Using forward matrix elements of local leading-twist operators, we present a determination of the isovector third Mellin moments < x^2 > of nucleon unpolarized, polarized, and transversity parton distribution functions. Two lattice QCD ensembles at the physical pion mass are used, which were generated using a tree-level Symanzik-improved gauge action and 2+1 flavor tree-level improved Wilson Clover fermions coupling via 2-level HEX-smearing. Leveraging a wide set of operators, two extraction methods for the matrix elements, and the automatic inclusion of model uncertainties via bootstrapped model averages, we extract values of the third Mellin moments. This is the first direct calculation of these observables performed at the physical pion mass.

The decay B→ρℓν[over ¯] is an attractive process for determining the magnitude of the smallest Cabibbo-Kobayashi-Maskawa matrix element, |V_{ub}|, and can provide new insights into the origin of the long-standing exclusive-inclusive discrepancy in determinations of this standard-model parameter. This requires a nonperturbative QCD calculation of the B→ρ form factors V, A_{0}, A_{1}, and A_{12}. The unstable nature of the ρ resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the B→ρ form factors in which the ρ is treated properly as a resonance in P-wave ππ scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the B→ππ form factors as a function of both momentum transfer and ππ invariant mass, and then analytically continue to the ρ resonance pole. This calculation is performed with 2+1 dynamical quark flavors at a pion mass of approximately 320 MeV, and demonstrates a clear path toward results at the physical point.

The decay $B \to \rho \ell \bar{\nu}$ is an attractive process for determining the magnitude of the smallest CKM matrix element, $|V_{ub}|$, and can provide new insights into the origin of the long-standing exclusive-inclusive discrepancy in determinations of this Standard-Model parameter. This requires a nonperturbative QCD calculation of the $B \to \rho$ form factors $V$, $A_0$, $A_1$, and $A_{12}$. The unstable nature of the $\rho$ resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the $B \to \rho$ form factors in which the $\rho$ is treated properly as a resonance in $P$-wave $\pi \pi$ scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the $B \to \pi \pi$ form factors as a function of both momentum transfer and $\pi \pi$ invariant mass, and then analytically continue to the $\rho$ resonance pole. This calculation is performed with $2+1$ dynamical quark flavors at a pion mass of approximately 320 MeV, and demonstrates a clear path toward results at the physical point.

The decay B→ρℓν[over ¯] is an attractive process for determining the magnitude of the smallest Cabibbo-Kobayashi-Maskawa matrix element, |V_{ub}|, and can provide new insights into the origin of the long-standing exclusive-inclusive discrepancy in determinations of this standard-model parameter. This requires a nonperturbative QCD calculation of the B→ρ form factors V, A_{0}, A_{1}, and A_{12}. The unstable nature of the ρ resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the B→ρ form factors in which the ρ is treated properly as a resonance in P-wave ππ scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the B→ππ form factors as a function of both momentum transfer and ππ invariant mass, and then analytically continue to the ρ resonance pole. This calculation is performed with 2+1 dynamical quark flavors at a pion mass of approximately 320 MeV, and demonstrates a clear path toward results at the physical point.

The decay B →ρℓν̅ is an attractive process for determining the magnitude of the smallest CKM matrix element, |V_ub|, and can provide new insights into the origin of the long-standing exclusive-inclusive discrepancy in determinations of this Standard-Model parameter. This requires a nonperturbative QCD calculation of the B →ρ form factors V, A_0, A_1, and A_12. The unstable nature of the ρ resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the B →ρ form factors in which the ρ is treated properly as a resonance in P-wave ππ scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the B →ππ form factors as a function of both momentum transfer and ππ invariant mass, and then analytically continue to the ρ resonance pole. This calculation is performed with 2+1 dynamical quark flavors at a pion mass of approximately 320 MeV, and demonstrates a clear path toward results at the physical point.

$V_{ub}$ is the smallest and least known of all CKM matrix elements; it is currently determined primarily through the exclusive process $B\to\pi\ell\bar{\nu}$, and additional channels to determine it are welcomed by the community. We will present progress toward a lattice QCD determination of $|V_{ub}|$ from the $B\to\pi\pi\ell\bar{\nu}$ process, where the $\pi\pi$ system is in a $P$-wave and features the $\rho(770)$ resonance as an enhancement. After an overview of the theoretical framework, we will discuss some preliminary results.

