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Heavy Jet Mass in Hadronic Higgs Decays

This paper presents state-of-the-art predictions for heavy jet mass distributions in hadronic Higgs decays by computing next-to-next-to-next-to-leading logarithmic resummation in the dijet limit and next-to-next-to-leading logarithmic resummation including Sudakov shoulder effects in the trijet limit, matched to next-to-next-to-leading order within Soft-Collinear Effective Theory.

Original authors: Luen Clingerman, Xiaoyuan Zhang

Published 2026-07-29

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CC BY 4.0

Original authors: Luen Clingerman, Xiaoyuan Zhang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, invisible Lego set. For decades, physicists have been trying to figure out exactly how the pieces snap together. At the very center of this puzzle is the Higgs boson, a particle discovered in 2012 that acts like the "glue" giving mass to other particles. But knowing the glue exists isn't enough; scientists need to know exactly how strong it is and how it behaves. To do this, they smash particles together at incredible speeds in massive machines called colliders. When these particles collide, they shatter into showers of smaller pieces, much like a glass vase exploding on a hard floor.

One of the most interesting ways to study these explosions is by looking at the shape of the debris. Physicists use a tool called "thrust" to see if the debris flies out in two neat, opposing jets (like a firework shooting two streams) or if it spreads out more chaotically. From this, they calculate something called "Heavy Jet Mass," which is essentially a measure of how heavy the biggest clump of debris is in a specific direction. Think of it like weighing the heaviest pile of shrapnel after an explosion. The problem is that the math describing these explosions gets incredibly messy. When the debris is very light and the jets are very narrow, the equations produce huge, confusing numbers that make predictions unreliable. It's like trying to predict the weather by counting every single raindrop; you need a better way to handle the storm.

This paper tackles that messiness by creating a super-precise map for these particle explosions, specifically when the Higgs boson decays into other particles. The authors, Luen Clingerman and Xiaoyuan Zhang, have developed a new mathematical technique to smooth out the rough spots in the predictions. They focused on a tricky region where the debris forms three distinct jets instead of two, creating a "shoulder" in the data graph—a bump that looks like a hiker's shoulder on a mountain range. In the past, this shoulder was a place where the math broke down and predictions went haywire. The team used a sophisticated framework called Soft-Collinear Effective Theory (SCET) to fix this. They didn't just guess; they calculated the behavior of these particles up to a level of precision never before achieved for this specific decay, matching their new "shoulder-smoothing" math with existing high-level data.

The result is a much clearer picture of what happens when a Higgs boson turns into gluons or quarks. By fixing the math at this "shoulder" point, the authors found that the predictions become far more stable and reliable. They showed that previous methods missed some important details, leading to errors in the predicted shape of the debris. Their new method, which combines different layers of calculation, suggests that the "shoulder" isn't a jagged cliff but a smooth curve, and they can now predict exactly how the particles behave there. This isn't just a theoretical exercise; it provides the best possible tools for future experiments at machines like the FCC-ee, which will act as "Higgs factories" to study this particle in extreme detail. With these improved maps, scientists will be able to measure the strength of the Higgs force with much higher accuracy, potentially revealing if there are any cracks in our current understanding of the universe's fundamental rules.

Technical Summary: Heavy Jet Mass in Hadronic Higgs Decays

Problem Statement
The paper addresses the theoretical description of the heavy jet mass (HJM) distribution in hadronic Higgs decays ( $H \to gg$ and $H \to q\bar{q}$ ). While fixed-order predictions for Higgs decays have reached high orders (N $^3$ LO for inclusive widths, N $^3$ LO for differential distributions), event shape observables like HJM suffer from large logarithmic enhancements in specific kinematic limits that spoil the convergence of perturbation theory.
Two distinct regimes require resummation:

The Dijet Limit ( $\rho \to 0$ ): Large logarithms arise from soft and collinear emissions in back-to-back jet configurations.
The Trijet Limit (Sudakov Shoulder, $\rho \to 1/3$ ): A "kink" or non-analytic behavior appears at $\rho = 1/3$ , corresponding to the symmetric three-jet configuration. In this region, the differential distribution develops logarithms of the distance to the boundary ( $\ln(1/3 - \rho)$ and $\ln(\rho - 1/3)$ ) due to the incomplete cancellation of infrared singularities between final states with different parton multiplicities. Standard fixed-order calculations are unreliable near this shoulder.

