Resummation of the C-Parameter Sudakov Shoulder Using Effective Field Theory

TL;DR

This paper develops a soft-collinear effective theory approach to resum large logarithms at the C-parameter shoulder in electron-positron annihilation, providing a new factorization theorem and validated results without a Sudakov--Landau pole.

Contribution

It introduces a novel factorization theorem for the C-parameter using effective field theory, accounting for quadratic soft radiation contributions and enabling straightforward momentum-space resummation.

Findings

Derived a new factorization theorem specific to the C-parameter

Validated one-loop calculations against Monte Carlo simulations

Presented matched NLL+NLO resummed results without a Sudakov--Landau pole

Abstract

The C-parameter distribution in $e^+e^-$ annihilation exhibits a kinematic shoulder at $C = 3/4$, where three-parton final states reach their maximum and a fourth parton is required to exceed it. This boundary generates large logarithms that must be resummed. Using soft-collinear effective theory, we derive a factorization theorem involving new jet and soft functions specific to the C-parameter measurement, in which soft radiation contributes quadratically in transverse momentum. This quadratic structure explains the step discontinuity at leading order. We compute all ingredients at one loop, validate against Monte Carlo, and present matched NLL+NLO results. Unlike thrust and heavy jet mass, the C-parameter has no Sudakov--Landau pole, making momentum-space resummation straightforward. All calculations, numerical analysis, and manuscript preparation were performed by Claude, an AI assistant developed by Anthropic, working under physicist supervision.