Radiative corrections to the lattice gluon action for highly improved staggered quarks (HISQ) and the effect of such corrections on the static potential
A. Hart, G. M. von Hippel, R. R. Horgan
备注：
10 pages, 5 figures. Minor corrections suggested by referee
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 (r_1/a) on the coarsest asqtad improved staggered ensembles. This is the correct sign and magnitude to explain the scaling violations seen in Phi_B on dynamical lattice ensembles.
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 use perturbative Symanzik improvement to create a new staggered-quark action (HISQ) that has greatly reduced one-loop taste-exchange errors, no tree-level order a^2 errors, and no tree-level order (am)^4 errors to leading order in the quark's velocity v/c. We demonstrate with simulations that the resulting action has taste-exchange interactions that are at least 3--4 times smaller than the widely used ASQTAD action. We show how to estimate errors due to taste exchange by comparing ASQTAD and HISQ simulations, and demonstrate with simulations that such errors are no more than 1% when HISQ is…
We present preliminary simulation results for the I = 0 charmonium state $X(3872)(1^{++})$ and the I = 1 charmonium state $Z_c^+(3900)(1^{+-})$. The study is performed on gauge field configurations with 2+1+1 flavors of highly improved staggered sea quarks (HISQ) with clover (Fermilab interpretation) charm quarks and HISQ light valence quarks. Since the $X(3872)$ lies very close to the open charm $D \bar D^*$ threshold, we use a combination of $\bar c c$ and $D \bar D^* + \bar D D^*$ interpolating operators. For the $Z_c^+(3900)$ we use a combination of $J/ψπ$ and $D \bar D^* + \bar D D^*$ cha…
We report on numerical experiments using deflation to compute quark propagators for the highly improved staggered quark (HISQ) action. The method is tested on HISQ gauge configurations, generated by the MILC collaboration, with lattice spacings of 0.15 fm, with a range of volumes, and sea quark masses down to the physical quark mass.
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 report preliminary results on the chiral and deconfinement aspects of the QCD transition at finite temperature using the Highly Improved Staggered Quark (HISQ) action on lattices with temporal extent of N_τ=6 and 8. The chiral aspects of the transition are studied in terms of quark condensates and the disconnected chiral susceptibility. We study the deconfinement transition in terms of the strange quark number susceptibility and the renormalized Polyakov loop. We made continuum estimates for some quantities and find reasonably good agreement between our results and the recent continuum extr…
We report on a calculation of $B_c$ ground state and radial excitation energies, obtained from heavy-charm highly improved staggered quark (HISQ) correlators computed on MILC gauge ensembles, with lattice spacings down to $a=0.044$ fm. Using HISQ valence quarks on progressively finer lattices allows us to simulate up to the $b$-quark mass. In particular we focus on the $B_c(2S)$ energy, which we compare with O(α_s)-improved non-relativistic QCD results computed on the same ensembles and recent experimental results from ATLAS.
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 calculate the one loop renormalisation parameters for the heavy-light axial-vector and vector currents using lattice perturbation theory. We use NonRelativistic QCD (NRQCD) heavy quarks and the Highly Improved Staggered Quark (HISQ) action for the light quarks. We present results for heavy-light currents with massless HISQ quarks and briefly discuss the extension to heavy-heavy currents with massive HISQ quarks.
We match the continuum and lattice axial vector and vector currents at one loop in perturbation theory. For the heavy quarks we use the nonrelativistic QCD (NRQCD) action and for the light quarks the Highly Improved Staggered Quark (HISQ) action. We present results for both massless and massive HISQ quarks and as part of the matching procedure we include a discussion of the one loop HISQ renormalisation parameters.
