We investigate the transverse profile of the chromoelectric field generated by a quark-antiquark pair in the vacuum of (2+1) flavor QCD. Monte Carlo simulations are performed adopting the HISQ/tree action discretization, as implemented in the publicly available MILC code, suitably modified to measure the chromoelectric field. We work on the line of constant physics, with physical strange quark mass $m_s$ and light to strange mass ratio $m_l/m_s = 1/20$.
We present a new (and general) algorithm for deriving lattice Feynman rules which is capable of handling actions as complex as the Highly Improved Staggered Quark (HISQ) action. This enables us to perform a perturbative calculation of the influence of dynamical HISQ fermions on the perturbative improvement of the gluonic action in the same way as we have previously done for asqtad fermions. We find the fermionic contributions to the radiative corrections in the Lüscher-Weisz gauge action to be somewhat larger for HISQ fermions than for asqtad.
We study QCD with (2+1)-HISQ fermions at nonzero temperature and nonzero imaginary baryon chemical potential. Monte Carlo simulations are performed using the MILC code along the line of constant physics with a light to strange mass ratio of $m_l/m_s=1/20$ on lattices up to $48^3 \times 12$ to check for finite cutoff effects. We determine the curvature of the pseudocritical line extrapolated to the continuum limit.
We present results on the curvature of the critical line of QCD with 2+1 HISQ fermions at nonzero temperature and quark density obtained by analytic continuation from imaginary chemical potentials. Monte Carlo simulations are performed by means of the MILC code, suitably modified to include a nonzero imaginary baryon chemical potential. We set the chemical potential at the same value for the three quark species and work on the line of constant physics with a light to strange mass ratio of 1/20 as determined in Ref.~\cite{Bazavov:2011nk}.
We perform a perturbative calculation of the influence of dynamical HISQ fermions on the perturbative improvement of the gluonic action in the same way as we have previously done for asqtad fermions. We find the fermionic contributions to the radiative corrections in the Luescher-Weisz gauge action to be somewhat larger for HISQ fermions than for asqtad. Using one-loop perturbation theory as a test, we estimate that omission of the fermion-induced radiative corrections in dynamical asqtad simulations will give a measurable effect. The one-loop result gives a systematic shift of about -0.6% in …
We present the results of the nucleon and $Ω$ baryon masses using staggered action for both valence and sea quarks. Three ensembles with the physical pion mass at approximate lattice spacings of $0.15$, $0.12$, and $0.088$fm are employed to extrapolate the masses to continuum and we obtain $M_N = 964(16)$ MeV and $M_Ω= 1678(9)$. Both statistical and systematic uncertainties are included in the nucleon mass, whereas only the statistical uncertainty is accounted for in the $Ω$ baryon mass.
We present results for the form factor $f_+^{K π}(0)$, needed to extract the CKM matrix element $|V_{us}|$ from experimental data on semileptonic $K$ decays, on the HISQ $N_f=2+1+1$ MILC configurations. The HISQ action is also used for the valence sector. The data set used for our final result includes three different values of the lattice spacing and data at the physical light quark masses. We discuss the error budget and how this calculation improves on our previous determination of $f_+^{K π}(0)$ on the asqtad $N_f=2+1$ MILC configurations.
We investigate the state-of-the-art Lanczos eigensolvers available in the Grid and QUDA libraries. They include Implicitly Restarted Lanczos, Thick-Restart Lanczos, and Block Lanczos. We measure and analyze their performance for the Highly Improved Staggered Quark (HISQ) Dirac operator. We also discuss optimization of Chebyshev acceleration.
