobius domain-wall fermions at three lattice spacings 0.044, 0.055 and 0.080 fm and the continuum limit is taken. The correlators calculated on the lattice after extrapolating to the physical point agree with those converted from the ALEPH data.
We compute the flavor singlet meson correlators and screening masses in quenched and $N_f=2$ QCD at $N_t=8$. The consequences of our results for the realization of the $U_A(1)$ symmetry at finite T are discussed and an interpretation of our measurements in terms of the behaviour of the low lying fermionic modes is proposed.
We use lattice QCD simulations, with MILC gluon configurations and HISQ c-quark propagators, to make very precise determinations of moments of charm-quark pseudoscalar, vector and axial-vector correlators. These moments are combined with new four-loop results from continuum perturbation theory to obtain several new determinations of the MSbar mass of the charm quark and of the MSbar coupling. We find m_c(3GeV)=0.986(10)GeV, or, equivalently, m_c(m_c)=1.268(9)GeV, both for n_f=4 flavors; and alpha_msb(3GeV,n_f=4)=0.251(6), or, equivalently, alpha_\msb(M_Z,n_f=5)=0.1174(12). The new mass agrees …
The nucleon axial form factors -- axial $G_A$, induced pseudoscalar $\widetilde{G}_P$ and pseudoscalar $G_P$ -- have displayed large systematics in lattice QCD calculations. The major symptoms were the violation of the partially conserved axial current (PCAC) relation between the three form factors, and the underestimation of the induced pseudoscalar coupling $g_P^\ast$ and the axial charge radius $r_A$ compared to phenomenological estimates. The small $g_P^\ast$ was a consequence of the failure of the pion-pole dominance (PPD) hypothesis, especially at low $M_π^2$. The small charge radius $r_…
We take a new look at plaquette-plaquette correlators in 4d compact U(1) lattice gauge theory which are separated in time, both in the confined and the deconfined phases. From the behaviour of these correlators we extract glueball masses in the scalar as well as the axial-vector channels. Also in the deconfined phase, the non-zero momentum axial-vector correlator gives us information about the photon which appears as a massless particle in the spectrum. Using the Luescher - Weisz multi-level algorithm, we are able to go to large time separations which were not possible previously.
We present a quenched calculation of meson correlators with the overlap fermion at very small masses 2.6--13 MeV. In this region the pion Compton wavelength is larger than our lattice size L\simeq 1.23fm and the system is in the so-called epsilon-regime of chiral perturbation theory. We found that the scalar and pseudo-scalar correlators are precisely approximated by a few hundred low-lying fermion eigenmodes in this regime, whereas axial-vector correlator receives significant contributions from higher eigenmodes. We also measure the disconnected pseudo-scalar correlator, which is well saturat…
Results from the first lattice QCD analysis of vacuum correlators of local hadronic currents using dispersion relations are presented. We have explored the vector, pseudoscalar, axial, and scalar meson channels, and the proton-like and delta-like baryon channels. The lattice results are shown to agree qualitatively with experimental results in channels where experimental data exist, and shed insight into interacting instanton approximations and sum rule calculations in the other channels. 3 figures included (as PostScript files): pi.ps, nd.ps, va.ps : Search for %%% to retrieve the files. Late…
We consider the simulation of finite temperature QCD with two flavors of dynamical overlap fermions in order to study the suppression of the axial U(1) symmetry breaking at the chiral phase transition point. As a preliminary study, pure gauge simulations are performed to investigate how fixing the topology affects physical quantities like the topological susceptibility, $χ_t$, at finite temperature, showing that it is possible to reconstruct known results from the fixed topology sector. First results on the degeneracy of meson correlators in the high temperature QGP sector are shown.
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…
We report on a non-perturbative computation of the renormalization factor Z_A of the axial vector current in three-flavour O(a) improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge action and also recall our recent determination of the improvement coefficient c_A. Our normalization and improvement conditions are formulated at constant physics in a Schrödinger functional setup. The normalization condition exploits the full, massive axial Ward identity to reduce finite quark mass effects in the evaluation of Z_A and correlators with boundary wave functions to suppress e…
We determine quark mass dependent order $a$ improvement terms of the form $b_J am$ for non-singlet scalar, pseudoscalar, vector and axialvector currents, using correlators in coordinate space. We use a set of CLS ensembles comprising non-perturbatively improved Wilson Fermions and the tree-level Luescher-Weisz gauge action at $β=3.4,3.46,3.55$ and $β=3.7$, corresponding to lattice spacings $a$ ranging from $0.05$ fm to $0.09$ fm. We report the values of the $b_J$ improvement coefficients which are proportional to non-singlet quark mass combinations and also discuss the possibility of determini…
