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Non--global logs and clustering impact on jet mass with a jet veto distribution

Kamel Khelifa-Kerfa

TL;DR

The paper investigates non-global and clustering-induced logarithms in the jet-mass distribution with a jet veto, deriving the full jet-radius non-global-log form for anti-$k_t$ and analyzing fixed-order clustering effects in both $C_F^2$ and $C_F C_A$ channels. It presents a detailed LO and NLO fixed-order treatment, computes the NGL coefficient $S_2$ (and CA variants) and identifies clustering logs (CLs) arising in the CA algorithm, then constructs partial resummations for anti-$k_t$ and CA to compare with EVENT2. Numerical results confirm the existence and behavior of NGLs and CLs, quantify the suppression of NGLs by clustering, and reveal that the sum over color channels aligns with EVENT2, validating the analytic structure. The work suggests that appropriate jet-radius choices could largely remove non-global corrections, though a full all-orders resummation including CLs and subleading NGLs remains for future study, with extensions to hadron colliders planned.

Abstract

There has recently been much interest in analytical computations of jet mass distributions with and without vetos on additional jet activity [1-6]. An important issue affecting such calculations, particularly at next-to-leading logarithmic (NLL) accuracy, is that of non-global logarithms as well as logarithms induced by jet definition, as we pointed out in an earlier work [3]. In this paper, we extend our previous calculations by independently deriving the full jet-radius analytical form of non-global logarithms, in the anti-$\kt$ jet algorithm. Employing the small-jet radius approximation, we also compute, at fixed-order, the effect of jet clustering on both $\CF^{2}$ and $\CF\CA$ colour channels. Our findings for the $\CF\CA$ channel confirm earlier analytical calculations of non-global logarithms in soft-collinear effective theory [5]. Moreover, all of our results, as well as those of [3], are compared to the output of the numerical program \texttt{EVENT2}. We find good agreement between analytical and numerical results both with and without final state clustering.

Non--global logs and clustering impact on jet mass with a jet veto distribution

TL;DR

The paper investigates non-global and clustering-induced logarithms in the jet-mass distribution with a jet veto, deriving the full jet-radius non-global-log form for anti- and analyzing fixed-order clustering effects in both and channels. It presents a detailed LO and NLO fixed-order treatment, computes the NGL coefficient (and CA variants) and identifies clustering logs (CLs) arising in the CA algorithm, then constructs partial resummations for anti- and CA to compare with EVENT2. Numerical results confirm the existence and behavior of NGLs and CLs, quantify the suppression of NGLs by clustering, and reveal that the sum over color channels aligns with EVENT2, validating the analytic structure. The work suggests that appropriate jet-radius choices could largely remove non-global corrections, though a full all-orders resummation including CLs and subleading NGLs remains for future study, with extensions to hadron colliders planned.

Abstract

There has recently been much interest in analytical computations of jet mass distributions with and without vetos on additional jet activity [1-6]. An important issue affecting such calculations, particularly at next-to-leading logarithmic (NLL) accuracy, is that of non-global logarithms as well as logarithms induced by jet definition, as we pointed out in an earlier work [3]. In this paper, we extend our previous calculations by independently deriving the full jet-radius analytical form of non-global logarithms, in the anti- jet algorithm. Employing the small-jet radius approximation, we also compute, at fixed-order, the effect of jet clustering on both and colour channels. Our findings for the channel confirm earlier analytical calculations of non-global logarithms in soft-collinear effective theory [5]. Moreover, all of our results, as well as those of [3], are compared to the output of the numerical program \texttt{EVENT2}. We find good agreement between analytical and numerical results both with and without final state clustering.

Paper Structure

This paper contains 20 sections, 72 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Fixed--order calculations: $\mathcal{O}(\alpha_{s})$
  3. Observable and jet algorithms definitions
  4. LO distribution
  5. Fixed--order calculations: $\mathcal{O}(\alpha_{s}^{2})$
  6. $\tau_{E_{0}}$ distribution in the anti--$k_{t}$ algorithm
  7. $C_{F}^{2}$ term
  8. $C_{F}C_{A}$ term and NGLs
  9. $\tau_{E_{0}}$ distribution in the C--A algorithm
  10. $C_{F}^{2}$ term
  11. $C_{F}C_{A}$ term
  12. Resummation of $\tau_{E_{0}}$ distribution
  13. Resummation with anti--$k_{t}$ algorithm
  14. Resummation with C--A algorithm
  15. Numerical results
  16. ...and 5 more sections

Figures (5)

  • Figure 1: Schematic representation of gluonic arrangement giving rise to NGLs. We have only shown the NGLs contributions to the $p_{R}$--jet. Identical contributions apply to the $p_{L}$--jet.
  • Figure 2: A schematic representation of a three--jet final state after applying the C--A algorithm on real emission along with virtual correction diagrams. The two gluons are clustered in the E--Scheme (see sec. \ref{['sec.fixed_order_1']}). Identical diagrams hold for the $p_{L}$--jet.
  • Figure 3: A schematic representation of a two--jet final state after applying the C--A algorithm on real emission along with virtual correction diagrams. The two gluons are clustered in the E--Scheme (see sec. \ref{['sec.fixed_order_1']}). Identical diagrams hold for the left ($p_{L}$--) jet.
  • Figure 4: Non--global coefficient $S_{2}$ in the anti--$k_{t}$ and C--A algorithms.
  • Figure 5: Comparison of analytical resummed differential distribution $\mathrm{d}\Sigma/\mathrm{d}\tau_{E_{0}}$ where: only primary term included \ref{['resum_tot_akt']}, primary and NGLs factor included in the anti--$k_{t}$ algorithm \ref{['resum_tot_akt']} and primary $+$ NGLs $+$ CLs factors included \ref{['resum_tot_CA']}. The plots are shown for various jet--radii with a jet veto $E_{0} = 0.1 Q$. The coupling is taken at the $Z$ mass to be $\alpha_{s}(M_{Z}) \simeq 0.118$. The plots are only meant to give a rough estimate of the effects of NGLs in non--clustered as well as clustered final states.