Gradient flow and scale setting on MILC HISQ ensembles

Abstract

We report on a scale determination with gradient-flow techniques on the N f = 2 + 1 + 1 HISQ ensembles generated by the MILC collaboration. The ensembles include four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales √ t 0 /a and w 0 /a and their tree-level improvements, √ t 0,imp and w 0,imp , are computed on each ensemble using Symanzik flow and the cloverleaf definition of the energy density E. Using a combination of continuum chiral perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We determine the scales √ t 0 = 0.1416( systematic errors. The precision of w 0 and √ t 0 is comparable to or more precise than the best previous estimates, respectively. We then find the continuum mass-dependence of √ t 0 and w 0 , which will be useful for estimating the scales of new ensembles. We also estimate the integrated autocorrelation length of E(t) . For long flow times, the autocorrelation length of E appears to be comparable to that of the topological charge.

New methods for B meson decay constants and form factors from lattice NRQCD

“…(23) we give an expansion to the same order for the combination of quark mass and pseudoscalar density, m b P, in terms of the same NRQCD-HISQ currents [23,24] …”

“…They are "second-generation" MILC configurations [23,24] using a gluon action fully corrected through α s a 2 [25] and HISQ quarks [8] with u, d, s. and c (n f ¼ 2 þ 1 þ 1) flavors in the sea. They include multiple values of the lattice spacing and multiple values of the u=d (taken to be degenerate) sea quark mass varying from one-fifth of the s quark mass down to the physical value.…”

B-meson decay constants: A more complete picture from full lattice QCD

“…The gluon field configurations that we use were generated by the MILC Collaboration [12,13]. These are n f ¼ 2 þ 1 þ 1 configurations that include the effect of light (up and down), strange and charm quarks in the sea with the HISQ action [7,14] and a Symanzik improved gluon action with coefficients correct through Oðα s a 2 ; n f α s a 2 Þ [15].…”

“…The values used in this calculation are the same as those in [5,10] and given in Table III along with other parameters. We end this section with a brief discussion of the assessment and removal of discretization errors in a calculation that uses NRQCD [6]. A typical procedure to [12,13]. β is the bare gauge coupling, a ϒ is the lattice spacing as determined by the ϒð2S − 1SÞ splitting in [6], where the three errors are statistics, NRQCD systematics and experiment.…”

Decay constants $f_B$ and $f_{B_s}$ from HISQ simulations

“…To achieve high precision, we employ highly improved staggered (HISQ) quarks [1,2,3] with masses heavier than the charm quark mass and adopt the HPQCD strategy of extrapolating to the bquark mass [4]. The extrapolation is guided by heavy-quark effective theory, which we incorporate in our chiral/continuum analysis.…”