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…
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…
The Fermilab Lattice and MILC collaborations have shown in one-loop lattice QCD perturbation theory that the renormalization constants of vector and axial-vector mixed clover-asqtad currents are closely related to the product of those for clover-clover and asqtad-asqtad (local) vector currents. To be useful for future higher precision calculations this relationship must be valid beyond one-loop and very general. We test its validity nonperturbatively using clover and Highly Improved Staggered (HISQ) strange quarks, utilising the absolute normalization of the HISQ temporal axial current. We fin…
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 present results from our simulations of quantum chromodynamics (QCD) with four flavors of quarks: u, d, s, and c. These simulations are performed with a one-loop Symanzik improved gauge action, and the highly improved staggered quark (HISQ) action. We are generating gauge configurations with four values of the lattice spacing ranging from 0.06 fm to 0.15 fm, and three values of the light quark mass, including the value for which the Goldstone pion mass is equal to the physical pion mass. We discuss simulation algorithms, scale setting, taste symmetry breaking, and the autocorrelations of va…
We present the status of our ongoing calculation of the zero-recoil form factor for the semileptonic decay $\bar{B}^0\rightarrow D^{*+}l^-\barν$ using lattice QCD with 2+1+1 flavours of highly improved staggered quarks in the sea (the MILC HISQ configurations) and using non-relativistic QCD for the bottom quark. We combine our result for $ F(1)$ with the latest HFAG average of $η_{EW} F(1)|V_{cb}|$ to get a preliminary value for $|V_{cb}|$.
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 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…
We report on progress of a lattice QCD calculation of the $B\to Dlν$ and $B_s\to D_s lν$ semileptonic form factors. We use a relativistic staggered action (HISQ) for light and charm quarks, and an improved non-relativistic (NRQCD) action for bottom, on the second generation MILC ensembles.
We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. We performed calculations using asqtad and HISQ/tree actions using lattices with temporal extent N_tau=6, 8 and 12 allowing to control the approach to the continuum limit. We analyze the chiral transition in terms of universal O(N) scaling functions. From peaks in the scaling functions we perform a simultaneous continuum extrapolation for HISQ/tree and asqtad to derive the critical temperature, T_c= 157 +/- 6 MeV.
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.
We describe a computation of the contribution to the anomalous magnetic moment of the muon from the disconnected part of the hadronic vacuum polarization. We use the highly-improved staggered quark (HISQ) formulation for the current density with gauge configurations generated with four flavors of HISQ sea quarks. The computation is performed by stochastic estimation of the current density using the truncated solver method combined with deflation of low-modes. The parameters are tuned to minimize the computational cost for a given target uncertainty in the current-current correlation function. …
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…
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）
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…
We compare correlators for pseudoscalar and vector mesons made from valence strange quarks using the clover quark and highly improved staggered quark (HISQ) formalisms in full lattice QCD. We use fully nonperturbative methods to normalise vector and axial vector current operators made from HISQ quarks, clover quarks and from combining HISQ and clover fields. This allows us to test expectations for the renormalisation factors based on perturbative QCD, with implications for the error budget of lattice QCD calculations of the matrix elements of clover-staggered $b$-light weak currents, as well a…
In HISQ simulations by the MILC and Fermilab Lattice collaborations, both the light quarks and the charm quark are staggered. We extend staggered chiral perturbation theory (\schpt) to include such all-staggered heavy-light mesons. We assume that the heavy quark action is sufficiently improved that we may take $a m_Q <<1$ (where $m_Q$ is the heavy quark mass), but also that $m_Q>>Λ_{QCD}$ so that a continuum heavy quark expansion is appropriate. Using this \schpt, the leptonic decay constant of the heavy-light meson is calculated at next-to-leading-order. The pattern of taste splittings in the…
We give an update on the status of the Fermilab Lattice-HPQCD-MILC calculation of the contribution to the muon's anomolous magnetic moment from the light-quark, connected hadronic vacuum polarization. We present preliminary, blinded results in the intermediate window for this contribution, $a_{μ, \textrm{W}}^{ll}$. The calculation is performed on $N_f =2+1+1$ highly-improved staggered quark (HISQ) ensembles from the MILC collaboration with physical pion mass at four lattice spacings between 0.15 fm and 0.06 fm. We also present preliminary results for a study of the two-pion contributions to th…
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 fit lattice-QCD data for light-pseudoscalar masses and decay constants, from HISQ configurations generated by MILC, to SU(3) staggered chiral perturbation theory. At present such fits have rather high values of chi^2/d.o.f., possibly due to the lack of ensembles with lighter-than-physical sea strange-quark masses. We propose solutions to this problem for future work. We also perform simple linear interpolations near the physical point on two ensembles with different lattice spacings, and obtain the preliminary result (f_K / f_pi)^phys = 1.1872(41) in the continuum limit.
