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arxiv: 2605.18679 · v1 · pith:YQDU6YHKnew · submitted 2026-05-18 · ✦ hep-ph

NLO EW and QCD dimension-6 SMEFT results for Higgs and gauge boson decays in POPxf format

Luigi Bellafronte , Sally Dawson , Clara Del Pio , Matthew Forslund , Pier Paolo Giardino This is my paper

Pith reviewed 2026-05-20 09:10 UTC · model grok-4.3

classification ✦ hep-ph
keywords SMEFTNLO correctionsHiggs decaysHiggs widthElectroweak precision observablesHiggstrahlungEffective field theoryQCD and EW corrections
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The pith

Dimension-6 SMEFT calculations at NLO give predictions for all Higgs decays and the total width plus gauge boson processes.

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

The paper computes next-to-leading-order QCD and electroweak corrections in the dimension-6 Standard Model Effective Field Theory for every two- and four-body Higgs decay, for Z and W decays together with electroweak precision observables, and for the Higgstrahlung process at center-of-mass energies of 240, 365, and 500 GeV. Results appear in the POPxf format so they can be plugged directly into experimental and phenomenological studies. The total Higgs width that includes every dimension-6 contribution at NLO receives special emphasis as a quantity useful across many analyses. Differential distributions for the four-lepton final state from Higgs decay are also supplied. Readers would care because these predictions supply a consistent baseline for spotting deviations from Standard Model expectations in precision Higgs measurements.

Core claim

We present next-to-leading-order QCD and electroweak results using the dimension-6 SMEFT for all 2- and 4-body Higgs decays, for Z and W decays along with the corresponding EW precision observables, and for the Higgstrahlung process e+e−→ZH at √s=240, 365 and 500 GeV. The results are presented in the POPxf format for ease of use in experimental and phenomenological studies. Of particular utility is the total Higgs width, including all dimension-6 contributions at NLO. In addition, we present the differential distributions dΓ/dm_{Z*} for H→l+l−Z*, Z*→l+l− at NLO in the SMEFT.

What carries the argument

The complete set of dimension-6 SMEFT operator contributions evaluated at NLO in both QCD and electroweak corrections, delivered in POPxf format.

If this is right

  • The total Higgs width now carries consistent NLO dimension-6 corrections for use in global fits to Higgs data.
  • Z and W decay widths and electroweak precision observables receive matching NLO SMEFT corrections from the same calculation.
  • Differential distributions for four-body Higgs decays become available for direct comparison with data.
  • Higgstrahlung cross sections at NLO are supplied for collider energies relevant to proposed future machines.
  • The POPxf output format permits immediate implementation in simulation codes and experimental analyses.

Where Pith is reading between the lines

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

  • These results could be combined with existing LHC measurements to extract tighter bounds on individual dimension-6 operator coefficients.
  • The same framework could be run at higher energies to test where the dimension-6 truncation ceases to be reliable.
  • Direct inclusion of the POPxf tables in Monte Carlo event generators would allow automated SMEFT studies of many final states.

Load-bearing premise

Higher-dimensional operators beyond dimension six remain negligible for the processes and energy scales under study.

What would settle it

A measurement of the total Higgs width or of dΓ/dm_{Z*} in H→l+l−Z* that falls outside the predicted band after all experimental and theoretical uncertainties are included would show the calculations miss relevant effects.

Figures

Figures reproduced from arXiv: 2605.18679 by Clara Del Pio, Luigi Bellafronte, Matthew Forslund, Pier Paolo Giardino, Sally Dawson.

