Pion Electromagnetic Form Factor from Bethe-Salpeter Amplitudes with Appropriate Kinematics

Abstract

Within the framework provided by quantum chromodynamics's Schwinger-Dyson equations (SDEs), the pion's electromagnetic form factor is computed using solutions of the Bethe-Salpeter equation (BSE) that have finite spacial momentum, and therefore allow the appropriate kinematics for a given momentum transfer. This removes, for the first time, a limiting approximation in previous SDE calculations where rest-frame solutions to the BSE are used for both the initial and final pion states. In performing these calculations, the rainbow-ladder truncation to the SDEs in the Landau gauge is used, with the quark-gluon interaction given by the Maris-Tandy model. Using Bethe-Salpeter amplitudes (BSAs) that have the correct spacial momentum for a given momentum transfer, $Q^2$, has a dramatic impact on results for the pion's electromagnetic form factor. The difference between results that use rest-frame BSAs and those with correct kinematics is less that 10\% for $0 \leqslant Q^2 \lesssim 1\,$GeV$^2$, however, these corrections grow with increasing momentum transfer and approach 100\% for $Q^2 \simeq 3\,$GeV$^2$.