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Resummation of non-global QCD observables

M. Dasgupta, G. P. Salam

TL;DR

This work identifies and resums non-global QCD effects that arise in observables sensitive to radiation in only part of phase space, such as single-hemisphere jet-mass distributions. It analytically computes the leading non-global term at ${\alpha_s^2}$, showing it originates from $C_F C_A$ interference and yields a distinct $\alpha_s^2 L^2$ contribution, encoded in the function ${\cal S}(\alpha_s L)$. Since exact all-orders treatment is intractable, the authors develop a large-$N_c$ dipole Monte Carlo method to determine ${\cal S}$ and provide a phenomenological fit, demonstrating the significant impact on the jet-mass peak and improving consistency with fixed-order results. The methodology and results extend to DIS observables and other single-hemisphere shapes, offering a framework to incorporate non-global logarithms in precision QCD predictions.

Abstract

We discuss issues related to the resummation of non-global observables in QCD, those that are sensitive to radiation in only a part of phase space. Examples of such observables are certain single-hemisphere event shapes in e+e- and DIS. Compared to global observables (those sensitive to all emissions, e.g. the e+e- thrust) a new class of single-logarithmic terms arises. These have been neglected in recent calculations in the literature. For a whole set of single hemisphere e+e- and DIS event shapes, we analytically evaluate the first such term, at order alpha_s^2, and give numerical results for the resummation of these terms in the large-Nc limit.

Resummation of non-global QCD observables

TL;DR

This work identifies and resums non-global QCD effects that arise in observables sensitive to radiation in only part of phase space, such as single-hemisphere jet-mass distributions. It analytically computes the leading non-global term at , showing it originates from interference and yields a distinct contribution, encoded in the function . Since exact all-orders treatment is intractable, the authors develop a large- dipole Monte Carlo method to determine and provide a phenomenological fit, demonstrating the significant impact on the jet-mass peak and improving consistency with fixed-order results. The methodology and results extend to DIS observables and other single-hemisphere shapes, offering a framework to incorporate non-global logarithms in precision QCD predictions.

Abstract

We discuss issues related to the resummation of non-global observables in QCD, those that are sensitive to radiation in only a part of phase space. Examples of such observables are certain single-hemisphere event shapes in e+e- and DIS. Compared to global observables (those sensitive to all emissions, e.g. the e+e- thrust) a new class of single-logarithmic terms arises. These have been neglected in recent calculations in the literature. For a whole set of single hemisphere e+e- and DIS event shapes, we analytically evaluate the first such term, at order alpha_s^2, and give numerical results for the resummation of these terms in the large-Nc limit.

Paper Structure

This paper contains 5 sections, 22 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Fixed order calculation
  3. Resummation
  4. Large-$\boldsymbol{N_C}$ limit and Monte Carlo implementation
  5. Checks and conclusions

Figures (3)

  • Figure 1: Kinematic configurations of interest
  • Figure 2: Left: the kind of diagram which must be considered in the calculation of ${\cal{S}}$. Right: the same diagram represented in the large-$N_C$ limit, with gluons shown as pairs of colour lines and quarks as single colour lines.
  • Figure 3: The difference between fixed order results from Event2 and the expansion of the resummed results. The left-hand plot shows results for the coefficient of ${\bar{\alpha}}_{{\textsc{s}}}^2C_FC_A$ --- the two sets of points correspond to neglecting or accounting for ${\cal{S}}$. The right-hand plot shows the coefficients of the $C_F T_f$ and $C_F^2$ pieces.