Lattice Quantum Chromodynamics (QCD) has significantly contributed to our understanding of the CKM matrix through precise determinations of hadronic matrix elements. With advancements in theoretical methodologies and computational resources, investigations can now extend to processes involving QCD-unstable hadrons such as the ρ and K^⋆(892). These resonances play vital roles in processes such as weak decays of B mesons, opening new avenues for exploration. Finite-volume lattice QCD techniques involving complex computational methods are used to determine the transition amplitudes. Here, we present preliminary results for B→ρℓν̅.

Quark orbital angular momentum in the proton is evaluated via a Lattice QCD calculation of the second Mellin moment of the twist-3 generalized parton distribution $\widetilde{E}_{2T} $ in the forward limit. The connection between this approach to quark orbital angular momentum and approaches previously utilized in Lattice QCD calculations, via generalized transverse momentum-dependent parton distributions and via Ji's sum rule, is reviewed. This connection can be given in terms of Lorentz invariance and equation of motion relations. The calculation of the second Mellin moment of $\widetilde{E}_{2T} $ proceeds via a finite-momentum proton matrix element of a quark bilocal operator with a straight-line gauge connection and separation in both the longitudinal and transverse directions. The dependence on the former component serves to extract the second Mellin moment, whereas the dependence on the latter component provides a transverse momentum cutoff for the matrix element. Furthermore, a derivative of the matrix element with respect to momentum transfer in the forward limit is required, which is obtained using a direct derivative method. The calculation utilizes a clover fermion ensemble at pion mass 317 MeV. The resulting quark orbital angular momentum is consistent with previous evaluations through alternative approaches, albeit with greater statistical uncertainty using a comparable number of samples.

Previous Lattice QCD calculations of nucleon transverse momentum-dependent parton distributions (TMDs) focused on the case of transversely polarized nucleons, and thus did not encompass two leading-twist TMDs associated with longitudinal polarization, namely, the helicity TMD and the worm-gear TMD corresponding to transversely polarized quarks in a longitudinally polarized nucleon.Based on a definition of TMDs via hadronic matrix elements of quark bilocal operators containing staple-shaped gauge connections, TMD observables characterizing the aforementioned two TMDs are evaluated, utilizing an RBC/UKQCD domain wall fermion ensemble at the physical pion mass.

V_ub is the smallest and least known of all CKM matrix elements; the community currently determines its magnitude primarily through the exclusive process B→πℓν̅. Here we present our progress toward a lattice QCD determination of the V_ub matrix element from a novel transition – B→ππℓν̅ process, where the ππ system is in a P wave and scattering features the ρ(770) resonance as an enhancement. We perform our calculation on N_f=2+1 isotropic clover fermions on a lattice of L≈ 3.6 fm and a pion mass of ≈ 320 MeV; for the b-quark we use the anisotropic clover action. After a brief overview of the theoretical framework, we will discuss some preliminary results.

We present a Lattice QCD calculation of the second Mellin moments of the nucleon axial, vector and tensor parton distribution functions (PDFs). The calculation is performed at the physical pion mass with two different lattice spacings, and includes both zero and non-zero nucleon momenta. In our preliminary analysis, we identify operators that greatly reduce excited-state contamination.

The low-energy spectrum and scattering of two-nucleon systems are studied with lattice quantum chromodynamics using a variational approach. A wide range of interpolating operators are used: dibaryon operators built from products of plane-wave nucleons, hexaquark operators built from six localized quarks, and quasi-local operators inspired by two-nucleon bound-state wavefunctions in low-energy effective theories. Sparsening techniques are used to compute the timeslice-to-all quark propagators required to form correlation-function matrices using products of these operators. Projection of these matrices onto irreducible representations of the cubic group, including spin-orbit coupling, is detailed. Variational methods are applied to constrain the low-energy spectra of two-nucleon systems in a single finite volume with quark masses corresponding to a pion mass of 806 MeV. Results for S- and D-wave phase shifts in the isospin singlet and triplet channels are obtained under the assumption that partial-wave mixing is negligible. Tests of interpolating-operator dependence are used to investigate the reliability of the energy spectra obtained and highlight both the strengths and weaknesses of variational methods. These studies and comparisons to previous studies using the same gauge-field ensemble demonstrate that interpolating-operator dependence can lead to significant effects on the two-nucleon energy spectra obtained using both variational and non-variational methods, including missing energy levels and other discrepancies. While this study is inconclusive regarding the presence of two-nucleon bound states at this quark mass, it provides robust upper bounds on two-nucleon energy levels that can be improved in future calculations using additional interpolating operators and is therefore a step toward reliable nuclear spectroscopy from the underlying Standard Model of particle physics.

