The Feynman-Hellmann theorem can be derived from the long Euclidean-time limit of correlation functions determined with functional derivatives of the partition function. Using this insight, we fully develop an improved method for computing matrix elements of external currents utilizing only two-point correlation functions. Our method applies to matrix elements of any external bilinear current, including nonzero momentum transfer, flavor-changing, and two or more current insertion matrix elements. The ability to identify and control all the systematic uncertainties in the analysis of the correlation functions stems from the unique time dependence of the ground-state matrix elements and the fact that all excited states and contact terms are Euclidean-time dependent. We demonstrate the utility of our method with a calculation of the nucleon axial charge using gradient-flowed domain-wall valence quarks on the Nf=2+1+1 MILC highly improved staggered quark ensemble with lattice spacing and pion mass of approximately 0.15 fm and 310 MeV respectively. We show full control over excited-state systematics with the new method and obtain a value of gA=1.213(26) with a quark-mass-dependent renormalization coefficient.

We report on the first application of the stochastic Laplacian Heaviside method for computing multiparticle interactions with lattice QCD to the two-nucleon system. Like the Laplacian Heaviside method, this method allows for the construction of interpolating operators which can be used to construct a set of positive-definite two-nucleon correlation functions, unlike nearly all other applications of lattice QCD to two nucleons in the literature. It also allows for a variational analysis in which optimal linear combinations of the interpolating operators are formed that couple predominantly to the eigenstates of the system. Utilizing such methods has become of paramount importance to help resolve the discrepancy in the literature on whether two nucleons in either isospin channel form a bound state at pion masses heavier than physical, with the discrepancy persisting even in the SU(3)-flavor-symmetric point with all quark masses near the physical strange quark mass. This is the first in a series of papers aimed at resolving this discrepancy. In the present work, we employ the stochastic Laplacian Heaviside method without a hexaquark operator in the basis at a lattice spacing of a≈0.086 fm, lattice volume of L=48a≈4.1 fm and pion mass mπ≈714 MeV. With this setup, the observed spectrum of two-nucleon energy levels strongly disfavors the presence of a bound state in either the deuteron or dineutron channel.

We report on salient features of a mixed lattice QCD action using valence Möbius domain-wall fermions solved on the dynamical Nf=2+1+1 highly improved staggered quark sea-quark 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 highly improved staggered quark 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 in Chroma. We provide tuned parameters of the action and performance of QUDA using ensembles with the lattice spacings a≃{0.15,0.12,0.09} fm and pion masses mπ≃{310,220,130} MeV. We have additionally generated two new ensembles with a∼0.12 fm and mπ∼{400,350} MeV. With a fixed flow time of tgf=1 in lattice units, the residual chiral symmetry breaking of the valence fermions is kept below 10% of the light quark mass on all ensembles, mres0.1×ml, with moderate values of the fifth dimension L5 and a domain-wall height M5≤1.3. As a benchmark calculation, we perform a continuum, infinite volume, physical pion and kaon mass extrapolation of FK±/Fπ± and demonstrate our results are independent of flow time and consistent with the FLAG determination of this quantity at the level of less than one standard deviation.

Excited state contamination remains one of the most challenging sources of systematic uncertainty to control in lattice QCD calculations of nucleon matrix elements and form factors: early time separations are contaminated by excited states and late times suffer from an exponentially bad signal-to-noise problem. High-statistics calculations at large time separations 1 fm are commonly used to combat these issues. In this work, focusing on gA, we explore the alternative strategy of utilizing a large number of relatively low-statistics calculations at short to medium time separations (0.2-1 fm), combined with a multistate analysis. On an ensemble with a pion mass of approximately 310 MeV and a lattice spacing of approximately 0.09 fm, we find this provides a more robust and economical method of quantifying and controlling the excited state systematic uncertainty. A quantitative separation of various types of excited states enables the identification of the transition matrix elements as the dominant contamination. The excited state contamination of the Feynman-Hellmann correlation function is found to reduce to the 1% level at approximately 1 fm while, for the more standard three-point functions, this does not occur until after 2 fm. Critical to our findings is the use of a global minimization, rather than fixing the spectrum from the two-point functions and using them as input to the three-point analysis. We find that the ground state parameters determined in such a global analysis are stable against variations in the excited state model, the number of excited states, and the truncation of early-time or late-time numerical data.

We report the results of a lattice quantum chromodynamics calculation of FK/Fπ using Möbius domain-wall fermions computed on gradient-flowed Nf=2+1+1 highly improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from 130 400 MeV, four lattice spacings of a∼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 functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that the a∼0.06 fm ensemble is helpful, but not necessary to achieve a subpercent determination of FK/Fπ. We also include an estimate of the strong isospin breaking corrections and arrive at a final result of FK+/Fπ+=1.1942(45) with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchmark for our lattice action. Combining our result with experimental measurements of the pion and kaon leptonic decays leads to a determination of |Vus|/|Vud|=0.2311(10).

We report on a subpercent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of Nf=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 tgf=1 in lattice units. The ensembles span four lattice spacings in the range 0.06a0.15 fm, six pion masses in the range 130mπ400 MeV and multiple lattice volumes. On each ensemble, the gradient-flow scales t0/a2 and w0/a and the omega baryon mass amω are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of t0=0.1422(14) fm and w0=0.1709(11) fm with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in both results is the stochastic uncertainty, though for t0 there are comparable continuum extrapolation uncertainties. For w0, there is a clear path for a few-per-mille uncertainty just through improved stochastic precision, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.