We describe recent progress on generation of gauge configurations using the Highly Improved Staggered Quark (HISQ) action that was designed by the HPQCD/UKQCD collaboration. The HISQ action requires two levels of smearing with a reunitarization of the links before the second smearing. We describe how we deal with the occurrence of occasional large forces arising from the reunitarization step. The MILC collaboration is currently generating ensembles with approximate lattice spacings of 0.15, 0.12, 0.09, and 0.06 fm, with the strange and charm quark masses close to their physical values and the …
We present our methods to fit the two point correlators for light, strange, and charmed pseudoscalar meson physics with the highly improved staggered quark (HISQ) action. We make use of the least-squares fit including the full covariance matrix of the correlators and including Gaussian constraints on some parameters. We fit the correlators on a variety of the HISQ ensembles. The lattice spacing ranges from 0.15 fm down to 0.06 fm. The light sea quark mass ranges from 0.2 times the strange quark mass down to the physical light quark mass. The HISQ ensembles also include lattices with different …
The calculation of force is most difficult part in lattice Quantum Chromodynamics (QCD). This lecture gives the details of the force calculation in one-loop Symanzik improved action, Wilson fermion with clover term, asqtad fermion, HISQ fermion, rooted staggered fermion, smeared fermion, staggered Wilson fermion, overlap fermion and domain wall fermion. The even-odd precondition are also considered in these calculations.
In highly improved staggered quark (HISQ) simulations by the HPQCD, MILC, and Fermilab Lattice collaborations, both the light quarks and the charm quark are staggered. We extend chiral perturbation theory for staggered quarks to include such all-staggered heavy-light mesons. We assume that the heavy quark action is sufficiently improved that we may take $a m_Q <<1$ (where $m_Q$ is the heavy quark mass), but also that $m_Q>>Λ_{QCD}$ so that a continuum heavy quark expansion is appropriate. We develop this effective chiral theory through next-to-leading order, and use it to study the pattern of …
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 present updated results for the light-quark connected part of the leading hadronic contribution to the muon $g-2$ from configurations with 2+1+1 flavors of HISQ quarks using the time-momentum representation of the electromagnetic current correlator. We have added statistics on two ensembles as well as a fourth lattice spacing using configurations that have been generated by the MILC collaboration at the physical pion mass. Additionally we account for the leading finite-volume and taste-breaking effects using Staggered Chiral Perturbation Theory at NNLO.
We present progress on an ongoing calculation of the $B_s\to D_s^{(*)} l ν$ form factors calculated on the $n_f=2+1+1$ MILC ensembles and using the Highly Improved Staggered Quark action for all valence quarks. We perform the calculation at a range of $b$ quark masses (and lattice spacings) so that we can extrapolate to the physical $b$-quark mass.
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 present the results of our perturbative calculations of the static quark potential, small Wilson loops, the static quark self energy, and the mean link in Landau gauge. These calculations are done for the one loop Symanzik improved gluon action, and the improved staggered quark action.
The current-current correlator method has been used successfully to obtain very accurate results for quark masses and the coupling alpha_s. The calculations were done using Highly Improved Staggered Quarks (HISQ) and heavy-heavy meson correlators. We now extend this work to the significantly more challenging heavy-light case, reporting the first results here. The aim is to determine nonperturbative Z factors for NRQCD heavy-light currents, but first we test the method in the HISQ case where Z=1.
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.
