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REVIEW 4 minor 98 references

Measurement of the Higgs boson decay to a low-mass dilepton system and a photon in $pp$ collisions at $\sqrt{s} =$ 13 and 13.6 TeV with the ATLAS detector

T0 review · 0 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read ATLAS measures the Higgs decay to a low-mass lepton pair plus a photon: combining 13 and 13.6 TeV data, the signal strength is $\mu = 1.03^{+0.35}_{-0.32}$, a 3.4$\sigma$ excess (3.3$\sigma$ expected) consistent with the Standard Model.

desk verdict First Run-3 H→ℓℓγ measurement and a Run-2+3 combination at 3.4σ; solid, honest analysis with a real but manageable background-modelling caveat—worth refereeing carefully. read the letter →

arxiv 2608.03369 v1 pith:K4EK3JIQ submitted 2026-08-04 hep-ex

ATLAS Collaboration This is my paper
classification hep-ex
keywords HiggsbosonH→ℓℓγdecaysignalstrengthATLASLHCRun3mergeddielectronsbackgroundparameterisationevidencesignificance
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Using 164 fb$^{-1}$ of 13.6 TeV collisions (2022–2024) combined with 139 fb$^{-1}$ of 13 TeV data, the ATLAS Collaboration measures the rare Higgs decay $H\to\ell\ell\gamma$ at low dilepton mass ($m_{\ell\ell}<30$ GeV), extracting the signal from a simultaneous fit across nine event categories. The central claim is that the combined signal strength is $\mu = 1.03^{+0.35}_{-0.32}$ against an expected $1.00$, a 3.4$\sigma$ observed excess (3.3$\sigma$ expected) that establishes the decay at evidence level and is consistent with the Standard Model. This matters because $H\to\ell\ell\gamma$ shares the loop-induced Higgs–photon vertex with $H\to\gamma\gamma$, so its rate tests that coupling nearly independently of Higgs production, while the off-shell intermediate photon adds sensitivity to new physics absent in the diphoton channel. The Run-3 dataset alone yields $\mu = 0.64^{+0.44}_{-0.39}$ (1.7$\sigma$ observed, 2.5$\sigma$ expected) and is statistically limited; the paper also states that no dedicated low-$m_{\ell\ell}$ branching-ratio calculation exists, so the signal prediction inherits a 6.9% uncertainty from the $H\to Z\gamma$ rate.

What carries the argument

The argument is carried by three mechanisms: nine mutually exclusive categories ($\mu\mu$, resolved $ee$, merged $ee$ $\times$ VBF, high/low-$p_{\mathrm{T}t}$); signal shapes fixed from simulation as double-sided Crystal Ball functions (a Gaussian core with power-law tails), plus per-category analytic background functions — exponential of a first-order polynomial, power-law, dijet-like, or second-order Bernstein — selected by spurious-signal tests on simulated templates; and an unbinned extended likelihood, profiled over nuisance parameters, that returns the signal strength $\mu$. A new BDT-based identification of merged dielectrons (collimated electron pairs) raises signal efficiency from 6

What would settle it

Repeat the simultaneous fit with each category's non-resonant background replaced by a neighbouring functional form of similar flexibility (for example, an exponential of a second-order polynomial, or a Bernstein polynomial one order higher) and compare the fitted signal strength: a shift in $\mu$ larger than the quoted 0.04 spurious-signal uncertainty would show the functional choice, not the physics, is setting the result. A complementary sideband check is to fit the chosen background functions to the 2022–2024 data below 120 GeV and above 130 GeV and extrapolate into the 120–130 GeV signal

Watch

Extended reading notes

Core claim

The central claim is that $H\to\gamma^*\gamma\to\ell\ell\gamma$ with $m_{\ell\ell}<30$ GeV is established at evidence level: combining the first 13.6 TeV measurement (164 fb$^{-1}$) with the earlier 13 TeV search (139 fb$^{-1}$), the observed signal strength is $\mu = 1.03^{+0.35}_{-0.32}$ (expected $1.00^{+0.34}_{-0.32}$), corresponding to an observed (expected) significance of 3.4 (3.3) standard deviations, and a measured cross-section times branching ratio of $4.1^{+2.8}_{-2.5}$ fb. The result is compatible with the Standard Model. Because the decay shares the loop-induced Higgs–photon coupling of $H\to\gamma\gamma$, a rate consistent with unity tests that coupling at the non-zero virtual