Methodology
The authors employ Soft-Collinear Effective Theory (SCET) to factorize and resum these large logarithms to all orders. The approach involves:

Dijet Resummation: The authors revisit the dijet factorization theorem, decomposing the cross-section into hard, jet, and soft functions. They compute the distribution at N $^3$ LL' (next-to-next-to-next-to-leading logarithmic prime) accuracy, matched to NNLO (next-to-next-to-leading order) fixed-order results. This includes the inclusion of non-global logarithms (NGLs) at two loops and a model for the three-loop NGLs.
Trijet (Shoulder) Resummation: The paper extends the Sudakov shoulder factorization theorem (previously applied to $e^+e^- \to q\bar{q}$ $e^{+} e^{-} \to q \overset{q}{ˉ}$ ) to hadronic Higgs decays.
- Analytic NLO Calculation: The authors perform a leading-power expansion of the four-parton matrix elements and phase space around the symmetric trijet configuration ( $\rho = 1/3$ ). They derive analytic expressions for the NLO ( $O(\alpha_s^2)$ ) shoulder logarithms for both $H \to gg$ and $H \to q\bar{q}$ processes, identifying the specific contributions from $2+2$ and $3+1$ hemisphere partitions.
- Factorization: The shoulder region is factorized into trijet hard functions, jet functions, and hemisphere soft functions. The hard functions are matched from QCD amplitudes to SCET operators at the symmetric point.
- Resummation: The authors perform NNLL (next-to-next-to-leading logarithmic) resummation for the shoulder region. To handle "Sudakov Landau poles" arising from the integration over hemisphere masses, they utilize a position-space (Fourier) resummation technique, similar to TMD resummation, before transforming back to momentum space.
Matching and Profile Scales: A unified prediction is constructed by matching the dijet and shoulder resummations to the fixed-order result. The authors introduce specific profile functions to smoothly turn off the dijet resummation as $\rho$ approaches $1/3$ and the shoulder resummation as $\rho$ moves away from $1/3$ , ensuring no double counting and a smooth transition between regimes.

Key Contributions

N $^3$ LL' Dijet Resummation: The paper provides the first N $^3$ LL' resummation for HJM in hadronic Higgs decays, matched to NNLO. This represents a state-of-the-art improvement over previous NNLL calculations.
Shoulder Factorization in Higgs Decays: The authors generalize the Sudakov shoulder framework to $H \to gg$ and $H \to q\bar{q}$ , deriving the necessary hard and soft functions for these channels.
Analytic NLO Shoulder Coefficients: New analytic results for the NLO shoulder logarithms ( $d^\pm_{22}$ and $d^\pm_{21}$ coefficients) are presented for both gluon and quark-initiated Higgs decays. These serve as non-trivial checks for the factorization theorem.
Unified Prediction: The paper delivers a combined prediction that includes dijet resummation, shoulder resummation, and fixed-order corrections, validated against numerical data from the Eerad3 program.

Results

Convergence: The combined resummation (N $^3$ LL' $_{dij}$ + NNLL $_{sh}$ + NNLO) demonstrates good perturbative convergence for both $H \to gg$ and $H \to q\bar{q}$ .
Shoulder Impact: The inclusion of shoulder resummation significantly improves the description of the distribution near $\rho = 1/3$ $ρ = 1/3$ . It smooths the "kink" present in fixed-order and standalone dijet-resummed predictions.
- For $H \to q\bar{q}$ , the shoulder correction is moderate but becomes sizable near the endpoint.
- For $H \to gg$ , the correction is substantial, reaching tens of percent before the endpoint and becoming order-one very close to the shoulder.
Peak Locations: The authors observe that the peak of the HJM distribution for $H \to gg$ occurs at a significantly larger $\rho$ ( $\sim 0.1$ ) compared to $H \to q\bar{q}$ ( $\sim 0.025$ ), reflecting the larger color charge and potentially stronger non-perturbative effects in the gluon channel.

Significance
The paper claims that these results provide state-of-the-art predictions for heavy jet mass in Higgs decays, which are essential for precision measurements at future lepton colliders (e.g., FCC-ee, CEPC, muon colliders). Specifically:

Strong Coupling ( $\alpha_s$ ): The HJM distribution offers a theoretically clean handle on $\alpha_s$ . The authors note that current extractions from event shapes at LEP show a tension with the world average; an independent determination from the gluon-initiated $H \to gg$ channel could help resolve this discrepancy.
Yukawa Couplings: The distribution allows for the simultaneous measurement of the effective Higgs-gluon coupling ( $\lambda$ ) and the bottom Yukawa coupling ( $y_b$ ), constraining their ratio directly from the shape of the distribution.
Non-perturbative Physics: The high-accuracy perturbative predictions are a prerequisite for extracting non-perturbative parameters, such as the gluon non-perturbative power correction parameter $\Omega_{1g}$ , which is currently unknown.

The authors conclude that while their work establishes the perturbative baseline, future extensions are needed to systematically incorporate non-perturbative shape functions, hadron-mass effects, and trijet power corrections to fully exploit the potential of HJM as a precision observable.

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