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Register a new userCritical line of 2+1 flavor QCD: Toward the continuum limit
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We determine the continuum limit of the curvature of the pseudocritical line of QCD with $n_f$=2+1 staggered fermions at nonzero temperature and quark density. We perform Monte Carlo simulations at imaginary baryon chemical potentials, adopting the HISQ/tree action discretization, as implemented in the code by the MILC collaboration. Couplings are adjusted so as to move on a line of constant physics, as determined in Ref.~cite{Bazavov:2011nk}, with the strange quark mass $m_s$ fixed at its physical value and a light-to-strange mass ratio $m_l/m_s=1/20$. The chemical potential is set at the same value for the three quark species, $mu_l=mu_sequiv mu$. We attempt an extrapolation to the continuum using the results on lattices with temporal size up to $L_t=12$. Our estimate for the continuum value of the curvature $kappa$ at zero baryon density, $kappa=0.020(4)$, is compared with recent lattice results and with experimental determinations of the freeze-out curve.
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We present physical results obtained from simulations using 2+1 flavors of domain wall quarks and the Iwasaki gauge action at two values of the lattice spacing $a$, ($a^{-1}$=,1.73,(3),GeV and $a^{-1}$=,2.28,(3),GeV). On the coarser lattice, with $24^3times 64times 16$ points, the analysis of ref.[1] is extended to approximately twice the number of configurations. The ensembles on the finer $32^3times 64times 16$ lattice are new. We explain how we use lattice data obtained at several values of the lattice spacing and for a range of quark masses in combined continuum-chiral fits in order to obtain results in the continuum limit and at physical quark masses. We implement this procedure at two lattice spacings, with unitary pion masses in the approximate range 290--420,MeV (225--420,MeV for partially quenched pions). We use the masses of the $pi$ and $K$ mesons and the $Omega$ baryon to determine the physical quark masses and the values of the lattice spacing. While our data are consistent with the predictions of NLO SU(2) chiral perturbation theory, they are also consistent with a simple analytic ansatz leading to an inherent uncertainty in how best to perform the chiral extrapolation that we are reluctant to reduce with model-dependent assumptions about higher order corrections. Our main results include $f_pi=124(2)_{rm stat}(5)_{rm syst}$,MeV, $f_K/f_pi=1.204(7)(25)$ where $f_K$ is the kaon decay constant, $m_s^{bar{textrm{MS}}}(2,textrm{GeV})=(96.2pm 2.7)$,MeV and $m_{ud}^{bar{textrm{MS}}}(2,textrm{GeV})=(3.59pm 0.21)$,MeV, ($m_s/m_{ud}=26.8pm 1.4$) where $m_s$ and $m_{ud}$ are the mass of the strange-quark and the average of the up and down quark masses respectively, $[Sigma^{msbar}(2 {rm GeV})]^{1/3} = 256(6); {rm MeV}$, where $Sigma$ is the chiral condensate, the Sommer scale $r_0=0.487(9)$,fm and $r_1=0.333(9)$,fm.
We present results for the equation of state in (2+1)-flavor QCD using the highly improved staggered quark action and lattices with temporal extent $N_{tau}=6,~8,~10$, and $12$. We show that these data can be reliably extrapolated to the continuum limit and obtain a number of thermodynamic quantities and the speed of sound in the temperature range $(130-400)$ MeV. We compare our results with previous calculations, and provide an analytic parameterization of the pressure, from which other thermodynamic quantities can be calculated, for use in phenomenology. We show that the energy density in the crossover region, $145~ {rm MeV} leq T leq 163$ MeV, defined by the chiral transition, is $epsilon_c=(0.18-0.5)~{rm GeV}/{rm fm}^3$, $i.e.$, $(1.2-3.1) epsilon_{rm nuclear}$. At high temperatures, we compare our results with resummed and dimensionally reduced perturbation theory calculations. As a byproduct of our analyses, we obtain the values of the scale parameters $r_0$ from the static quark potential and $w_0$ from the gradient flow.
We determine the hyperon vector couplings $f_1(0)$ for $Sigma^{-}rightarrow nl^-bar{ u_l}$ and $Xi^0rightarrowSigma^{+}l^-bar{ u_l}$ semileptonic decays in the continuum limit with (2+1)-flavors of dynamical domain-wall fermions, using the Iwasaki gauge action at two different lattice spacings of $a$=0.114(2) and 0.086(2) fm. A theoretical estimation of flavor SU(3)-breaking effect on the vector coupling is required to extract $V_{us}$ from the experimental rate of hyperon beta decays. We obtain the vector couplings $f_1(0)$ for $Sigmarightarrow N$ and $Xirightarrow Sigma$ beta-decays with an accuracy of less than one percent. We then find that lattice results of $f_1(0)$ combined with the best estimate of $|V_{us}|$ with imposing Cabibbo-Kobayashi-Maskawa (CKM) unitarity are slightly deviated from the experimental result of $|V_{us}f_1(0)|$ for the $Sigmarightarrow N$ beta-decay. This discrepancy can be attributed to an assumption made in the experimental analysis on $|V_{us}f_1(0)|$, where the induced second-class form factor $g_2$ is set to be zero regardless of broken SU(3) symmetry. We report on this matter and then estimate the possible value of $g_2(0)$, which is evaluated from the experimental decay rate with our lattice result of $f_1(0)$ under the first-row CKM-unitarity condition.
We study correlation functions of spatially separated static quark-antiquark pairs in (2+1)-flavor QCD in order to investigate onset and nature of color screening at high temperatures. We perform lattice calculations in a wide temperature range, $140 le T le 5814,{rm MeV}$, using the highly improved staggered quark action and several lattice spacings to control discretization effects. By comparing at high temperatures our lattice results to weak-coupling calculations as well as to the zero temperature result for the energy of a static quark-antiquark pair, we observe that color screening sets in at $rT approx 0.3$. Furthermore, we also observe that in the range $0.3 lesssim r T lesssim 0.6$ weak-coupling calculations in the framework of suitable effective field theories provide an adequate picture of color screening.
We present the first results of the PACS-CS project which aims to simulate 2+1 flavor lattice QCD on the physical point with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at the lattice spacing of $a=0.0907(13)$fm on a $32^3times 64$ lattice with the use of the DDHMC algorithm to reduce the up-down quark mass. Further algorithmic improvements make possible the simulation whose ud quark mass is as light as the physical value. The resulting PS meson masses range from 702MeV down to 156MeV, which clearly exhibit the presence of chiral logarithms. An analysis of the PS meson sector with SU(3) ChPT reveals that the NLO corrections are large at the physical strange quark mass. In order to estimate the physical ud quark mass, we employ the SU(2) chiral analysis expanding the strange quark contributions analytically around the physical strange quark mass. The SU(2) LECs ${bar l}_3$ and ${bar l}_4$ are comparable with the recent estimates by other lattice QCD calculations. We determine the physical point together with the lattice spacing employing $m_pi$, $m_K$ and $m_Omega$ as input. The hadron spectrum extrapolated to the physical point shows an agreement with the experimental values at a few % level of statistical errors, albeit there remain possible cutoff effects. We also find that our results of $f_pi=134.0(4.2)$MeV, $f_K=159.4(3.1)$MeV and $f_K/f_pi=1.189(20)$ with the perturbative renormalization factors are compatible with the experimental values. For the physical quark masses we obtain $m_{rm ud}^msbar=2.527(47)$MeV and $m_{rm s}^msbar=72.72(78)$MeV extracted from the axial-vector Ward-Takahashi identity with the perturbative renormalization factors.
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