Abstract: The baryon electromagnetic form factors are expressed in terms of two-dimensional densities describing the distribution of charge and magnetization in transverse space at fixed light-front time. We calculate the transverse densities of the spin-1/2 flavor-octet baryons at peripheral distances b = O(M-pi(-1)) using methods of relativistic chiral effective field theory (chi EFT) and dispersion analysis. The densities are represented as dispersive integrals over the imaginary parts of the form factors in the timelike region (spectral functions). The isovector spectral functions on the two-pion cut t > 4 M-pi(2) are calculated using relativistic chi EFT including octet and decuplet baryons. The chi EFT calculations are extended into the rho meson mass region using an N / D method that incorporates the pion electromagnetic form factor data. The isoscalar spectral functions are modeled by vector meson poles. We compute the peripheral charge and magnetization densities in the octet baryon states, estimate the uncertainties, and determine the quark flavor decomposition. The approach can be extended to baryon form factors of other operators and the moments of generalized parton distributions.

Abstract: We study theoretically the effects of finite volume for pi pi scattering in order to extract physical observables for infinite volume from lattice QCD. We compare three different approaches for pi pi scattering (lowest order Bethe-Salpeter approach, N/D and inverse amplitude methods) with the aim of studying the effects of the finite size of the box in the potential of the different theories, specially the left-hand cut contribution through loops in the crossed t, u-channels. We quantify the error made by neglecting these effects in usual extractions of physical observables from lattice ()CD spectrum. We conclude that for pi pi phase-shifts in the scalar-isoscalar channel up to 800 MeV this effect is negligible for box sizes bigger than 2,5m(pi)(-1) and of the order of 5% at around 1.5 – 2m(pi)(-1). For isospin 2 the finite size effects can reach up to 10% for that energy. We also quantify the error made when using the standard Luscher method to extract physical observables from lattice QCD, which is widely used in the literature but is an approximation of the one used in the present work.

Abstract: The three-particle K-matrix, K-df,K-3, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions in all isospin channels through next-to-leading order in Chiral Perturbation Theory, generalizing previous work done at maximum isospin. We obtain analytic expressions through quadratic order (or cubic order, in the case of zero isospin) in the expansion about the three-pion threshold.