The Thrust Distribution at NNLO+NNLL in Higgs Decays to Quarks and Gluons

TL;DR

This work delivers the first NNLO+NNLL predictions for the thrust distribution in hadronic Higgs decays to $H\to q\bar{q}$ and $H\to gg$. By combining NNLO fixed-order results from NNLOJET with an analytic NNLL resummation in the ARES framework and employing logR matching, it provides a precise description of the small-$\tau$ region while preserving fixed-order accuracy in the large-$\tau$ region. The authors analytically extract the $c_2$ and $G_{31}$ coefficients for both decay channels, and validate the resummed expansion against fixed-order calculations in the infrared. The resulting NNLO+NNLL predictions reduce theoretical uncertainties and offer a robust benchmark for parton-shower approaches, with potential extensions to higher-logarithmic accuracy and other event-shape observables.

Abstract

We present a calculation of the thrust distribution in Higgs decays to quarks and gluons, $H\to b\bar{b}$, $H\to c\bar{c}$, and $H\to gg$, including the resummation of large logarithmic corrections that arise in the two-particle limit at next-to-next-to-leading logarithmic (NNLL) accuracy, and match it to fixed-order results for three-particle decays at next-to-next-to-leading order (NNLO) in the strong coupling. The resummation is performed analytically within the ARES framework and combined with the fixed-order results using the logR matching technique. The fixed-order calculation is carried out numerically with the NNLOJET parton-level event generator, using the antenna subtraction method. We perform detailed cross-validation in the two-particle region, demonstrating that the expansion of the NNLL resummed result correctly reproduces the logarithmic structure of the fixed-order calculation to $\mathcal{O}(α_\mathrm{s}^3)$, up to a predictable N$^{3}$LL term at $\mathcal{O}(α_\mathrm{s}^3L)$. In addition to providing the first NNLO+NNLL accurate predictions for the thrust distribution in Higgs decays to quarks and gluons, we analytically extract the $\mathcal{O}(α_\mathrm{s}^2)$ hard-virtual correction $c_2$ and the $α_\mathrm{s}^3L$ term $G_{31}$ in both the $H\to q\bar{q}$ ($q=b,c$) and $H\to gg$ decay channels.

Figures (7)

• 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: Comparison of resummed results for thrust at LL (green), NLL (blue), and NNLL (red) in $H\to q\bar{q}$ decays (left) and $H\to gg$ decays (right).
• Figure 3: Comparison between the expansion of the resummation formula (solid lines) and the fixed-order results (dashed lines) up to $\mathcal{O}(\alpha\xspace_s)$ (LO, green), up to $\mathcal{O}(\alpha\xspace_s^2)$ (NLO, blue) and up to $\mathcal{O}(\alpha\xspace_s^3)$ (NNLO, red). The difference between the fixed-order and the expansion of the resummation formula is shown in the lower frames.
• Figure 4: Thrust distribution results for fixed-order predictions matched to resummation in the logR scheme, for the $H\to q\bar{q}$ channel (left column) and the $H\to gg$ channel (right column), on a linear scale (top row) and on a log scale (bottom row). The curves represent the LO calculation matched to NLL resummation (green), NLO matched to NNLL (blue) and NNLO matched to NNLL (red).
• Figure 5: Comparison between NNLO (dashed line) and NNLO+NNLL (solid line) predictions for the thrust distribution in the hadronic decay of a Higgs boson in the Yukawa (left) and gluonic (right) modes.