Next-to-Next-to-Leading-Order QCD Prediction for the Pion Form Factor

TL;DR

This paper presents the first two-loop QCD calculation of the pion electromagnetic form factor, improving theoretical precision and aiding the extraction of the pion distribution amplitude from experimental data.

Contribution

It provides the first rigorous two-loop computation of the leading-twist pion form factor using effective field theory and multi-loop techniques, including scale independence validation.

Findings

Two-loop QCD correction is numerically significant at accessible energies.

The correction improves the determination of the pion distribution amplitude.

Scale independence of the form factor is explicitly confirmed at ${\cal O}(\alpha_s^3)$.

Abstract

We accomplish for the first time the two-loop computation of the leading-twist contribution to the pion electromagnetic form factor by employing the effective field theory formalism rigorously. The next-to-next-to-leading-order short-distance matching coefficient is determined by evaluating the appropriate $5$-point QCD amplitude with the modern multi-loop technique and subsequently by implementing the ultraviolet renormalization and infrared subtractions with the inclusion of evanescent operators. The renormalization/factorization scale independence of the obtained form factor is then validated explicitly at ${\cal O}(\alpha_s^3)$. The yielding two-loop QCD correction to this fundamental quantity turns out to be numerically significant at experimentally accessible momentum transfers. We further demonstrate that the newly computed two-loop radiative correction is highly beneficial for an improved determination of the leading-twist pion distribution amplitude.