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

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.