Load-bearing premise

The load-bearing premise is that the smooth analytic functions chosen to model the non-resonant background in each of the nine categories correctly describe the true background inside the 110–160 GeV fitted window; this choice is validated only by spurious-signal tests on simulated templates, and since the signal is a small bump on the continuum (2–25% of events in the signal window), a functional bias that slipped through those tests would shift the fitted signal strength di

Editorial extensions

If this is right

  • With the measurement statistically limited (0.40 vs 0.17 systematic on $\mu$), the remaining Run-3 data and the HL-LHC should push $H\to\ell\ell\gamma$ from 3.4$\sigma$ evidence toward a 5$\sigma$ observation without new techniques.
  • The rate consistent with the Standard Model ($\mu \approx 1$) tightens the constraint on the loop-induced Higgs–photon coupling at non-zero $\gamma^*$ virtuality, complementing $H\to\gamma\gamma$ and $H\to Z\gamma$ measurements.
  • The BDT-based merged-dielectron identification — about 90% signal efficiency at the cut-based background rate — transfers directly to $H\to Z\gamma$ and other final states with collimated low-mass electron pairs.
  • The same $\ell\ell\gamma$ sample can probe the CP properties of the Higgs boson through the forward–backward asymmetry of its decay products, a use the paper motivates in its introduction.
  • The combination yields the first combined 13 + 13.6 TeV measurement of $\sigma(H)\times B(H\to\ell\ell\gamma) = 4.1^{+2.8}_{-2.5}$ fb.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The combined 3.4$\sigma$ evidence is not evenly carried by the two datasets: Run-2 alone observed 3.2$\sigma$ on an expected 2.1$\sigma$ ($\mu=1.5\pm0.5$), while Run-3 alone observed 1.7$\sigma$ on an expected 2.5$\sigma$ ($\mu=0.64$). The combination thus leans on the Run-2 upward fluctuation — a point the paper reports numerically but does not emphasise.
  • Because the intermediate $\gamma^*$ carries a virtuality set by $m_{\ell\ell}$, the dilepton-mass spectrum is a differential handle on new physics that a total-rate measurement washes out: couplings that modify the off-shell Higgs–photon form factor would distort the $m_{\ell\ell}$ shape before moving the inclusive rate. A differential $d\sigma/dm_{\ell\ell}$ measurement is a natural, testable ext
  • The Run-3 deficit relative to expectation (1.7$\sigma$ observed vs 2.5$\sigma$ expected) is consistent with a statistical fluctuation at the current sample size, and the 2025–2026 dataset should distinguish a genuine rate shortfall from noise; the category-level pattern, including negative best-fit signal strengths in some $ee$ VBF categories, is worth watching as data accumulate.
  • The paper approximates VBF-category fake-lepton fractions with values measured in the low-$p_{\mathrm{T}t}$ categories because of limited statistics; this is a modelling approximation worth revisiting, since VBF categories have the highest signal fractions (13–25%).
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

0 major / 4 minor

Summary. The paper reports a measurement of the Higgs boson decay to a low-mass dilepton pair and a photon, H→ℓℓγ with m_ℓℓ < 30 GeV, using 164 fb^-1 of Run-3 pp collisions at 13.6 TeV, and combines it with the earlier Run-2 search using 139 fb^-1. Events are classified into nine categories (three lepton final states × VBF/high-pTt/low-pTt). The signal is extracted by an unbinned simultaneous maximum-likelihood fit to m_ℓℓγ in 110–160 GeV, with signal shapes from simulation and non-resonant backgrounds described by analytic functions chosen per category via spurious-signal studies. The Run-3 result is μ = 0.64 +0.44/−0.39, with observed (expected) significance 1.7σ (2.5σ). The combination yields μ = 1.03 +0.35/−0.32, with observed (expected) significance 3.4σ (3.3σ), providing evidence for the decay. A BDT-based merged-dielectron identification improves the expected significance by 5% relative to the cut-based approach.

