Soft spectator scattering in the nucleon form factors at large $Q^2$ within the SCET approach

TL;DR

This paper investigates the soft rescattering contribution to proton form factors at large $Q^2$ using SCET, providing a new factorization framework that includes both hard and soft effects relevant at intermediate momentum transfers.

Contribution

It introduces a two-step SCET-based factorization approach to account for soft spectator effects in nucleon form factors at large $Q^2$, extending previous hard-only models.

Findings

Successful two-step factorization within SCET for soft rescattering

Derivation of a complete formula for Dirac form factor including soft contributions

Qualitative insights into phenomenological implications of soft rescattering

Abstract

The proton form factors at large momentum transfer are dominated by two contributions which are associated with the hard and soft rescattering respectively. Motivated by a very active experimental form factor program at intermediate values of momentum transfers, $Q^{2}\sim 5-15 \text{GeV}^{2}$, where an understanding in terms of only a hard rescattering mechanism cannot yet be expected, we investigate in this work the soft rescattering contribution using soft collinear effective theory (SCET). Within such description, the form factor is characterized, besides the hard scale $Q^2$, by a semi-hard scale $Q \Lambda$, which arises due to presence of soft spectators, with virtuality $\Lambda^2$ ($\Lambda \sim 0.5$ GeV), such that $Q^{2}\gg Q\Lambda\gg \Lambda^{2}$. We show that in this case a two-step factorization can be successfully carried out using the SCET approach. In a first step (SCET$_I$), we perform the leading order matching of the QCD electromagnetic current onto the relevant SCET$_I$ operators and perform a resummation of large logarithms using renormalization group equations. We then discuss the further matching onto a SCET$_{II}$ framework, and propose the complete factorization formula for the Dirac form factor, accounting for both hard and soft contributions. We also present a qualitative discussion of the phenomenological consequences of this new framework.