The nature of the thermal phase transition of two flavor QCD in the chiral limit has an important implication for the QCD phase diagram. We carry out lattice QCD simulations in an attempt to address this problem. Simulations are conducted with a Symanzik-improved gauge action and the HISQ fermion action. Within the imaginary chemical potential formulation, five different quark masses, $am=0.020,\, 0.018, \, 0.015, \, 0.013,\, 0.010$, and four different lattice volumes $N_s=8, \, 12,\, 16, \, 20$ with temporal extent $N_t=4$ are used to explore the scaling behavior. At each of the quark masses,…
We report on recent progress in employing the Highly Improved Staggered Quark (HISQ) action introduced by the HPQCD/UKQCD collaboration in simulations with dynamical fermions. The HISQ action is an order $a^2$ Symanzik-improved action with further suppressed taste symmetry violations. The improvement in taste symmetry is achieved by introducing Fat7 smearing of the original gauge links and reunitarization (projection to an element of U(3) or SU(3)) followed by Asq-type smearing. Major challenges for calculating the fermion force are related to the reunitarization step. We present a preliminary…
Adopting a mixed action approach, we report here results on hadron spectra containing one or more charm quarks. We use overlap valence quarks on a background of 2+1+1 flavor HISQ gauge configurations generated by the MILC collaboration. We also study the ratio of leptonic decay constants, f_Ds*/f_Ds. Results are obtained at two lattice spacings.
We report here results on charm and strange hadron spectra. Adopting a mixed action approach, we use overlap fermions for valence quarks, on a background of 2+1+1 flavours HISQ gauge configurations of MILC collaboration. Two lattice spacings (0.09 fm and 0.06 fm) are used. We find the hyperfine splitting of 1S charmonia to be 114(3)(-2) MeV and 109(4)(-3) MeV, and the splitting (m(Omega_ccc)-3/2 m(JΨ)) is found to be 110(20)(-10) MeV and 120(10) MeV, corresponding to lattices with spacings a = 0.09 and 0.06 fm respectively. We also look at the ratio of the leptonic decay constant f_Ds*/f_Ds.
After briefly reviewing recent progress by the HotQCD collaboration in studying the 2+1 flavor QCD equation of state, we will focus on results on fluctuations of conserved charges by the BNL-Bielefeld and HotQCD collaborations. Higher order cumulants of the net-charge distributions are increasingly dominated by a universal scaling behavior, which arises due to a critical point of QCD in the chiral limit. Considering cumulants up to the 6^{th} order, we observe that they generically behave as expected from universal scaling laws, which is quite different from cumulants calculated within the had…
Kaon leptonic and semileptonic decays with $N_f=2+1+1$ HISQ fermions
Michigan State University（密歇根州立大学）；Washington University（华盛顿大学）；University of Utah（犹他大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Indiana University（印第安纳大学）；University of Maryland（马里兰大学）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；Colorado State University（科罗拉多州立大学）
We present results from an ongoing study of the phase diagram of (2+1)-flavor QCD using the HISQ action with smaller than physical light quark masses in the Roberge-Weiss (RW) plane on lattices with temporal extent $N_τ=4$. We find that the endpoint of the $1^{st}$ order RW transition line remains $2^{nd}$ order at least down to light quark masses corresponding to Goldstone pion masses of $55$ MeV. Furthermore, we show that the chiral condensate is sensitive to the RW transition and may serve as a energy-like operator characterizing universal behavior close to the RW endpoint.
We study the phase structure of QCD with three degenerate flavors in the external magnetic fields using highly improved staggered quarks (HISQ). The simulations are performed on $16^3\times 6$ lattice. In order to investigate the quark mass dependence of the chiral transition we choose the values of the bare quark masses 0.015 and 0.0009375 in the lattice unit, corresponding to $m_π=320$ MeV and 80 MeV in the continuum limit. We found no indication of a first order phase transition in the current window of quark masses and external magnetic fields. Unlike to the case with standard staggered fe…
We studied the QCD phase transition as a function of quark mass in the $N_f=3$ QCD at vanishing baryon density. Lattice simulations have been performed using Highly Improved Staggered Quarks on $N_τ=6$ lattices with quark masses that correspond to pion masses in the region $80 \lesssim m_π \lesssim 230 $MeV. We found no evidence of the first order phase transition in the current pion mass window. The pion mass at the critical point where the first order phase transition starts is estimated to be $m^c_π\lesssim 45$ MeV.
