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Resummed $C$-Parameter Distribution in $e^+e^-$ Annihilation

S. Catani, B. R. Webber

TL;DR

The paper develops a perturbative framework for the $C$-parameter distribution in $e^+e^-$ annihilation, including resummation of large logarithms in the small-$C$ (two-jet) region and matching to fixed-order results. By exploiting a thrust–$C$ connection, it achieves next-to-leading logarithmic accuracy and implements a log-$R$ matching scheme to blend resummed and fixed-order predictions. It also incorporates leading non-perturbative power corrections via a dispersive approach with a Milan-factor-adjusted shift, and compares to LEP data, finding good agreement with a best-fit $A_1 frac{ ext{(GeV)}}{Q}$ around 0.24 GeV and $ar{oldsymbol{eta}}_0$-consistent $ar{oldsymbol{eta}}_0$. The work provides a cohesive perturbative-plus-nonperturbative description of the $C$-parameter and demonstrates consistency with thrust-based analyses, informing future precision tests of QCD event shapes.

Abstract

We give perturbative predictions for the distribution of the $C$-Parameter event shape variable in $e^+e^-$ annihilation, including resummation of large logarithms in the two-jet (small-$C$) region, matched to next-to-leading order results. We also estimate the leading non-perturbative power correction and make a preliminary comparison with experimental data.

Resummed $C$-Parameter Distribution in $e^+e^-$ Annihilation

TL;DR

The paper develops a perturbative framework for the -parameter distribution in annihilation, including resummation of large logarithms in the small- (two-jet) region and matching to fixed-order results. By exploiting a thrust– connection, it achieves next-to-leading logarithmic accuracy and implements a log- matching scheme to blend resummed and fixed-order predictions. It also incorporates leading non-perturbative power corrections via a dispersive approach with a Milan-factor-adjusted shift, and compares to LEP data, finding good agreement with a best-fit around 0.24 GeV and -consistent . The work provides a cohesive perturbative-plus-nonperturbative description of the -parameter and demonstrates consistency with thrust-based analyses, informing future precision tests of QCD event shapes.

Abstract

We give perturbative predictions for the distribution of the -Parameter event shape variable in annihilation, including resummation of large logarithms in the two-jet (small-) region, matched to next-to-leading order results. We also estimate the leading non-perturbative power correction and make a preliminary comparison with experimental data.

Paper Structure

This paper contains 8 sections, 38 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Kinematics of the $C$-parameter
  3. $C$-parameter and thrust at small $C$
  4. The $C$-parameter in perturbation theory
  5. Resummation for $C \to 0$
  6. Matching with fixed order
  7. Non-perturbative power corrections
  8. Comparison with data

Figures (3)

  • Figure 1: Fixed-order predictions of the $C$-parameter distribution for $\alpha_S = 0.12$. Dashed: ${\cal O}(\alpha_S)$. Solid: ${\cal O}(\alpha_S^2)$.
  • Figure 2: Second-order prediction of the $C$-parameter distribution for $C\to 0$. Points: EVENT Monte Carlo. Curve: Eqs. (\ref{['Bint']},\ref{['C2G21']}).
  • Figure 3: The $C$-parameter distribution at $Q=M_Z$. Solid curve: Eq. (\ref{['Rpow']}) with $A_1=0.24$ GeV. Dashed: $A_1=0$. Dot-dashed: ${\cal O}(\alpha_S^2)$.