High energy behaviour of form factors

TL;DR

This work addresses the infrared structure of photon-quark form factors in perturbative QCD for both massive and massless quarks by solving the renormalization group (RG) equations that govern their Sudakov-type divergences. The authors derive and solve the KG integro-differential equations for the massive form factor $ ilde{F}$ and the massless form factor $ar{F}$, expressing the solutions as expansions in the (bare) coupling $ ilde{a}_s$ or $a_s$, and using the cusp anomalous dimension $A$ along with the mass-dependent function $K$ and the boundary-matching function $C$. By matching to recent planar results at three loops (massive) and four loops (massless), they determine integration constants and provide explicit four-loop predictions for the massive form factor and five-loop predictions for the massless form factor in the planar limit, including detailed pole structures in $oldsymbol{rac{1}{oldsymbol{ extepsilon}}}$ and color-factor decompositions. They also derive universal, scheme-independent conversion factors $Z_{[q]}^{(m|0)}$ bridging dimensional regularization and small-mass regularization, extending these factors to higher orders in $oldsymbol{ extepsilon}$ and in the planar limit. Overall, the paper advances the understanding of infrared factorization in QCD form factors and provides concrete high-loop predictions that can feed into precision calculations and resummations of IR effects.

Abstract

We solve renormalization group equations that govern infrared divergences of massless and massive form factors. By comparing to recent results for planar massive three-loop and massless four-loop form factors in QCD, we give predictions for the high-energy limit of massive form factors at the four- and for the massless form factor at five-loop order. Furthermore, we discuss the relation which connects infrared divergences regularized dimensionally and via a small quark mass and extend results present in the literature to higher order.