We report on investigations of the chiral and deconfinement aspects of the finite temperature transition in 2+1 flavor QCD using the Highly Improved Staggered Quark (HISQ) action on lattices with temporal extent $N_τ=6$ and $N_τ=8$. We have calculated several physical observables, including the renormalized Polyakov loop, strangeness fluctuations, the renormalized chiral condensate and the chiral susceptibility in the crossover region for physical values of the strange quark mass $m_s$ and light quark masses $m_l=0.2m_s$ and $0.05m_s$. We compare our findings with previous calculations that us…
We discuss the reduction of errors in the calculation of the form factor $f_+^{K π}(0)$ with HISQ fermions on the $N_f=2+1+1$ MILC configurations from increased statistics on some key ensembles, new data on ensembles with lattice spacings down to 0.042 fm and the study of finite-volume effects within staggered ChPT. We also study the implications for the unitarity of the CKM matrix in the first row and for current tensions with leptonic determinations of $\vert V_{us}\vert$.
We report on the status of our kaon semileptonic form factor calculations using the highly-improved staggered quark (HISQ) formulation to simulate the valence fermions. We present results for the form factor f_+^{K π}(0) on the asqtad N_f=2+1 MILC configurations, discuss the chiral-continuum extrapolation, and give a preliminary estimate of the total error. We also present a more preliminary set of results for the same form factor but with the sea quarks also simulated with the HISQ action; these results include data at the physical light quark masses. The improvements that we expect to achiev…
We calculate cumulants of fluctuations of net-baryon number, net-electric charge and net-strangeness, in the framework of lattice regularized QCD. We use a highly improved staggered quark (HISQ) action on lattices with temporal extent of N_tau=6,8 and 12 and almost physical quark masses. By means of a Taylor expansion in various chemical potentials and under demanding both strangeness neutrality as well as the correct isospin asymmetry, we evaluate these fluctuations at conditions met in heavy ion collisions. Cumulants of net-electric charge fluctuations can, in principle, also be measured in …
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 measure the spatial distribution of all components of the color fields surrounding a static quark antiquark pair in QCD with (2+1) HISQ flavors. We isolate the nonperturbative component of the longitudinal chromoelectric color field responsible for the linear term in the confining potential.
We study the lattice spacing dependence, or scaling, of physical quantities using the highly improved staggered quark (HISQ) action introduced by the HPQCD/UKQCD collaboration, comparing our results to similar simulations with the asqtad fermion action. Results are based on calculations with lattice spacings approximately 0.15, 0.12 and 0.09 fm, using four flavors of dynamical HISQ quarks. The strange and charm quark masses are near their physical values, and the light-quark mass is set to 0.2 times the strange-quark mass. We look at the lattice spacing dependence of hadron masses, pseudoscala…
We report on the computation of the light quark vacuum polarization with 2+1+1 flavors of H ISQ fermions at the physical point and its contribution to the muon anomalous magnetic moment. Three ensembles, generated by the MILC collaboration, are used to take the continuum limit. We compare our result with recent ones in the literature.
