Initial nucleon structure results with chiral quarks at the physical point

We report initial nucleon structure results computed on lattices with 2+1 dynamical M\"obius domain wall fermions at the physical point generated by the RBC and UKQCD collaborations. At this stage, we evaluate only connected quark contributions. In particular, we discuss the nucleon vector and axial-vector form factors, nucleon axial charge and the isovector quark momentum fraction. From currently available statistics, we estimate the stochastic accuracy of the determination of $g_A$ and $_{u-d}$ to be around 10%, and we expect to reduce that to 5% within the next year. To reduce the computational cost of our calculations, we extensively use acceleration techniques such as low-eigenmode def…

Nucleon form factors with light Wilson quarks

Jeremy Green∗,a† Michael Engelhardt,b Stefan Krieg,cd Stefan Meinel,a John Negele,a Andrew Pochinskya and Sergey Syritsyne aCenter for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA bDepartment of Physics, New Mexico State University, Las Cruces, New Mexico 88003, USA cBergische Universitat Wuppertal, D-42119 Wuppertal, Germany dIAS, Julich Supercomputing Centre, Forschungszentrum Julich, D-52425 Julich, Germany eLawrence Berkeley National Laboratory, Berkeley, California 94720, USA E-mail: green@kph.uni-mainz.de, engel@nmsu.edu, s.krieg@fz-juelich.de, smeinel@mit.edu, negele@mit.edu, avp@mit.edu,

TRANSVERSE MOMENTUM-DEPENDENT PARTON DISTRIBUTIONS FROM LATTICE QCD

Starting from a definition of transverse momentum-dependent parton distributions for semi-inclusive deep inelastic scattering and the Drell-Yan process, given in terms of matrix elements of a quark bilocal operator containing a staple-shaped Wilson connection, a scheme to determine such observables in lattice QCD is developed and explored. Parametrizing the aforementioned matrix elements in terms of invariant amplitudes permits a simple transformation of the problem to a Lorentz frame suited for the lattice calculation. Results for the Sivers and Boer-Mulders transverse momentum shifts are presented, focusing in particular on their dependence on the staple extent and the Collins-Soper evol…

Lattice QCD calculations of transverse momentum-dependent parton distributions (TMDs)

An ongoing program of evaluating TMD observables within Lattice QCD is reviewed, summarizing recent progress with respect to several challenges faced by such calculations. These lattice calculations are based on a definition of TMDs through hadronic matrix elements of quark bilocal operators containing staple-shaped gauge connections. A parametrization of the matrix elements in terms of invariant amplitudes serves to cast them in the Lorentz frame preferred for a lattice calculation. Data on the naively T-odd Sivers and Boer-Mulders effects as well as the transversity TMD are presented.

Nucleon structure from Lattice QCD using a nearly physical pion mass

We report the first Lattice QCD calculation using the almost physical pion mass mpi=149 MeV that agrees with experiment for four fundamental isovector observables characterizing the gross structure of the nucleon: the Dirac and Pauli radii, the magnetic moment, and the quark momentum fraction. The key to this success is the combination of using a nearly physical pion mass and excluding the contributions of excited states. An analogous calculation of the nucleon axial charge governing beta decay has inconsistencies indicating a source of bias at low pion masses not present for the other observables and yields a result that disagrees with experiment.

I=1/2 S -wave and P -wave Kπ scattering and the κ and K* resonances from lattice QCD

We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $K\ensuremath{\pi}$ scattering amplitudes as a function of the center-of-mass energy using L\"uscher's method. We perform global fits of $K$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $\sqrt{3}\frac{2\ensuremath{\pi}}{L}$; this includes irreducible representations (irreps) that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the $K$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $\ensuremath{\ka…

ππ and Kπ scattering amplitudes from lattice QCD

Quark transverse charge densities in the from lattice QCD

Abstract We extend the formalism relating electromagnetic form factors to transverse quark charge densities in the light-front frame to the case of a spin-3/2 baryon and calculate these transverse densities for the Δ ( 1232 ) isobar using lattice QCD. The transverse charge densities for a transversely polarized spin-3/2 particle are characterized by monopole, dipole, quadrupole, and octupole patterns representing the structure beyond that of a pure point-like spin-3/2 particle. We present lattice QCD results for the Δ-isobar electromagnetic form factors for pion masses down to approximatively 350 MeV for three cases: quenched QCD, two-degenerate flavors of dynamical Wilson quarks, and three…

Computing the nucleon Dirac radius directly at $Q^2=0$

We describe a lattice approach for directly computing momentum derivatives of nucleon matrix elements using the Rome method, which we apply to obtain the isovector magnetic moment and Dirac radius. We present preliminary results calculated at the physical pion mass using a 2HEX-smeared Wilson-clover action. For removing the effects of excited-state contamination, the calculations were done at three source-sink separations and the summation method was used.

Muonic Isotope Shifts in the Even Fe Nuclei

P -wave nucleon-pion scattering amplitude in the Δ(1232) channel from lattice QCD

We determine the $\mathrm{\ensuremath{\Delta}}(1232)$ resonance parameters using lattice QCD and the L\"uscher method. The resonance occurs in elastic pion-nucleon scattering with ${J}^{P}=3/{2}^{+}$ in the isospin $I=3/2$, $P$-wave channel. Our calculation is performed with ${N}_{f}=2+1$ flavors of clover fermions on a lattice with $L\ensuremath{\approx}2.8\text{ }\text{ }\mathrm{fm}$. The pion and nucleon masses are ${m}_{\ensuremath{\pi}}=255.4(1.6)\text{ }\text{ }\mathrm{MeV}$ and ${m}_{N}=1073(5)\text{ }\text{ }\mathrm{MeV}$, respectively, and the strong decay channel $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}\ensuremath{\pi}N$ is found to be above the threshold. To thorough…

High-precision calculation of the strange nucleon electromagnetic form factors

We report a direct lattice QCD calculation of the strange nucleon electromagnetic form factors $G_E^s$ and $G_M^s$ in the kinematic range $0 \leq Q^2 \lesssim 1.2\: {\rm GeV}^2$. For the first time, both $G_E^s$ and $G_M^s$ are shown to be nonzero with high significance. This work uses closer-to-physical lattice parameters than previous calculations, and achieves an unprecedented statistical precision by implementing a recently proposed variance reduction technique called hierarchical probing. We perform model-independent fits of the form factor shapes using the $z$-expansion and determine the strange electric and magnetic radii and magnetic moment. We compare our results to parity-violatin…

Lattice study of the Boer-Mulders transverse momentum distribution in the pion

The Boer-Mulders transverse momentum-dependent parton distribution (TMD) characterizes polarized quark transverse momentum in an unpolarized hadron. Techniques previously developed for lattice calculations of nucleon TMDs are applied to the pion. These techniques are based on the evaluation of matrix elements of quark bilocal operators containing a staple-shaped Wilson connection. Results for the Boer-Mulders transverse momentum shift in the pion, obtained at a pion mass of $m_{\pi} = 518\, \mbox{MeV} $, are presented and compared to corresponding results in the nucleon.