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arxiv: 2605.24131 · v1 · pith:B7MO2JZVnew · submitted 2026-05-22 · ✦ hep-ph · hep-ex

Associated ZH production in gluon fusion process at NLO+NLL

Pulak Banerjee , Chinmoy Dey , Niraj Koirala , M.C. Kumar , Vaibhav Pandey This is my paper

Pith reviewed 2026-06-30 15:41 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords ZH productiongluon fusionNLONLL resummationthreshold logarithmsQCD correctionsLHC phenomenologytop quark mass
0
0 comments X

The pith

NLO+NLL matching for gluon-fusion ZH production increases the cross section by 20% at 13.6 TeV.

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

This paper calculates the associated production of Z and Higgs bosons via gluon fusion, incorporating next-to-leading order QCD corrections matched with next-to-leading logarithmic threshold resummation. The calculation uses the exact dependence on the top quark mass in the virtual corrections. At the LHC operating at 13.6 TeV, the matched NLO+NLL result boosts the total cross section by roughly 20 percent over the pure NLO value. In the differential distributions at an invariant mass of 3000 GeV, the theoretical uncertainty from renormalization and factorization scales shrinks from 20 percent at NLO to 12 percent after resummation. The gluon-fusion results are further combined with Drell-Yan contributions resummed to N3LL accuracy to obtain the most precise predictions currently available.

Core claim

Precise results are presented for invariant mass distributions and inclusive cross sections of ZH production in gluon fusion. NLL threshold logarithms are matched to NLO with exact top-quark mass dependence. The NLO+NLL cross section at 13.6 TeV is about 20% larger than NLO, and scale uncertainties at 3000 GeV drop from 20% to 12%. These are combined with Drell-Yan N3LL results for the highest precision in hadron collisions.

What carries the argument

The threshold resummation at NLL accuracy matched to the full NLO calculation with exact top quark mass dependence.

If this is right

  • The total cross section rises by 20% at LHC 13.6 TeV compared to NLO.
  • Scale uncertainties in distributions reduce to 12% at 3000 GeV invariant mass.
  • The combined gluon fusion plus Drell-Yan prediction at high accuracy provides the benchmark for experimental comparisons.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This matched approach may be extended to other Higgs-associated processes to similarly reduce uncertainties.
  • Lower theoretical errors could enhance the sensitivity of LHC measurements to deviations from standard model predictions.
  • The improvement in high-mass regions suggests potential for better background estimates in searches for heavy resonances.

Load-bearing premise

The matching between NLL resummation and NLO with exact top mass dependence introduces no substantial additional uncertainties beyond those already considered.

What would settle it

A precise measurement of the inclusive ZH cross section at 13.6 TeV LHC that differs significantly from the NLO+NLL prediction, outside the combined theoretical and experimental uncertainties, would indicate a problem with the calculation.

read the original abstract

We present precise results for invariant mass distributions and inclusive cross-sections, of associated $ZH$ production through gluon fusion in QCD. We include threshold logarithms at next-to-leading-logarithmic (NLL) accuracy and match the results to full next-to-leading-order (NLO) results with exact top-quark mass dependence in the virtual amplitudes. At 13.6 TeV energy at LHC, the NLO+NLL cross-section increases the NLO counterpart by about $20\%$. For differential distributions, at 3000 GeV, the uncertainties arising out of the unphysical renormalization and factorization scales is about $20\%$ for NLO; whereas for the resummed results it is around $12\%$. We also combine these results to the Drell-Yan type results at N$^3$LL and present the most precise results in hadron collisions.

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 / 0 minor

Summary. The manuscript presents NLO+NLL QCD calculations for gluon-fusion associated ZH production, incorporating threshold resummation at NLL matched to full NLO results that retain exact top-quark mass dependence in the virtual amplitudes. It reports an approximately 20% increase in the inclusive cross section at 13.6 TeV LHC relative to NLO alone, and a reduction in renormalization/factorization scale uncertainties from ~20% (NLO) to ~12% (NLO+NLL) for differential distributions at 3000 GeV invariant mass. The results are further combined with Drell-Yan-type contributions at N³LL accuracy.

Significance. If the matching is free of unaccounted mass-dependent higher-order artifacts, the work supplies more precise predictions and reduced scale uncertainties for an important Higgs-associated channel at the LHC. The combination with N³LL DY-like terms would represent a notable advance in phenomenological accuracy for hadron-collider ZH production.

major comments (1)
  1. [Abstract] Abstract: the matching of NLL threshold resummation (typically formulated with mass-independent hard functions) onto NLO virtual amplitudes retaining exact top-quark mass dependence is stated but not accompanied by an explicit subtraction formula or numerical test isolating mass-dependent O(α_s²) terms at high invariant mass; this matching is load-bearing for the quoted 20% enhancement and the uncertainty reduction from 20% to 12%.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for identifying this important point about the matching procedure. We address the comment below and will revise the manuscript accordingly to improve clarity.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the matching of NLL threshold resummation (typically formulated with mass-independent hard functions) onto NLO virtual amplitudes retaining exact top-quark mass dependence is stated but not accompanied by an explicit subtraction formula or numerical test isolating mass-dependent O(α_s²) terms at high invariant mass; this matching is load-bearing for the quoted 20% enhancement and the uncertainty reduction from 20% to 12%.

    Authors: We thank the referee for this observation. The NLL threshold resummation employs the standard mass-independent hard and soft functions, as the leading threshold logarithms are process-independent. Matching to the full massive NLO is performed via the standard procedure: the NLO expansion of the resummed (massless) result is subtracted from the complete massive NLO cross section before adding the resummed contribution. This retains all exact top-mass dependence present at NLO while resumming the higher-order threshold logs. Mass-dependent O(α_s²) contributions beyond NLO are not resummed but are power-suppressed at large invariant mass; their numerical size is expected to be modest. To make this fully explicit, the revised manuscript will include the subtraction formula in the methods section and add a numerical test (e.g., comparing massive vs. massless NLO at Q=3000 GeV) to quantify the impact on the 20% enhancement and scale-uncertainty reduction. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is a standard perturbative matching

full rationale

The paper computes NLO+NLL results for gg -> ZH by matching threshold-resummed logarithms (NLL) to full NLO virtual amplitudes retaining exact top-mass dependence, then combines with Drell-Yan N3LL results. No quoted equation reduces a prediction to a fitted parameter by construction, no self-citation supplies a uniqueness theorem or ansatz that bears the central claim, and no renaming of known results occurs. The numerical claims (20% enhancement, scale-uncertainty reduction) follow directly from the matching procedure applied to external parton distributions and standard resummation kernels, rendering the chain self-contained against benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Since only the abstract is available, the ledger is based on typical assumptions for such perturbative calculations in QCD; no new entities or ad-hoc fitted parameters beyond standard scale variations are indicated.

free parameters (2)
  • renormalization scale
    Unphysical scale varied to estimate uncertainty, as mentioned in the abstract for NLO and resummed results.
  • factorization scale
    Unphysical scale varied to estimate uncertainty, as mentioned in the abstract for NLO and resummed results.
axioms (1)
  • domain assumption Perturbative QCD expansion is valid and applicable at LHC energies for this process
    Underlying the NLO and NLL calculations described in the abstract.

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discussion (0)

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Reference graph

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