Factorization, Power Corrections, and the Pion Form Factor

TL;DR

The paper uses Soft-Collinear Effective Theory to systematically analyze pion form factors, focusing on how end-point configurations contribute power corrections. It shows that both the transition and electromagnetic form factors receive Λ/Q corrections, with the latter potentially enhanced by 1/α_s(Q) when √(ΛQ) is nonperturbative, offering a possible explanation for the observed data discrepancy. A two-stage SCET framework (SCETI and SCETII) and time-ordered products of leading and subleading Lagrangians enable a transparent, factorized treatment of these corrections, highlighting the role of soft components and end-point dynamics. The results suggest that the soft structure functions may be universal across processes, and that nonperturbative effects in the intermediate scale could significantly affect exclusive processes at accessible energies.

Abstract

This letter is an investigation of the pion form factor utilizing recently developed effective field theory techniques. The primary results reported are: Both the transition and electromagnetic form factors are corrected at order $Λ/Q$. However, these corrections only arise due to time ordered products which are sensitive to soft components of the pion. The usual higher twist wave function corrections contribute only at order $Λ^2/Q^2$, when the quark mass vanishes. In the case of the electromagnetic form factor the $Λ/Q$ power correction is enhanced by a power of $1/α_s(Q)$ relative to the leading order result of Brodsky and Lepage, if the scale $\sqrt{ΛQ}$ is non-perturbative. This enhanced correction could explain the discrepancy with the data.

Figures (1)

• Figure 1: Integrating out modes with virtuality $\sqrt{\Lambda Q}$ lead to operators which represent the "soft" piece of the wave function. The solid (hatched) circle represents modes off-shell by $Q$ ($\sqrt{\Lambda Q}$).