We utilize the eigenvalue filtering technique combined with the stochastic estimate of the mode number to determine the eigenvalue spectrum. Simulations of (2 + 1)-flavor QCD are performed using the Highly Improved Staggered Quarks (HISQ/tree) action on $N_τ$ = 8 lattices with aspect ratios $N_σ/N_τ$ ranging from 5 to 7. The strange quark mass is fixed to its physical value $m_{s}^{\rm phy}$, and the light quark masses $m_{l}$ are varied from $m_{s}^{\rm phy}/40$ to $m_{s}^{\rm phy}/160$ which correspond to pion mass $m_π$ ranging from 110 MeV to 55 MeV in the continuum limit. We compute the c…
We calculate the intrinsic strangeness of the nucleon, <N|ss|N> - <0|ss|0>, using the MILC library of improved staggered gauge configurations using the Asqtad and HISQ actions. Additionally, we present a preliminary calculation of the intrinsic charm of the nucleon using the HISQ action with dynamical charm. The calculation is done with a method which incorporates features of both commonly-used methods, the direct evaluation of the three-point function and the application of the Feynman- Hellman theorem. We present an improvement on this method that further reduces the statistical error, and c…
It is well established that lattice artifacts can be suppressed substantially by the use of SU(3)-projected smeared links in the fermion action. An example is the Highly Improved Staggered Quark action where the ASQ-like effective links are constructed from reunitarized Fat7 links. A general procedure is presented for computing the derivative of the fermion action with respect to the base links (fermion force) - a key component in dynamical simulations using molecular dynamics evolution. The method is iterative and can be applied to actions with arbitrary levels of smearing and reunitarization…
We report on salient features of a mixed lattice QCD action using valence Möbius domain-wall fermions solved on the dynamical $N_f=2+1+1$ HISQ ensembles generated by the MILC Collaboration. The approximate chiral symmetry properties of the valence fermions are shown to be significantly improved by utilizing the gradient-flow scheme to first smear the HISQ configurations. The greater numerical cost of the Möbius domain-wall inversions is mitigated by the highly efficient QUDA library optimized for NVIDIA GPU accelerated compute nodes. We have created an interface to this optimized QUDA solver i…
We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic gauge configurations. We study both the unimproved and the HISQ Dirac operators. We compare the spectral flow index with the index obtained by identifying low-lying modes of large chirality.
We studied the temporal correlation function of mesons in the pseudo-scalar channel in (2+1)-flavor QCD in the presence of external magnetic fields at zero temperature. The simulations were performed on $32^3 \times 96$ lattices using the Highly Improved Staggered Quarks (HISQ) action with $m_π \approx $ 230 MeV. The strength of magnetic fields $|eB|$ ranges from 0 to around 3.3 GeV$^2$ ($\sim 60 m_π^2$). We found that the masses of neutral pseudo-scalar particles, e.g. neutral pion and kaon, monotonouslly decrease as the magnetic field grows and then saturate at a nonzero value. It is observe…
Flavor diagonal nucleon charges using clover fermions on MILC HISQ ensembles
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Thomas Jefferson National Accelerator Facility（托马斯·杰斐逊国家加速器设施）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Ibsyn Scientific（Ibsyn科学公司）；Michigan State University（密歇根州立大学）；NVIDIA Corporation（英伟达公司）
Taste symmetry violations in staggered fermion formulations correlate strongly with the cut-off (lattice spacing) dependence in thermodynamic quantities. Better taste symmetry on the lattice can be achieved either by decreasing the lattice spacing and going to larger temporal extent in finite-temperature calculations, or by further improving the action. The highly improved staggered quark (HISQ) action offers a further degree of improvement and substantially reduces taste violations. We report on our studies of the 2+1 flavor QCD thermodynamics with the HISQ/tree action. By systematically comp…
One of the fundamental properties of the quark-gluon plasma (QGP), the equation of state, is a subject of extensive studies in lattice QCD and an essential requirement for the correct hydrodynamic modeling of heavy-ion collisions. Lattice QCD provides first-principle calculations for the physics in the non-perturbative regime. In this contribution, we report on recent progress by the HotQCD collaboration in studying the 2+1 flavor equation of state on lattices with the temporal extent N_tau=6, 8, 10 and 12 in Highly Improved Staggered Quarks (HISQ) discretization scheme. Comparisons with equat…
We report the results of a lattice quantum chromodynamics calculation of $F_K/F_π$ using Möbius domain-wall fermions computed on gradient-flowed $N_f=2+1+1$ highly-improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from $130 \lesssim m_π\lesssim 400$ MeV, four lattice spacings of $a\sim 0.15, 0.12, 0.09$ and $0.06$ fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation fu…
We report on investigations of the chiral and deconfinement aspects of the finite temperature transition in 2+1 flavor QCD using the Highly Improved Staggered Quark (HISQ) action on lattices with temporal extent $N_τ=6$ and $N_τ=8$. We have performed the calculations for physical values of the strange quark mass $m_s$ and the light quark masses $m_l=0.2m_s$ and $0.05m_s$. Several finite temperature observables, including the renormalized Polyakov loop, the renormalized chiral condensate and the chiral susceptibility have been calculated. We also study the fluctuations and correlations of diffe…
SU(3) gauge theory with eight massless fundamental fermions seems to be near the conformal boundary, and is a candidate theory of walking technicolor. Along the series of study by LatKMI collaboration using HISQ fermions, S-parameter and vector decay constant, which provide important constraints in the model of electroweak symmetry breaking, are calculated for this theory. Use of various volumes allows a systematic investigation of finite volume effects. A strong sensitivity of the S-parameter to the volume is found.
