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 ∆(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 ∆-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 flavors of quarks using a mixed action that combines domain wall valence quarks and dynamical staggered sea quarks. We extract transverse quark charge densities from these lattice results and find that the ∆ is prolately deformed, as indicated by the fact that the quadrupole moment G E2 (0) is larger than the value −3 characterizing a point particle and the fact that the transverse charge density in a ∆ + of maximal transverse spin projection is elongated along the axis of the spin.

Baryons as relativistic three-quark bound states

“…Given the lack of experimental information, model calculations are usually compared to lattice QCD simulations. The most recent lattice calculations of G E0 , G M 1 and G E2 using dynamical quarks were presented in [398,467,470] for different values of the pion mass, the lowest one being ∼ 350 MeV, whereas G M 3 has only been calculated using the quenched approximation [603]. The data provided by these calculations still show large uncertainties which are visible in Fig.…”

“…[398] with results from two rainbow-ladder Dyson-Schwinger calculations. One of them solves the three-body equation without further approximations [488] 16 and the other uses the quark-diquark approximation [496]; in both cases the We compare lattice data [398] with the Dyson-Schwinger three-quark [488] and quark-diquark calculations [496]; the coloured bands show the sensitivity to varying the η parameter in (3.96). The plot on the bottom right shows the current-mass evolution of the static quantities from the quark-diquark calculation [496], where stars denote the experimental magnetic moments of the ∆ + and Ω − baryon.…”

“…The deformation of the ∆ is encoded in its electric quadrupole and magnetic octupole form factors. Nonrelativistically, a negative sign for the electric quadrupole moment G E2 (0) indicates an oblate charge distribution for the ∆ in the Breit frame, with a different interpretation arising in the infinite-momentum frame [398]. From the measurement of the γN → ∆ transition one can infer the value G E2 (0) = −1.87 (8) in the large-N C limit [398,604]; comparable values are predicted by a range of constituent-quark models [605] and they are in the ballpark of the lattice results.…”

Electromagnetic excitation of nucleon resonances

“…The main motivation for exploring the nucleon transition form factors is to obtain a precise knowledge of the nucleon excitation spectrum, which provides -together with the elastic form factors -a complete description of the nucleon's electromagnetic structure. This structure can be compared with QCD inspired quark models and, in recent years, more and more also with lattice QCD calculations [65,66,67,68]. Moreover, the nucleon transition form factors provide an essential input for dispersive calculations of both sum rules and two-photon corrections to electron scattering [69,70,71,72,73].…”

Nucleon and Δ electromagnetic form factors

“…At this moment all theoretical predictions (e. g., Ref. 27) can be compared only to lattice-regularized QCD results, 28 unfortunately, these results produce very large ∆-baryon masses and the form factors obtained therewith should be interpreted carefully.…”