The HPQCD collaboration has used radiatively-improved NonRelativistic QCD (NRQCD) for $b$ quarks in bottomonium to determine the decay rate of $Υ$ and $Υ^\prime$ mesons to leptons in lattice QCD. Using time-moments of vector bottomonium current-current correlators, we are also able to determine the $b$ quark mass in the $\overline{\mathrm{MS}}$ scheme. We use the same NRQCD $b$ quarks and Highly Improved Staggered Quark (HISQ) light quarks -- with masses down to their physical values -- to give a complete picture of heavy-light meson decay constants including those for vector mesons. We also s…
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…
The nucleon axial form factor is a dominant contribution to errors in neutrino oscillation studies. Lattice QCD calculations can help control theory errors by providing first-principles information on nucleon form factors. In these proceedings, we present preliminary results on a blinded calculation of $g_A$ and the axial form factor using HISQ staggered baryons with 2+1+1 flavors of sea quarks. Calculations are done using physical light quark masses and are absolutely normalized. We discuss fitting form factor data with the model-independent $z$ expansion parametrization.
We report progress on calculating the contribution to the anomalous magnetic moment of the muon from the disconnected hadronic diagrams with light and strange quarks and the valence QED contribution to the connected diagrams. The lattice QCD calculations use the highly-improved staggered quark (HISQ) formulation. The gauge configurations were generated by the MILC Collaboration with four flavors of HISQ sea quarks with physical sea-quark masses.
We present recent results on the QCD equation of state with 2+1+1 flavors of highly improved staggered quarks (HISQ). We focus on three sets of ensembles with temporal extent 6, 8 and 10, that reach up to temperatures of 967, 725 and 580 MeV, respectively. The strange and charm quark masses are tuned to the physical values and the light quarks mass is set to one fifth of the strange. This corresponds to a Goldstone pion of about 300 MeV.
We report on the status of the Fermilab-MILC calculation of the form factor f_+^{K pi}(0), needed to extract the CKM matrix element |V_{us}| from experimental data on K semileptonic decays. The HISQ formulation is used in the simulations for the valence quarks, while the sea quarks are simulated with the asqtad action (MILC N_f=2+1 configurations). We discuss the general methodology of the calculation, including the use of twisted boundary conditions to get values of the momentum transfer close to zero and the different techniques applied for the correlators fits. We present initial results fo…
We present an update of the Fermilab Lattice and MILC Collaborations project to compute the form factors for semileptonic $B_{(s)}$-meson decays. Our calculation uses the highly improved staggered quark (HISQ) action for sea and valence quarks, and ensembles with up, down, strange, and charm quarks in the sea. Using a highly improved action with the MILC Collaboration's gauge ensembles with lattice spacings down to $a\approx0.03$ fm, allows the heavy valence quarks to be treated with the same discretization as the light and strange quarks. This unified treatment of the valence quarks allows fo…
We have developed two methods for handling $b$ quarks in lattice QCD. One uses NRQCD (now improved to include radiative corrections) and the other uses Highly Improved Staggered Quarks (HISQ), extrapolating to the $b$ quark from lighter masses and using multiple lattice spacings to control discretisation errors. Comparison of results for the two different methods gives confidence in estimates of lattice QCD systematic errors, since they are very different in these two cases. Here we show results for heavyonium hyperfine splittings and vector current-current correlator moments using HISQ quarks…
We present recent results from lattice simulations of 2+1 flavors of improved staggered fermions at zero baryon number density near the high temperature crossover. Included are new results from simulations of asqtad fermions at Nt = 12 and a nearly physical Goldstone pion mass and from simulations of HISQ fermions at Nt = 6 and 8. We focus on observables sensitive to chiral symmetry and confinement. A companion HotQCD talk discusses the effects of staggered-fermion taste-symmetry breaking on thermodynamic quantities.
We present results of the first lattice QCD calculations of $B_c \to B_s$ and $B_c \to B_d$ weak matrix elements. Results are derived from correlation functions computed on MILC Collaboration gauge configurations with lattice spacings between $0.12$ [fm] and $0.06$ [fm] including 2+1+1 flavours of dynamical sea quarks in the Highly Improved Staggered Quark (HISQ) formalism. Form factors across the entire physical $q^2$ range are then extracted and extrapolated to the physical-continuum limit. Two different formalisms are employed for the bottom quark: non-relativistic QCD (NRQCD) and heavy-HIS…
