Determination of the Collins-Soper Kernel from Lattice QCD.

This Letter presents a determination of the quark Collins-Soper kernel, which relates transverse-momentum-dependent parton distributions (TMDs) at different rapidity scales, using lattice quantum chromodynamics (QCD). This is the first such determination with systematic control of quark mass, operator mixing, and discretization effects. Next-to-next-to-leading logarithmic matching is used to match lattice-calculable distributions to the corresponding TMDs. The continuum-extrapolated lattice QCD results are consistent with several recent phenomenological parametrizations of the Collins-Soper kernel and are precise enough to disfavor other parametrizations.

Lattice QCD Constraints on the Parton Distribution Functions of

The fraction of the longitudinal momentum of ^{3}He that is carried by the isovector combination of u and d quarks is determined using lattice QCD for the first time. The ratio of this combination to that in the constituent nucleons is found to be consistent with unity at the few-percent level from calculations with quark masses corresponding to m_{π}∼800 MeV. With a naive extrapolation to the physical quark masses, this constraint is consistent with, and more precise than, determinations from global nuclear parton distribution function fits through the nnnpdf framework. It is thus concretely demonstrated that lattice QCD calculations of light nuclei have imminent potential to enable more precise determinations of the u and d parton distributions in light nuclei and to reveal the QCD origins of the EMC effect.

Equivariant Flow-Based Sampling for Lattice Gauge Theory.

We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and find that, at small bare coupling, the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as hybrid Monte Carlo and heat bath.

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD.

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.

Proton-Proton Fusion and Tritium ß Decay from Lattice Quantum Chromodynamics.

The nuclear matrix element determining the pp→de^{+}ν fusion cross section and the Gamow-Teller matrix element contributing to tritium ß decay are calculated with lattice quantum chromodynamics for the first time. Using a new implementation of the background field method, these quantities are calculated at the SU(3) flavor-symmetric value of the quark masses, corresponding to a pion mass of m_{π}∼806 MeV. The Gamow-Teller matrix element in tritium is found to be 0.979(03)(10) at these quark masses, which is within 2σ of the experimental value. Assuming that the short-distance correlated two-nucleon contributions to the matrix element (meson-exchange currents) depend only mildly on the quark masses, as seen for the analogous magnetic interactions, the calculated pp→de^{+}ν transition matrix element leads to a fusion cross section at the physical quark masses that is consistent with its currently accepted value. Moreover, the leading two-nucleon axial counterterm of pionless effective field theory is determined to be L_{1,A}=3.9(0.2)(1.0)(0.4)(0.9) fm^{3} at a renormalization scale set by the physical pion mass, also agreeing within the accepted phenomenological range. This work concretely demonstrates that weak transition amplitudes in few-nucleon systems can be studied directly from the fundamental quark and gluon degrees of freedom and opens the way for subsequent investigations of many important quantities in nuclear physics.

Isotensor Axial Polarizability and Lattice QCD Input for Nuclear Double-ß Decay Phenomenology.

The potential importance of short-distance nuclear effects in double-ß decay is assessed using a lattice QCD calculation of the nn→pp transition and effective field theory methods. At the unphysical quark masses used in the numerical computation, these effects, encoded in the isotensor axial polarizability, are found to be of similar magnitude to the nuclear modification of the single axial current, which phenomenologically is the quenching of the axial charge used in nuclear many-body calculations. This finding suggests that nuclear models for neutrinoful and neutrinoless double-ß decays should incorporate this previously neglected contribution if they are to provide reliable guidance for next-generation neutrinoless double-ß decay searches. The prospects of constraining the isotensor axial polarizabilities of nuclei using lattice QCD input into nuclear many-body calculations are discussed.