Asymptotic behavior of the heavy quark form factors at higher order

J Blümlein,P Marquard,N Rana

doi:10.1103/physrevd.99.016013

Abstract

In the asymptotic limit $Q^2 \gg m^2$, the heavy quark form factors exhibit Sudakov behavior. We study the corresponding renormalization group equations of the heavy quark form factors which do not only govern the structure of infrared divergences, but also control the high energy logarithms. This enables us to obtain the complete logarithmic three--loop and partial four--loop contributions to the heavy quark form factors in perturbative Quantum Chromodynamics.

Highlights

Amplitudes for hard scattering processes in quantum chromodynamics (QCD) at higher order do provide precise phenomenological predictions for scattering processes and a clear insight into underlying principles such as factorization or the universality of infrared (IR) singularities
We study the corresponding renormalization group equations of the heavy quark form factors which do govern the structure of infrared divergences and control the high energy logarithms
We study the asymptotic behavior of the different heavy quark form factors following the method proposed for massless cases in [15,16] and in the massive case of Ref. [10], maintaining the complete color structure to three-loop order and for leading color at four-loop order

Summary

INTRODUCTION

Amplitudes for hard scattering processes in quantum chromodynamics (QCD) at higher order do provide precise phenomenological predictions for scattering processes and a clear insight into underlying principles such as factorization or the universality of infrared (IR) singularities. While a first step was taken in [12] to obtain the IR structure of a generic two-loop amplitude without considering the small mass limit, in [13] the general solution was presented for the singular structure of a generic scattering amplitude containing massless and massive partons. In the asymptotic limit, the amplitudes with massive partons exhibit the Sudakov behavior It was first studied in [10] and a general factorization formula was presented. We study the asymptotic behavior of the different heavy quark form factors following the method proposed for massless cases in [15,16] and in the massive case of Ref. We present yet approximate four-loop results, combining all ingredients known at present and outline which missing terms still need to be calculated

THE SUDAKOV BEHAVIOR

PHENOMENOLOGICAL RESULTS

CONCLUSION