We examine the taste structure of eigenvectors of the staggered-fermion Dirac operator. We derive a set of conditions on the eigenvectors of modes with small eigenvalues (near-zero modes), such that staggered fermions reproduce the 't Hooft vertex in the continuum limit. We also show that, assuming these conditions, the correlators of flavor-singlet mesons are free of contributions singular in $1/m$, where $m$ is the quark mass. This conclusion holds also when a single flavor of sea quark is represented by the fourth root of the staggered-fermion determinant. We then test numerically, using th…
We report on a sub-percent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of $N_f=2+1+1$ highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is Möbius Domain-Wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of $t_{\rm gf}=1$ in lattice units. The ensembles span four lattice spacings in the range $0.06 \lesssim a \lesssim 0.15$ fm, six pion masses in the range $130 \lesssim m_π\lesss…
We present studies of universal properties of the chiral phase transition in $N_f$=2+1 QCD based on the simulations using Highly Improved Staggered fermions on lattices with temporal extent $N_τ$=6. We analyze the quark mass and volume dependence of the chiral condensates and chiral susceptibilities in QCD with two degenerate light quarks and a strange quark. The strange quark mass is chosen to be fixed to its physical value ($m^{phy}_s$) and five values of light quark masses ($m_l$) that are varied in the interval 1/20$\gtrsim m_l/m^{phy}_s \gtrsim$1/80. Here various quark masses correspond t…
We present preliminary results for the contributions to the neutron EDM arising from the QCD $θ$-term, the Weinberg three-gluon and the quark chromo-EDM operators from our ongoing lattice calculations using clover valence quarks on the MILC HISQ lattices. We use the gradient-flow technique to smooth the lattices and renormalize the gluonic operators, and use the Schwinger source method to incorporate the quark chromo-EDM interactions in the quark propagator. For the QCD $θ$-term and the Weinberg three-gluon operator, we report results in the gradient-flow scheme from 8 ensembles at four lattic…
We calculate the renormalization constants (RCs) of vector, axial, vector scalar, pseudoscalar and tensor quark operators of the overlap valence fermion, on the 11 gauge ensembles with dynamical fermion using either Domain wall fermion~(DWF) action orHighly improved stagger quark~(HISQ) action at lattice spacings from 0.04 fm to 0.20 fm. We find the results under the $\overline{\text{MS}}$ scheme using either the RI/MOM or RI/SMOM scheme are consistent with each other, once the proper $a^2p^2$ extrapolation is applied and the systematic uncertainties are estimated cautiously. Our results with …
We present the vector, scalar and tensor renormalization constants (RCs) using overlap fermions with either regularization independent momentum subtraction (RI/MOM) or symmetric momentum subtraction (RI/SMOM) as the intermediate scheme on the lattice with lattice spacings $a$ from 0.04 fm to 0.12 fm. Our gauge field configurations from the MILC and RBC/UKQCD collaborations include sea quarks using either the domain wall or the HISQ action, respectively. The results show that RI/MOM and RI/SMOM can provide consistent renormalization constants to the $\overline{\textrm{MS}}$ scheme, after proper…
The quark chromo-electric dipole moment operator and the pseudo-scalar fermion bilinear with which it mixes under renormalization can both be included in a calculation of the electromagnetic form factor of the nucleon using the Schwinger source method. A preliminary calculation of these operators using clover quarks on HISQ lattices generated by MILC collaboration will be presented showing the quality of the signal in the correlators necessary for calculating the neutron electric dipole moment.