Significance. If accepted, this is the first evidence for the H→γ*γ→ℓℓγ process at the LHC based on a combination of Run-2 and Run-3 data, and the first measurement of this channel at 13.6 TeV. The result is consistent with the SM and provides a complementary test of the loop-induced Hγγ coupling. The analysis is technically careful: it includes nine category fits, a spurious-signal-driven background function selection, a detailed systematic breakdown (Table 3), and a statistically consistent combination of two data-taking periods. The paper is clearly written and follows established ATLAS practice. The main limitation, the absence of a dedicated theory uncertainty for the low-m_ℓℓ branching ratio, is acknowledged and proxied by the H→Zγ uncertainty; this is acceptable for the current precision.

minor comments (4)
  1. [Section 6.2.3 / Table 3] The spurious-signal test validates the chosen background functions against the data-reweighted simulated template, not directly against data. I would encourage a closure/robustness check in which alternative functional forms (e.g., exponential of a second-order polynomial, higher-order Bernstein polynomials) are fitted to the data sidebands and the resulting shift in the fitted signal strength is examined. This would further quantify the residual data/MC shape sensitivity beyond the 0.04 spurious-signal uncertainty quoted in Table 3. I do not consider this a blocker, as the background parameters are free in the final fit and the template is reweighted to data (Section 6.2.2), but it would strengthen the paper.
  2. [Section 3, last paragraph] The overall signal selection efficiency of 12.5% is quoted relative to generated H→γ*γ→ℓℓγ events with 2m_ℓ < m_ℓℓ < 90 GeV, while the analysis selects m_ℓℓ < 30 GeV. Please clarify whether the denominator includes the full generated phase space up to 90 GeV or only events that would pass the m_ℓℓ < 30 GeV selection; as written, the efficiency definition is ambiguous.
  3. [Section 8, first paragraph] The decomposition μ = 0.64 +0.40/−0.39 (stat.) +0.18/−0.08 (syst.) does not appear to add exactly in quadrature on the negative side. Please state explicitly how the asymmetric systematic component is computed (e.g., from the profile likelihood or from the quadrature of individual nuisance impacts) or provide the covariance information.
  4. [Section 6.2.3] The description of the spurious-signal criterion would benefit from a reference to the ATLAS recommendation paper [90] at the point where the '20% of the statistical uncertainty' threshold is introduced; this helps readers understand the choice of the threshold.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measurement is self-contained, with the observed signal strength extracted from a data fit against MC signal templates normalized to external SM inputs.

full rationale

The paper's central claim is a measurement, not a derivation from a model. The signal strength is defined as the ratio of the measured signal yield to the SM prediction (Section 6.3: 'The parameter of interest is the signal strength μ, defined as the ratio of the measured signal yield to the SM prediction'), with the SM prediction coming from Geant4-simulated Monte Carlo normalized to SM cross-sections and branching ratios cited from the literature (Section 3: 'The samples are normalised to the SM production cross-sections... The branching ratios are taken as B(H→eeγ)=7.20×10^-5 and B(H→μμγ)=3.42×10^-5'). The observed μ is therefore not defined in terms of its own fit output; it is a fitted parameter compared with an external expectation. The expected signal strength and expected significance are computed from the same simulated signal samples and are not claimed to be data-derived predictions. The background functional forms are chosen via spurious-signal tests on simulated background templates (Section 6.2.3); this is a validation of the analytic ansatz, not a fitting of the signal to data. Any concern about template fidelity is a modeling systematic, which the paper assigns a 0.04 spurious-signal uncertainty (Table 3), rather than a circular step. The self-citations are methodological (Ref. [15] for strategy) or provide an external uncertainty input (Ref. [20] for the 6.9% branching-ratio uncertainty). The paper explicitly notes the absence of a dedicated theory calculation for the low-m_ll branching ratio and borrows a conservative uncertainty from H→Zγ; this is an input limitation, not a circular reduction of the measured signal strength. No step in the derivation reduces by construction to its own inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on external SM inputs (branching ratios and cross-sections from cited theory), simulated signal shapes, and data-fitted background functions. The only ad hoc element is the proxy branching-ratio uncertainty (6.9% from H to Z gamma), which the paper itself flags in Section 3. There are no invented entities; the merged-dielectron BDT is a technique, not a new physical object. Free parameters are the per-category background coefficients and spurious-signal nuisance terms fitted in the likelihood, plus the hand-chosen BDT working point.

