Analytic results for Sudakov form factors in QCD

TL;DR

This paper derives an exact analytic expression for the QCD Sudakov form factor, enabling fast and precise calculations crucial for resummation in factorized cross sections, improving over numerical methods.

Contribution

It introduces a new exact analytic formula for the QCD Sudakov form factor, enhancing computational efficiency and precision in perturbative calculations.

Findings

Provides a fast, numerically exact expression for the Sudakov form factor.

Improves upon approximate solutions by maintaining renormalization group invariance.

Facilitates more efficient resummation in QCD calculations.

Abstract

Sudakov form factors appear ubiquitously in factorized cross sections where they allow one to resum large logarithms to all orders in perturbation theory. Their exact evaluation requires numerical integrals over anomalous dimensions, which in practice can hamper efficiency. Alternatively, one can use approximate analytic solutions, which provide fast evaluation at the cost of numerical precision and loss of properties such as renormalization group invariance. We provide an exact analytic expression of the QCD Sudakov form factor which allows one to obtain fast and numerically exact results.