We investigate the temperature and density dependence of the color flux tube structure of dense two-color QCD with $N_f = 2$ Wilson fermions by using a lattice simulation. From Refs. [1] and [2], we have already clarified the rich phase structure in the low temperature region, including the hadronic and superfluid phases. In this study we measure the quark-antiquark potential and color flux tube profiles in such a low temperature region and find that even in the high density superfluid phase, the color electric field is squeezed into a flux tube as in the low density hadronic phase.
As a part of the project studying large $N_f$ QCD, the LatKMI Collaboration has been investigating the SU(3) gauge theory with four fundamental fermions (four-flavor QCD). The main purpose of studying four-flavor QCD is to provide a qualitative comparison to $N_f= 8$, $12$, $16$ QCD; however, a quantitative comparison to real-world QCD is also interesting. To make such comparisons more meaningful, it is desirable to use the same kind of lattice action consistently, so that qualitative difference of different theories are less affected by artifacts of lattice discretization. Here, we adopt the …
We calculate the fermion propagator and the quark-antiquark Green's functions for a complete set of ultralocal fermion bilinears, ${{\cal O}_Γ}$ [$Γ$: scalar (S), pseudoscalar (P), vector (V), axial (A) and tensor (T)], using perturbation theory up to one-loop and to lowest order in the lattice spacing. We employ the staggered action for fermions and the Symanzik Improved action for gluons. From our calculations we determine the renormalization functions for the quark field and for all ultralocal taste-singlet bilinear operators. The novel aspect of our calculations is that the gluon links whi…
We revisit Nambu's model of quark confinement by a tube of magnetic flux, with two additional features. The quarks are taken to be magnetic monopoles external to the tube, which seal the ends, and are also taken to be fermions. This ensures that the model is inconsistent unless there are at least two species of fermions being confined.
We report the calculation of the flavor-singlet scalar in the SU(3) gauge theory with the degenerate twelve fermions in the fundamental representation using a HISQ-type action at a fixed $β$. In order to reduce the large statistical error coming from the vacuum-subtracted disconnected correlator, we employ a noise reduction method and a large number of configurations. We observe that the flavor-singlet scalar is lighter than the pion in this theory from the calculations with the fermion bilinear and gluonic operators. This peculiar feature is considered to be due to the infrared conformality o…
We present high-statistics estimates of the isovector charges of the nucleon from four 2+1-flavor ensembles generated using Wilson-clover fermions with stout smearing and tree-level tadpole improved Symanzik gauge action at lattice spacings $a=0.114$ and $0.080$ fm and with $M_π\approx 315$ and 200 MeV. The truncated solver method with bias correction and the coherent source sequential propagator construction are used to cost-effectively achieve $O(10^5)$ measurements on each ensemble. Using these data, the analysis of two-point correlation functions is extended to include four states in the f…
We study the abelian color flux of two- and three-quark systems in the maximally abelian gauge in lattice QCD with dynamical fermions. We find that the abelian flux tube formed between quark and antiquark is very much the same as in quenched QCD up to quark separations of $R$$\sim$ 2fm. The profile of the color electric field in three-quark system suggests $Y$ ansatz, which might be interpreted as the result of the vacuum pressure in the confined phase. In order to clarify the flux structure, we investigate the color electric field of the three-quark system splittting the abelian gauge field i…
We study infrared conformality of the twelve-flavor QCD on the lattice. Utilizing the highly improved staggered quarks (HISQ) type action which is useful to study the continuum physics, we analyze the lattice data of the mass and the decay constant of a pseudoscalar meson and the mass of a vector meson as well at several values of lattice spacing and fermion mass. Our result is consistent with the conformal hypothesis for the mass anomalous dimension $γ_m \sim 0.4-0.5$.
