Search

Advances in machine learning methods provide tools that have broad applicability in scientific research. These techniques are being applied across the diversity of nuclear physics research topics, leading to advances that will facilitate scientific discoveries and societal applications. This Colloquium provides a snapshot of nuclear physics research, which has been transformed by machine learning techniques.

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).

Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and ^{3}He at SU(3)-symmetric values of the quark masses corresponding to a pion mass m_{π}∼806  MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elements of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O(10%), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.

The role of gluons in the structure of the nucleon and light nuclei is investigated using lattice quantum chromodynamics (QCD) calculations. The first moment of the unpolarized gluon distribution is studied in nuclei up to atomic number A=3 at quark masses corresponding to pion masses of mπ∼450 and 806 MeV. Nuclear modification of this quantity defines a gluonic analogue of the EMC effect and is constrained to be less than ∼10% in these nuclei. This is consistent with expectations from phenomenological quark distributions and the momentum sum rule. In the deuteron, the combination of gluon distributions corresponding to the b1 structure function is found to have a small first moment compared with the corresponding momentum fraction. The first moment of the gluon transversity structure function is also investigated in the spin-1 deuteron, where a nonzero signal is observed at mπ∼806 MeV. This is the first indication of gluon contributions to nuclear structure that can not be associated with an individual nucleon.

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.

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 a lattice QCD calculation of the nucleon axial charge, $g_A$,using M\"{o}bius Domain-Wall fermions solved on the dynamical $N_f=2+1+1$ HISQensembles after they are smeared using the gradient-flow algorithm. Thecalculation is performed with three pion masses, $m_\pi\sim\{310,220,130\}$MeV. Three lattice spacings ($a\sim\{0.15,0.12,0.09\}$ fm) are used with theheaviest pion mass, while the coarsest two spacings are used on the middle pionmass and only the coarsest spacing is used with the near physical pion mass. Onthe $m_\pi\sim220$ MeV, $a\sim0.12$ fm point, a dedicated volume study isperformed with $m_\pi L \sim \{3.22,4.29,5.36\}$. Using a new strategymotivated by the Feynman-Hellmann Theorem, we achieve a precise determinationof $g_A$ with relatively low statistics, and demonstrable control over theexcited state, continuum, infinite volume and chiral extrapolation systematicuncertainties, the latter of which remains the dominant uncertainty. Our finaldetermination at 2.6\% total uncertainty is $g_A = 1.278(21)(26)$, with thefirst uncertainty including statistical and systematic uncertainties fromfitting and the second including model selection systematics related to thechiral and continuum extrapolation. The largest reduction of the seconduncertainty will come from a greater number of pion mass points as well as moreprecise lattice QCD results near the physical pion mass.