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.

Parton Distribution Functions from Ioffe Time Pseudodistributions from Lattice Calculations: Approaching the Physical Point.

We present results for the unpolarized parton distribution function of the nucleon computed in lattice QCD at the physical pion mass. This is the first study of its kind employing the method of Ioffe time pseudodistributions. Beyond the reconstruction of the Bjorken-x dependence, we also extract the lowest moments of the distribution function using the small Ioffe time expansion of the Ioffe time pseudodistribution. We compare our findings with the pertinent phenomenological determinations.

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.

Unitary Limit of Two-Nucleon Interactions in Strong Magnetic Fields.

Two-nucleon systems are shown to exhibit large scattering lengths in strong magnetic fields at unphysical quark masses, and the trends toward the physical values indicate that such features may exist in nature. Lattice QCD calculations of the energies of one and two nucleons systems are performed at pion masses of m_{π}∼450 and 806 MeV in uniform, time-independent magnetic fields of strength |B|∼10^{19}-10^{20} G to determine the response of these hadronic systems to large magnetic fields. Fields of this strength may exist inside magnetars and in peripheral relativistic heavy ion collisions, and the unitary behavior at large scattering lengths may have important consequences for these systems.

Ab initio Calculation of the np→dγ Radiative Capture Process.

Lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process np→dγ, and the photo-disintegration processes γ^{(*)}d→np. In nuclear potential models, such contributions are described by phenomenological meson-exchange currents, while in the present work, they are determined directly from the quark and gluon interactions of QCD. Calculations of neutron-proton energy levels in multiple background magnetic fields are performed at two values of the quark masses, corresponding to pion masses of m_{π}~450 and 806 MeV, and are combined with pionless nuclear effective field theory to determine the amplitudes for these low-energy inelastic processes. At m_{π}~806 MeV, using only lattice QCD inputs, a cross section σ^{806 MeV}~17 mb is found at an incident neutron speed of v=2,200 m/s. Extrapolating the short-distance contribution to the physical pion mass and combining the result with phenomenological scattering information and one-body couplings, a cross section of σ^{lqcd}(np→dγ)=334.9(+5.2-5.4) mb is obtained at the same incident neutron speed, consistent with the experimental value of σ^{expt}(np→dγ)=334.2(0.5) mb.

Multipion systems in lattice QCD and the three-pion interaction.

The ground-state energies of 2, 3, 4, and 5 pi(+)'s in a spatial volume V approximately (2.5 fm)(3) are computed with lattice QCD. By eliminating the leading contribution from three-pi(+) interactions, particular combinations of these n-pi(+) ground-state energies provide precise extractions of the pi(+)pi(+) scattering length in agreement with that obtained from calculations involving only two pi(+)'s. The three-pi(+) interaction can be isolated by forming other combinations of the n-pi(+) ground-state energies. We find a result that is consistent with a repulsive three-pi(+) interaction for m_(pi) less, similar352 MeV.