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NNLO+NNLL Predictions for Heavy-Jet Mass and C-parameter in Higgs Decays to Quarks and Gluons

Elliot Fox, Aude Gehrmann-De Ridder, Thomas Gehrmann, Nigel Glover, Matteo Marcoli, Christian T. Preuss

TL;DR

This work delivers NNLO+NNLL predictions for heavy-jet mass and the $C$-parameter in hadronic Higgs decays, by matching fixed-order NNLO results to analytic NNLL resummation in the two-particle limit using the ARES formalism. It analyzes the decay channels $H\to b\bar{b}$, $H\to c\bar{c}$, and $H\to gg$, with a logR matching scheme to ensure consistent predictions across all kinematic regions. The study finds reduced theoretical uncertainties and clear channel-dependent effects, notably a substantial shift in the $C$-parameter peak for $H\to gg$ due to an unmatched single-logarithm $\alpha_s^3 L$ term, while the heavy-jet mass is less sensitive to higher-order corrections. These results advance precision Higgs phenomenology and motivate future inclusion of Sudakov-shoulder resummation and extension to additional event shapes and higher resummation accuracy.

Abstract

We consider the resummation of large logarithmic corrections arising in the two-particle limit at next-to-next-to-leading logarithmic (NNLL) accuracy for the heavy-jet mass and $C$-parameter distributions in the decay of a Higgs boson to quarks and gluons: $H\to b\bar{b}$, $H\to c\bar{c}$, and $H\to gg$. We demonstrate how the matched NNLO+NNLL results clarify the relative contributions of key hadronic Higgs-decay channels ($H\to b\bar{b}$, $H\to c\bar{c}$, $H\to gg$) yielding reduced uncertainties for both event-shape observables -- especially for heavy-jet mass -- while revealing substantial effects that shift the $C$-parameter peak in gluonic decays.

NNLO+NNLL Predictions for Heavy-Jet Mass and C-parameter in Higgs Decays to Quarks and Gluons

TL;DR

This work delivers NNLO+NNLL predictions for heavy-jet mass and the -parameter in hadronic Higgs decays, by matching fixed-order NNLO results to analytic NNLL resummation in the two-particle limit using the ARES formalism. It analyzes the decay channels , , and , with a logR matching scheme to ensure consistent predictions across all kinematic regions. The study finds reduced theoretical uncertainties and clear channel-dependent effects, notably a substantial shift in the -parameter peak for due to an unmatched single-logarithm term, while the heavy-jet mass is less sensitive to higher-order corrections. These results advance precision Higgs phenomenology and motivate future inclusion of Sudakov-shoulder resummation and extension to additional event shapes and higher resummation accuracy.

Abstract

We consider the resummation of large logarithmic corrections arising in the two-particle limit at next-to-next-to-leading logarithmic (NNLL) accuracy for the heavy-jet mass and -parameter distributions in the decay of a Higgs boson to quarks and gluons: , , and . We demonstrate how the matched NNLO+NNLL results clarify the relative contributions of key hadronic Higgs-decay channels (, , ) yielding reduced uncertainties for both event-shape observables -- especially for heavy-jet mass -- while revealing substantial effects that shift the -parameter peak in gluonic decays.

Paper Structure

This paper contains 7 sections, 25 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Calculation
  3. Results
  4. Conclusions
  5. Fixed-order expansion coefficients
  6. Heavy-jet mass
  7. $C$-parameter

Figures (3)

  • Figure 1: Hadronic Higgs decay categories: $H\to q\bar{q}$ with a Yukawa coupling (left) and $H\to gg$ via an effective coupling (right).
  • Figure 2: Heavy-jet mass distribution results for fixed order predictions matched to resummation in the logR scheme for the $H\to q\bar{q}$ channel (left column), $H\to gg$ channel (middle column) and the sum over all channels (right column) for both linear-binning (top row) and logarithmic-binning (bottom row). For the frames in the two leftmost columns, the curves represent the LO calculation matched to NLL resummation (green), NLO matched to NNLL (blue), and NNLO matched to NNLL (red), and the ratio to NLO+NNLL is shown in the lower frame. For the frames in the rightmost column, the curves represent the sum over all decay channels at NNLO matched to NNLL (teal), the $H\to b\bar{b}$ channel (orange), the $H\to gg$ channel (purple) and the $H \to c\bar{c}$ channel (light blue), and the ratio to the sum is shown in the lower frame.
  • Figure 3: $C$-parameter distribution results for fixed order predictions matched to resummation in the logR scheme for the $H\to q\bar{q}$ channel (left column), $H\to gg$ channel (middle column) and the sum over all channels (right column) for both linear-binning (top row) and logarithmic-binning (bottom row). For the frames in the two leftmost columns, the curves represent the LO calculation matched to NLL resummation (green), NLO matched to NNLL (blue), and NNLO matched to NNLL (red), and the ratio to NLO+NNLL is shown in the lower frame. For the frames in the rightmost column, the curves represent the sum over all decay channels at NNLO matched to NNLL (teal), the $H\to b\bar{b}$ channel (orange), the $H\to gg$ channel (purple) and the $H \to c\bar{c}$ channel (light blue), and the ratio to the sum is shown in the lower frame.