Ideas of four-fermion operators in electromagnetic form factor calculations

Chueng-Ryong Ji,Bernard L.G Bakker,Alfredo T Suzuki,Ho-Meoyng Choi

doi:10.1051/epjconf/20147306006

Abstract

Four-fermion operators have been utilized in the past to link the quark-exchange processes in the interaction of hadrons with the effective meson-exchange amplitudes. In this presentation, we apply the similar idea of Fierz rearrangement to the electromagnetic processes and focus on the electromagnetic form factors of nucleon and electron. We explain the motivation of using four-fermion operators and discuss the advantage of this method in computing electromagnetic processes.

Highlights

The calculation of the nucleon form factors based on a quark-diquark model certainly differs from the calculation of the electron form factors using quantum electrodynamics (QED), one may still discern commonalities between the two apparently different calculations
We explain the motivation of using four-fermion operators and discuss the advantage of this method in computing electromagnetic processes
While the contents of the lines drawn in the two triangle diagrams are certainly different, both calculations share the same type of one-loop integration for the amplitudes given by three vertices connected by three propagators

Summary

Introduction

The calculation of the nucleon form factors based on a quark-diquark model certainly differs from the calculation of the electron form factors using quantum electrodynamics (QED), one may still discern commonalities between the two apparently different calculations Both calculations in the one-loop level share essentially the same shape of triangle diagram as shown in Fig. 1 for the computation of amplitudes. The basic idea of early developments was to provide a basis of the one-boson-exchange interactions of baryons at low energy from the gluon exchange which mediates quark exchange scattering in conjunction with quark interchange in a non-perturbative bag model framework [2,3,4,5,6] In this presentation, we apply the Fierz-rearranged FFO in the form factors shown in Fig. 1 and present a global formula to cover most (if not all) triangle diagrams for the form factor calculations.

Basic idea

Application to form factors

Conclusion and outlook