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arxiv: 2603.18875 · v1 · submitted 2026-03-19 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Hadron production through Higgs decay at next-to-leading order in the general-mass variable-flavor-number scheme

S. Mohammad Moosavi Nejad
Authors on Pith no claims yet

Pith reviewed 2026-05-15 08:47 UTC · model grok-4.3

classification ✦ hep-ph
keywords Higgs decayB-meson productionGeneral-mass variable-flavor-number schemeNext-to-leading order QCDFragmentation functionsScaled-energy distributionBottom quark mass effects
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The pith

Mass effects of B-mesons enhance the partial decay width of Higgs to B-jets at low scaled energies while b-quark mass enhances the peak region.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper calculates the scaled-energy distribution of B-mesons from Higgs decays into bottom quarks while including the masses of both the b-quarks and the B-mesons. It applies the general-mass variable-flavor-number scheme at next-to-leading order in perturbative QCD for the first time. Earlier work used massless approximations that omitted these effects. The calculation shows clear enhancements to the decay rate in distinct regions of the scaled-energy variable x_B. Readers should care because this refines predictions for the dominant Higgs decay channel used to probe Higgs properties at the LHC.

Core claim

About 60% of Higgses produced at the CERN-LHC decay into bottom quarks that hadronize into B-mesons. The study of the scaled-energy distribution of B-mesons in H to B plus jets therefore offers a channel to extract Higgs characteristics. This work studies the mass effects of b-quarks and produced mesons on the x_B distribution by working in the general-mass variable-flavor-number scheme at next-to-leading order. The meson mass produces a significant enhancement of the partial decay width in the low-x_B region while the b-quark mass produces an enhancement in the peak region and above.

What carries the argument

The general-mass variable-flavor-number scheme at next-to-leading order, which incorporates the masses of heavy quarks and hadrons into perturbative calculations together with fragmentation functions.

Load-bearing premise

The general-mass variable-flavor-number scheme at next-to-leading order with fitted fragmentation functions captures the mass effects without significant higher-order or non-perturbative corrections beyond those already included.

What would settle it

A high-precision measurement of the B-meson scaled-energy spectrum in Higgs decays at the LHC that matches the massless-scheme prediction with no extra enhancement in the low-x_B or peak regions would falsify the claimed importance of the mass effects.

Figures

Figures reproduced from arXiv: 2603.18875 by S. Mohammad Moosavi Nejad.

Figure 1
Figure 1. Figure 1: Higgs decay Feynman diagrams at NLO: (A) tree [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: 1/Γ˜0 × dΓ(H → B + X)/dxB as a function of xB in the GM-VFN scheme. The NLO result (blue dot-dashed line) is compared to the LO one (black solid line) and broken up into the contributions due to b → B (green dotted line) and g → B (red dashed line) fragmentation. Here we set mB = 0. decay width increases about 6% at xB ≈ 0.55. As was previously mentioned, in Eqs. (27,28) we can use different values for the… view at source ↗
Figure 4
Figure 4. Figure 4: 1/Γ0 × dΓ(H → B + X)/dxB as a function of xB at NLO in the GM-VFN (mb 6= 0) scheme with (red dashed line) and without (blue solid line) finite-mB corrections. Both results are normalized to the ZM-VFN result (mb = 0) for mB = 0. Here, we set µ = mH. make a more detailed study of Higgs bosons, specifically via their decay processes. Over 80% of Higgs boson de￾cays are fully hadronic, of which around 60% dec… view at source ↗
Figure 5
Figure 5. Figure 5: 1/Γ˜0 ×dΓ(H → B + X)/dxB as a function of xB at NLO in the GM-VFN scheme considering various values for the scale µ, i.e. mH/2 ≤ µ ≤ 2mH. The result for µ = mH is also shown (black dashed line). work we studied the process of B-mesons production in the decays of Higgs bosons at NLO pQCD, i.e., H → b ¯b(+g) → B + Jets. For this study we evaluated the dis￾tribution in the scaled-energy of B-mesons which woul… view at source ↗
read the original abstract

It is known that about $60\%$ of all Higgses produced at the CERN-LHC decay into a pair of bottom quarks. Bottoms quickly hadronize, in most cases, into bottom-flavored (B) hadrons before they decay. Therefore, the study of scaled-energy distribution of B-mesons in the decay process $H\to B+Jets$ can be considered as a channel to search for the Higgs characteristics. In all previous studies, authors have ignored the mass effect of b-quarks as well as B-mesons by working in the massless scheme. In this work we, for the first time, study the mass effect of b-quarks as well as produced mesons on the scaled-energy ($x_B$) distribution of B-mesons by working in the massive scheme or general-mass variable-flavor-number scheme (GM-VFNs). We find that the meson mass is responsible for a significant enhancement of partial decay width in the low-$x_B$ region while the b-quark mass leads to an enhancement of the partial decay rate in the peak region and above.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper computes the scaled-energy (x_B) distribution of B-mesons in Higgs decay H → B + jets at NLO in the general-mass variable-flavor-number scheme (GM-VFNS), incorporating finite b-quark and B-meson masses for the first time. It reports that the B-meson mass produces a significant enhancement of the partial decay width at low x_B, while the b-quark mass enhances the distribution in the peak region and above.

