Charge-conjugation symmetric complete impulse approximation for the pion electromagnetic form factor in the Covariant Spectator Theory

TL;DR

This paper develops a charge-conjugation invariant approach within the Covariant Spectator Theory to calculate the pion electromagnetic form factor, revealing that additional pole contributions are significant at small pion masses but do not change the form factor shape.

Contribution

It introduces a $C$-symmetric complete impulse approximation that includes all pole contributions, improving the previous spectator pole-only calculations.

Findings

Pole contributions are significant at small pion masses across all $Q^2$ values.

Including all poles does not alter the form factor shape obtained from spectator poles alone.

Charge conjugation invariance is preserved in the calculation.

Abstract

The pion form factor is calculated in the framework of the charge-conjugation invariant Covariant Spectator Theory. This formalism is established in Minkowski space and the calculation is set up in momentum space. In a previous calculation we included only the leading pole coming from the spectator quark (referred to as the relativistic impulse approximation). In this paper we also include the contributions from the poles of the quark which interacts with the photon and average over all poles in both the upper and lower half planes in order to preserve charge conjugation invariance (referred to as the $C$-symmetric complete impulse approximation). We find that for small pion mass these contributions are significant at all values of the four-momentum transfer $Q^2$ but, surprisingly, do not alter the shape obtained from the spectator poles alone.