Bound state structure and electromagnetic form factor beyond the ladder approximation

Abstract

We investigate the response of the bound state structure of a two-boson system, within a Yukawa model with a scalar boson exchange, to the inclusion of the crossladder contribution to the ladder kernel of the Bethe-Salpeter equation. The equation is solved by means of the Nakanishi integral representation and light-front projection. The valence light-front wave function and the elastic electromagnetic form factor beyond the impulse approximation, with the inclusion of the two-body current, generated by the cross-ladder kernel, are computed. The valence wave function and electromagnetic form factor, considering both ladder and ladder plus crossladder kernels, are studied in detail. Their asymptotic forms are found to be quite independent of the inclusion of the cross-ladder kernel, for a given binding energy. The asymptotic decrease of form factor agrees with the counting rules. This analysis can be generalized to fermionic systems, with a wide application in the study of the meson structure.

Minkowski space approach for the Bethe-Salpeter equation

“…In particular, for large transverse distances an exponential fall-off behavior was singled out in agreement with the non-relativistic case in the 3D Euclidean space. The success in applying the NIR to the BS formalism for the spectrum of bosonic systems, as outlined here and detailed in [13,14], provides enough motivation for possible extensions, as to consider these studies beyond the ladder approximation [9]. Following previous investigations on two-fermion systems within the NIR [11,12], it is quite relevant also to look for the corresponding excited bound-state spectrum.…”

“…Further simplifications to the integral equation derived in [5] were achieved by using the uniqueness conjecture of the Nakanishi weight-function, as shown in [6,7] by considering e-mail: tomio@ift.unesp.br the ladder kernel. The exploration of the method to include kernels beyond the ladder has successfully been performed in [8,9]. Moreover, in [10], within the NIR the effect of the self-energy contribution to the binding energy of the ground state has been explored in the scalar theory.…”

A short review about the Bethe-Salpeter equation and the solution of the c2f model in Minkowski space

“…In possession of the off-shell BSA for bound and scattering states, observables like electromagnetic elastic form factor [19] as well as the transitions one [20], can be easily computed even considering cross-ladder kernels [21]. At this point it is interesting to note that the availability of the BSA in Minkowski space is necessary once the Wick rotation is not well-defined in the integrals of the form factor and then, calculations in Euclidean and Minkowski space can show considerable differences [19].…”

Few-Body Systems in Minkowski Space: The Bethe-Salpeter Equation Challenge

“…There have been also investigations of the cross-diagram contribution to the kernel (second diagram in Fig. 2) [14], and its effect on the calculation of the electromagnetic form factor [28].…”