Δ-baryon electromagnetic form factors in lattice QCD
We develop techniques to calculate the four Delta electromagnetic form factors using lattice QCD, with particular emphasis on the sub-dominant electric quadrupole form factor that probes deformation of the Delta. Results are presented for pion masses down to approximately 350 MeV for three cases: quenched QCD, two flavors of dynamical Wilson quarks, and three flavors of quarks described by a mixed action combining domain wall valence quarks and dynamical staggered sea quarks. The magnetic moment of the Delta is chirally extrapolated to the physical point and the Delta charge density distributions are discussed.
Model-independent determination of the nucleon charge radius from lattice QCD
Lattice QCD calculations of nucleon form factors are restricted to discrete values of the Euclidean four-momentum transfer. Therefore, the extraction of radii typically relies on parametrizing and fitting the lattice QCD data to obtain its slope close to zero momentum transfer. We investigate a new method, which allows to compute the nucleon radius directly from existing lattice QCD data, without assuming a functional form for the momentum dependence of the underlying form factor. The method is illustrated for the case of the isovector mean square charge radius of the nucleon $\langle r^2_\mathrm{isov} \rangle$ and the quark-connected contributions to $\langle r^2_p\rangle$ and $\langle r^2…
Quark transverse charge densities in the from lattice QCD
Abstract We extend the formalism relating electromagnetic form factors to transverse quark charge densities in the light-front frame to the case of a spin-3/2 baryon and calculate these transverse densities for the Δ ( 1232 ) isobar using lattice QCD. The transverse charge densities for a transversely polarized spin-3/2 particle are characterized by monopole, dipole, quadrupole, and octupole patterns representing the structure beyond that of a pure point-like spin-3/2 particle. We present lattice QCD results for the Δ-isobar electromagnetic form factors for pion masses down to approximatively 350 MeV for three cases: quenched QCD, two-degenerate flavors of dynamical Wilson quarks, and three…
Colloquium: The Shape of Hadrons
This Colloquium addresses the issue of the shape of hadrons and, in particular, that of the proton. The concept of shape in the microcosm is critically examined. Special attention is devoted to properly define the meaning of shape for bound-state systems of near massless quarks. The ideas that lead to the expectation of nonsphericity in the shape of hadrons, the calculations that predict it, and the experimental information obtained from recent high-precision measurements are examined. Particular emphasis is given to the study of the electromagnetic transition between the nucleon and its first excited state, the Δ(1232) resonance. The experimental evidence is critically examined and compare…
Nucleon electromagnetic and axial form factors with N$_f$=2 twisted mass fermions at the physical point
We present results for the nucleon electromagnetic and axial form factors using an N$_f$=2 twisted mass fermion ensemble with pion mass of about 131 MeV. We use multiple sink-source separations to identify excited state contamination. Dipole masses for the momentum dependence of the form factors are extracted and compared to experiment, as is the nucleon magnetic moment and charge and magnetic radii.
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…
Parton distributions and lattice QCD calculations: A community white paper
Progress in particle and nuclear physics 100, 107 - 160 (2018). doi:10.1016/j.ppnp.2018.01.007