Moments of the quark density, helicity, and transversity distributions are calculated in unquenched lattice QCD. Calculations of proton matrix elements of operators corresponding to these moments through the operator product expansion have been performed on 163 × 32 lattices for Wilson fermions at β = 5.6 using configurations from the SESAM collaboration and at β = 5.5 using configurations from SCRI. One-loop perturbative renormalization corrections are included. At quark masses accessible in present calculations, there is no statistically significant difference between quenched and full QCD results, indicating that the contributions of quark-antiquark excitations from the Dirac Sea are small. Close agreement between calculations with cooled configurations containing essentially only instantons and the full gluon configurations indicates that quark zero modes associated with instantons play ∗present address DESY/Zeuthen

Generalized transverse momentum-dependent parton distributions (GTMDs) provide a comprehensive framework for imaging the internal structure of the proton. In particular, by encoding the simultaneous distribution of quark transverse positions and momenta, they allow one to directly access longitudinal quark orbital angular momentum, and, moreover, to correlate it with the quark helicity. The relevant GTMD is evaluated through a lattice calculation of a proton matrix element of a quark bilocal operator (the separation in which is Fourier conjugate to the quark momentum) featuring a momentum transfer (which is Fourier conjugate to the quark position), as well as the Dirac structure appropriate for capturing the quark helicity. The weighting by quark transverse position requires a derivative with respect to momentum transfer, which is obtained in unbiased fashion using a direct derivative method. The lattice calculation is performed directly at the physical pion mass, using domain wall fermions to mitigate operator mixing effects. Both the Jaffe-Manohar as well as the Ji quark spin-orbit correlations are extracted, yielding evidence for a strong quark spin-orbit coupling in the proton.

Giorgio Silvi, 2, ∗ Srijit Paul, Constantia Alexandrou, 5 Stefan Krieg, 2 Luka Leskovec, 7 Stefan Meinel, John Negele, Marcus Petschlies, Andrew Pochinsky, Gumaro Rendon, Sergey Syritsyn, 13 and Antonino Todaro 14, 2 Forschungszentrum Jülich GmbH, Jülich Supercomputing Centre, 52425 Jülich, Germany Faculty of Mathematics und Natural Sciences, University of Wuppertal Wuppertal-42119, Germany Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany Department of Physics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA Department of Physics, Old Dominion University, Norfolk, VA 23529, USA Department of Physics, University of Arizona, Tucson, AZ 85721, USA Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Helmholtz-Institut für Strahlenund Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Nußallee 14-16, 53115 Bonn, Germany Department of Physics, Brookhaven National Laboratory, Upton, NY 11973, USA Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794, USA RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA Dipartimento di Fisica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Rome, Italy (Dated: January 5, 2021)

Modern advances in algorithms for lattice QCD calculations have steadily driven down the resources required to generate gauge field ensembles and calculate quark propagators, such that, in cases relevant to nuclear physics, performing quark contractions to assemble correlation functions from propagators has become the dominant cost. This work explores a propagator sparsening algorithm for forming correlation functions describing multi-hadron systems, such as light nuclei, with reduced computational cost. The algorithm constructs correlation functions from sparsened propagators defined on a coarsened lattice geometry, where the sparsened propagators are obtained from propagators computed on the full lattice. This algorithm is used to study the low-energy QCD ground-state spectrum using a single Wilson-clover lattice ensemble with $m_{\pi} \approx 800$ MeV. It is found that the extracted ground state masses and binding energies, as well as their statistical uncertainties, are consistent when determined from correlation functions constructed from sparsened and full propagators. In addition, while evidence of modified couplings to excited states is observed in sparsened correlation functions, it is demonstrated that these effects can be removed, if desired, with an inexpensive modification to the sparsened estimator.

We report on our investigation of low-energy pion-nucleon scattering from lattice QCD with Wilson type fermions. Our focus is on the isospin I = 3/2 channel, which couples to the Delta resonance. We discuss our calculations aiming at the extraction of the Delta resonance mass, width and effective coupling at pion mass 250 MeV, using the Lüscher finite-volume method to extract the phase shift δJ=3/2,l=1.