Sudakov Safety in Perturbative QCD

TL;DR

This paper introduces the concept of Sudakov safety in perturbative QCD, defining it through conditional probabilities and analyzing a family of observables that interpolate between safe and unsafe regimes, revealing fixed point behavior.

Contribution

It provides a concrete definition of Sudakov safety and studies a family of observables that bridge safe and unsafe regimes, highlighting their fixed point properties.

Findings

Sudakov safe observables are calculable via all-orders resummation.

Distribution at the boundary is independent of the strong coupling constant.

Ultraviolet fixed point behavior observed in the generalized fragmentation function.

Abstract

Traditional calculations in perturbative quantum chromodynamics (pQCD) are based on an order-by-order expansion in the strong coupling $\alpha_s$. Observables that are calculable in this way are known as "safe". Recently, a class of unsafe observables was discovered that do not have a valid $\alpha_s$ expansion but are nevertheless calculable in pQCD using all-orders resummation. These observables are called "Sudakov safe" since singularities at each $\alpha_s$ order are regulated by an all-orders Sudakov form factor. In this letter, we give a concrete definition of Sudakov safety based on conditional probability distributions, and we study a one-parameter family of momentum sharing observables that interpolate between the safe and unsafe regimes. The boundary between these regimes is particularly interesting, as the resulting distribution can be understood as the ultraviolet fixed point of a generalized fragmentation function, yielding a leading behavior that is independent of $\alpha_s$.