Significance. If the numerical results hold under consistent mass treatment, the work supplies the first NLO GM-VFNS predictions for this observable, filling a gap left by prior massless-scheme calculations. This could refine LHC analyses of Higgs decays to bottom quarks by quantifying mass-induced shifts in the B-meson spectrum.

major comments (1)
  1. [§3 and §4] §3 (methodology) and §4 (numerical results): The central attribution of enhancements to meson mass at low x_B and b-quark mass at the peak relies on convolving NLO GM-VFNS coefficients with fragmentation functions fitted in external schemes (typically zero-mass or differently resummed). No explicit variation of FF parametrizations or refit within GM-VFNS is shown to confirm that the reported shifts survive; this mixing of non-perturbative inputs risks confounding the mass-effect separation.
minor comments (2)
  1. [§2] Notation for the scaled variable x_B and the partial decay width should be defined explicitly at first use in §2 to avoid ambiguity with standard fragmentation variables.
  2. [§4] Figure captions in §4 should state the precise scale choices (μ_R, μ_F) and FF set used for each curve to improve reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment. We address the major point below.

read point-by-point responses

  1. Referee: [§3 and §4] §3 (methodology) and §4 (numerical results): The central attribution of enhancements to meson mass at low x_B and b-quark mass at the peak relies on convolving NLO GM-VFNS coefficients with fragmentation functions fitted in external schemes (typically zero-mass or differently resummed). No explicit variation of FF parametrizations or refit within GM-VFNS is shown to confirm that the reported shifts survive; this mixing of non-perturbative inputs risks confounding the mass-effect separation.

    Authors: We thank the referee for highlighting this aspect of our methodology. In our calculation the NLO GM-VFNS coefficient functions contain the explicit b-quark and B-meson mass dependence, while the fragmentation functions are taken from established parametrizations in the literature. The same FF set is used for all mass configurations (massless limit, finite b-quark mass only, and full GM-VFNS), so that the reported enhancements at low x_B and in the peak region arise solely from the mass terms in the perturbative coefficients. A complete refit of the FFs inside the GM-VFNS would require a global analysis of multiple processes and lies beyond the scope of the present work, which focuses on the first NLO implementation for this observable. In the revised manuscript we will add a short paragraph in Section 4 discussing the choice of FFs and the robustness of the mass-effect separation under this standard procedure. revision: partial

Circularity Check

0 steps flagged

No significant circularity; mass enhancements arise from explicit perturbative coefficients

full rationale

The paper performs a standard NLO calculation of the scaled-energy distribution in the GM-VFNS, inserting b-quark and meson masses directly into the hard-scattering kernels and convoluting with externally fitted fragmentation functions. The reported low-x_B enhancement from meson mass and peak-region enhancement from b-quark mass are numerical outputs of this convolution; they do not reduce to the fit parameters by construction, nor does any load-bearing step rely on self-citation or an imported uniqueness theorem. The derivation chain is self-contained against external benchmarks and follows established factorization theorems without redefining inputs as predictions.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The result rests on perturbative QCD validity at Higgs mass scales, the GM-VFNs factorization scheme, and non-perturbative fragmentation functions fitted to data from other processes; no new entities are introduced.

free parameters (2)
  • Fragmentation function parameters
    Non-perturbative B-meson fragmentation functions are fitted to experimental data from other collisions and enter the calculation of the distribution.
  • Renormalization and factorization scales
    Choice of scales in the NLO calculation, typically varied to estimate uncertainty.
axioms (2)
  • domain assumption Perturbative QCD applies reliably at the energy scale of Higgs decay to bottom quarks
    Standard assumption for NLO calculations in hep-ph; invoked implicitly for the validity of the GM-VFNs scheme.
  • domain assumption The general-mass variable-flavor-number scheme correctly interpolates between massive and massless regimes for heavy quarks
    Core scheme choice for including mass effects without double-counting.

pith-pipeline@v0.9.0 · 5493 in / 1445 out tokens · 39202 ms · 2026-05-15T08:47:00.051526+00:00 · methodology

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Reference graph

Works this paper leans on

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