free parameters (4)
  • Non-resonant background shape and normalisation coefficients (e.g., p0, p1 of the exponential-of-polynomial functions) = fitted to data in the global likelihood, per category
    The background normalisation and shape are free in each of the nine categories; the signal strength extraction depends on these fitted parameters not absorbing the signal bump. This is disclosed as the standard approach.
  • Spurious-signal nuisance parameters = Gaussian-constrained to zero with per-category width |SS|
    Introduced to encode background-model uncertainty; the 0.04 effect on mu (Table 3) is estimated from template studies rather than derived, and the acceptance criterion (|SS| less than 20% of statistical uncertainty or 10% of expected yield, Section 6.2.3) is a threshold chosen by the analysis.
  • Non-resonant reweighting function parameters (p0..p3) for the low-pT resolved-ee category = fitted to data sidebands via chi2/ndf criterion (Section 6.2.2)
    A linear-plus-exponential reweighting is chosen for one category; its four parameters are fitted and affect the background template from which the final analytic function is selected.
  • BDT identification working-point threshold = chosen to match the 10-20% background efficiency of the cut-based ID (Section 4.1)
    Hand-picked operating point; at this point signal efficiency rises from about 62% to about 90%, directly setting the expected signal yield in the merged-ee channels.
assumptions (5)
  • domain assumption B(H to ee gamma) = 7.20e-5 and B(H to mu mu gamma) = 3.42e-5 for m_ll < 30 GeV (Firan-Stroynowski)
    Taken from Ref [8] and used to normalise the SM expectation to which mu = 1 refers (Section 3). If this branching ratio is off, the measured mu shifts correspondingly.
  • ad hoc to paper No dedicated theory uncertainty exists for the low-m_ll H to ell ell gamma branching ratio; the 6.9% H to Z gamma branching-ratio uncertainty is adopted as a proxy
    Explicitly stated in Section 3: 'no theoretical uncertainty calculation exists for the low-m_ll H to ell ell gamma branching ratio. Therefore, the theoretical uncertainty of 6.9% on the H to Z gamma branching ratio is used.' This proxy enters the expected uncertainty on mu and the combination.
  • domain assumption The DSCB signal shape fitted to simulated events (with a +0.09 GeV mass shift) describes the true signal in data
    All six DSCB parameters are fixed from fits to MC per category (Section 6.1). A mismodelled signal width or tail would bias the extracted yield; the 5.8% mass-resolution uncertainty is the only allowance for this.
  • domain assumption The H to gamma gamma resonant background has the same shape as the H to gamma*-gamma signal
    Shape parameters of the H to gamma gamma background are fixed to the signal DSCB shape with yields from simulation (Section 6.2). This matters for the electron categories, where H to gamma gamma is 2.4% (resolved) and 16% (merged) of the signal.
  • domain assumption SM production cross-sections (ggF at N3LO QCD + NLO EW, VBF, VH, ttH at NLO/NNLO from Refs [37] and [70]) normalise the expected signal
    Signal samples are normalised to SM cross-sections (Section 3); category-level QCD scale and parton-shower uncertainties of up to 16-23% are assigned on top, but the central values come from external theory.

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Cite this review

Pith. "Pith review of Measurement of the Higgs boson decay to a low-mass dilepton system and a photon in $pp$ collisions at $\sqrt{s} =$ 13 and 13.6 TeV with the ATLAS detector." pith.science (2026). https://pith.science/paper/K4EK3JIQ

@misc{pith2026260803369,
  author       = {Pith},
  title        = {Pith review of: Measurement of the Higgs boson decay to a low-mass dilepton system and a photon in $pp$ collisions at $\sqrts =$ 13 and 13.6 TeV with the ATLAS detector},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K4EK3JIQ}},
  note         = {Machine review of arXiv:2608.03369}
}
abstract

A measurement is presented for the Higgs boson decaying into a photon and a pair of electrons or muons with an invariant mass $m_{\ell\ell} <$ 30 GeV, using $pp$ collision data at $\sqrt{s} =$ 13.6 TeV recorded by the ATLAS detector at the Large Hadron Collider during the years 2022-2024, corresponding to an integrated luminosity of 164 fb$^{-1}$. The best-fit value of the signal strength parameter, defined as the ratio of the observed signal yield to the one expected in the Standard Model, is measured to be $\mu = 0.64^{+0.44}_{-0.39}$ compared with the expected value of $\mu = 1.00^{+0.47}_{-0.41}$. The corresponding observed (expected) signal significance is 1.7 (2.5) standard deviations under the background-only hypothesis. The result is combined with a similar search performed using 139 fb$^{-1}$ of $pp$ collision data at $\sqrt{s} =$ 13 TeV collected during the years 2015-2018. This combination gives an observed (expected) signal strength of $\mu = 1.03^{+0.35}_{-0.32}\,(\mu = 1.00^{+0.34}_{-0.32})$, corresponding to an observed (expected) significance of 3.4 (3.3) standard deviations.

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