Figure 1
Figure 1. Figure 1: SMEFT contributions to the branching ratio of Higgs decay to [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SMEFT contributions to the branching ratio of Higgs decay to [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: SMEFT contribution to the branching ratio of Higgs decay to [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: SMEFT contributions to the total Higgs width normalized to the best SM [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: SMEFT contributions to the total Higgs width normalized to the best SM [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: SMEFT contributions to the total Higgs width normalized to the best SM [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: SMEFT contribution to branching ratio H → e +e −µ +µ −. LHS: The curves with OS and MS renormalization are indistinguishable. -0.004 -0.002 0.002 0.004 -0.0005 0.0005 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: SMEFT contribution to branching ratio H → e +e −µ +µ −. cays and for all 2-body Z-pole decays using the POPxf data structure. These results can be straightforwardly implemented into global fits and experimental codes. For completeness, we have also presentd NLO SMEFT results for e +e − → ZH in the POPxf format. The eventual goal of the dimension-6 NLO QCD/EW SMEFT program is to have all the ingredients req… view at source ↗
Figure 9
Figure 9. Figure 9: SMEFT contributions to the dΓ /dMZ∗ differential distributions for H → e +e −µ +µ − [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: SMEFT contributions to the dΓ /dMZ∗ differential distributions for H → e +e −e +e −. MCIN/AEI/10.13039/501100011033 and by FSE+, and by the Spanish Research Agency (Agen￾cia Estatal de Investigación) through the grant IFT Centro de Excelencia Severo Ochoa No CEX2020- 001007-S. The work of L.B. is supported in part by the U.S. Department of Energy under Grant No. DE-SC0010102 and by the College of Arts and… view at source ↗
Figure 11
Figure 11. Figure 11: Results for ΓZ proportional to CφD at LO and NLO in different input schemes normalized to the most accurate theoretical prediction. -0.0010 -0.0005 0.0005 0.0010 -0.00004 -0.00002 0.00002 0.00004 [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Results for ΓZ proportional to CφW B at LO and NLO in different input schemes normalized to the most accurate theoretical prediction. -0.0010 -0.0005 0.0005 0.0010 -5. × 10-7 5. × 10-7 [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Results for ΓZ proportional to C (3) lq at LO and NLO in different input schemes normalized to the most accurate theoretical prediction. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Results for Re proportional to CφD at LO and NLO in different input schemes normalized to the most accurate theoretical prediction. -0.0010 -0.0005 0.0005 0.0010 -0.00004 -0.00002 0.00002 0.00004 [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Results for Re proportional to CφW B at LO and NLO in different input schemes normalized to the most accurate theoretical prediction. -0.0010 -0.0005 0.0005 0.0010 -3. × 10-6 -2. × 10-6 -1. × 10-6 1. × 10-6 2. × 10-6 3. × 10-6 [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Results for Re proportional to C (3) lq at LO and NLO in different input schemes normalized to the most accurate theoretical prediction. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Results for Ae proportional to CφD at LO and NLO in different input schemes normalized to the most accurate theoretical prediction. -0.0010 -0.0005 0.0005 0.0010 -0.002 -0.001 0.001 0.002 [PITH_FULL_IMAGE:figures/full_fig_p012_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Results for Ae proportional to CφW B at LO and NLO in different input schemes normalized to the most accurate theoretical prediction. -0.0010 -0.0005 0.0005 0.0010 -0.000015 -0.000010 -5. × 10-6 5. × 10-6 0.000010 0.000015 [PITH_FULL_IMAGE:figures/full_fig_p012_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Results for Ae proportional to C (3) lq at LO and NLO in different input schemes normalized to the most accurate theoretical prediction. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_19.png] view at source ↗
read the original abstract

We present next-to-leading-order (NLO) QCD and electroweak (EW) results using the dimension-6 SMEFT for all 2- and 4- body Higgs decays, for $Z$ and $W$ decays along with the corresponding EW precision observables, and for the Higgstrahlung process $e^+e^-\rightarrow ZH$ at $\sqrt{s}=240$, $365$ and $500$ GeV. The results are presented in the POPxf format for ease of use in experimental and phenomenological studies. Of particular utility is the total Higgs width, including all dimension-6 contributions at NLO. In addition, we present the differential distributions $d\Gamma/dm_{Z*}$ for $H\rightarrow l^+l^- Z^*, Z^*\rightarrow l^+l^-$ at NLO in the SMEFT.

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

0 major / 3 minor

Summary. The paper presents next-to-leading-order (NLO) QCD and electroweak corrections in the dimension-6 SMEFT for all 2- and 4-body Higgs decays, Z and W decays with associated EW precision observables, and the Higgstrahlung process e+e−→ZH at √s=240, 365 and 500 GeV. Results are given in POPxf format, with emphasis on the total Higgs width at NLO and the differential distribution dΓ/dm_Z* for H→l+l−Z*, Z*→l+l−.

Significance. If the NLO computations are complete and correctly implemented, the work supplies a practical resource of SMEFT predictions in a standardized format that can be directly ingested by experimental analyses and global fits. The simultaneous treatment of QCD and EW corrections at NLO for a broad set of processes, together with the total width, addresses a concrete need for precision phenomenology at the LHC and future e+e− colliders.

minor comments (3)
  1. Abstract: the phrase 'all 2- and 4-body Higgs decays' is broad; an explicit list of the final states retained (or a reference to the operator basis used) would remove ambiguity about coverage.
  2. Section describing the POPxf output: a short usage example or pointer to the accompanying data files would improve immediate usability for phenomenologists.
  3. Discussion of the differential distribution: the kinematic cuts or binning choices applied to dΓ/dm_Z* should be stated explicitly so that the results can be reproduced without additional assumptions.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our work and for recommending minor revision. The referee correctly identifies the scope of our NLO QCD and EW results in the dimension-6 SMEFT, including the total Higgs width and differential distributions in POPxf format. We appreciate the recognition of its utility for experimental analyses and global fits.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper is a computational phenomenology study that enumerates NLO QCD and EW corrections to Higgs, Z, W decays and related processes in the dimension-6 SMEFT using the Warsaw basis. No derivation chain is claimed that reduces a central result to a fitted parameter, self-definition, or self-citation load-bearing premise. All results follow from standard one-loop renormalization and matching applied to the SMEFT Lagrangian, with explicit inclusion of all relevant operators and interference terms. The presentation in POPxf format is a data-delivery choice, not a redefinition of any quantity. The work is self-contained against external benchmarks and contains no load-bearing step that collapses to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The calculations rest on the standard SMEFT framework truncated at dimension 6 and perturbative NLO expansion in QCD and EW couplings. No new free parameters are introduced beyond the Wilson coefficients, which serve as inputs rather than fitted outputs of this work.

axioms (1)
  • domain assumption The SMEFT truncated at dimension-6 operators is an adequate description for the Higgs and gauge boson processes at the considered energies.
    This truncation assumption underpins the inclusion of all dimension-6 contributions at NLO as stated in the abstract.

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