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Hemisphere mass up to four-loops with generalised $k_t$ algorithms

K. Khelifa-Kerfa, M. Benghanem

TL;DR

The paper computes the fixed-order distribution of the non-global hemisphere mass in $e^+e^-$ annihilation up to four loops for $k_t$ and Cambridge/Aachen algorithms, revealing the full abelian clustering (CLs) and non-abelian (NGLs) non-global logarithms in this setting. Using eikonal theory and strong-energy ordering, it provides full-colour results and demonstrates an exponentiation pattern for both CLs and NGLs, with CLs generally dominating NGLs and increasing the resummed distribution in the peak region. The authors construct all-orders resummations by exponentiating fixed-order terms and compare with Monte Carlo results, showing that neglecting non-global effects yields unreliable predictions and that algorithm choice significantly impacts the Sudakov peak and tail. The findings underscore the importance of incorporating CLs and NGLs in parton-shower simulations and offer a framework applicable to other non-global observables and generalised $k_t$-family jet algorithms.

Abstract

We compute the fixed-order distribution of the non-global hemisphere mass observable in $e^+ e^-$ annihilation up to four loops for various sequential recombination jet algorithms. In particular, we focus on the $k_t$ and Cambridge/Aachen algorithms. Using eikonal theory and strong-energy ordering of the final-state partons, we determine the complete structure of both abelian (clustering) and non-abelian non-global logarithms through four loops in perturbation theory. We compare the resulting resummed expressions for both jet algorithms with the standard Sudakov form factor and demonstrate that neglecting these logarithms leads to unreliable phenomenological predictions for the observable's distribution.

Hemisphere mass up to four-loops with generalised $k_t$ algorithms

TL;DR

The paper computes the fixed-order distribution of the non-global hemisphere mass in annihilation up to four loops for and Cambridge/Aachen algorithms, revealing the full abelian clustering (CLs) and non-abelian (NGLs) non-global logarithms in this setting. Using eikonal theory and strong-energy ordering, it provides full-colour results and demonstrates an exponentiation pattern for both CLs and NGLs, with CLs generally dominating NGLs and increasing the resummed distribution in the peak region. The authors construct all-orders resummations by exponentiating fixed-order terms and compare with Monte Carlo results, showing that neglecting non-global effects yields unreliable predictions and that algorithm choice significantly impacts the Sudakov peak and tail. The findings underscore the importance of incorporating CLs and NGLs in parton-shower simulations and offer a framework applicable to other non-global observables and generalised -family jet algorithms.

Abstract

We compute the fixed-order distribution of the non-global hemisphere mass observable in annihilation up to four loops for various sequential recombination jet algorithms. In particular, we focus on the and Cambridge/Aachen algorithms. Using eikonal theory and strong-energy ordering of the final-state partons, we determine the complete structure of both abelian (clustering) and non-abelian non-global logarithms through four loops in perturbation theory. We compare the resulting resummed expressions for both jet algorithms with the standard Sudakov form factor and demonstrate that neglecting these logarithms leads to unreliable phenomenological predictions for the observable's distribution.

Paper Structure

This paper contains 11 sections, 66 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Kinematics
  3. Observable definition
  4. Jet algorithms
  5. Observable distribution
  6. Fixed-order calculations
  7. Two loops
  8. Three loops
  9. Four loops
  10. All-orders and comparison to MC
  11. Conclusions

Figures (3)

  • Figure 1: Resummed differential distribution of the hemisphere mass for the anti-$k_t$ algorithm with various approximations of the NGLs form factor.
  • Figure 2: Resummed differential distribution of the hemisphere mass for the $k_t$ (top) and C/A (bottom) algorithms with various approximations of the CLs and NGLs form factors.
  • Figure 3: Resummed differential distribution of the hemisphere mass for all three jet algorithms.