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First lattice QCD determination of the Standard Model neutrino background for J/ψ → γ + invisible yields 1.00(9)(7)×10^-10.

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2026-08-03 08:04 UTC pith:A7OJBJO5

load-bearing objection First lattice QCD number for the J/psi neutrino floor; useful and mostly sound, but the precision claim needs shoring up and the abstract/main-text mismatch is sloppy. the 3 major comments →

arxiv 2601.18209 v2 pith:A7OJBJO5 submitted 2026-01-26 hep-lat hep-exhep-ph

Lattice determination of the neutrino background for J/psi rightarrow γ + textrm{invisible}

Yu Meng , Ning Li , Chuan Liu , Haobo Yan , Ke-Long Zhang , Xue-Ze Zhang This is my paper
classification hep-lat hep-exhep-ph PACS 12.38.Gc13.20.Gd
keywords lattice QCDJ/psi radiative invisible decayneutrino backgroundbranching fractionform factorcharmoniumtwisted-mass fermionsdark matter searches
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper attempts to establish, from first principles, the Standard Model decay rate for J/ψ → γ ν ν̄, which is the irreducible neutrino background that contaminates searches for J/ψ → γ + invisible. Using lattice QCD with three lattice spacings and a method that captures the full photon-energy distribution, it obtains a branching fraction of 1.00(9)(7)×10^-10. A sympathetic reader would care because next-generation charm-factory experiments aim to reach exactly this sensitivity level; having a parameter-free, ab initio number to subtract is what turns any remaining events into evidence for invisible new particles. The calculation also provides a template for computing similar neutrino backgrounds in other quarkonium channels.

Core claim

The paper claims that the branching fraction for the Standard Model decay J/ψ → γ ν ν̄ is Br = 1.00(9)(7)×10^-10, where the first uncertainty is statistical (including lattice-spacing and continuum-extrapolation errors) and the second is an estimate of systematic effects. This is presented as the first lattice QCD calculation of this quantity, obtained by computing the hadronic matrix element ⟨0|T{J_em^μ(x) J_Z^ν(0)}|J/ψ⟩ nonperturbatively, parameterizing it with a single form factor, and integrating over the full phase space. The paper contrasts this ab initio result with an earlier phenomenological estimate of 0.7×10^-10 and argues that the lattice value is model-independent and precise en

What carries the argument

The central object is the hadronic tensor H^{μνα}(q,p) = ε^{μναβ} q_β F_{γνν̄}(q^2), which reduces all strong-interaction physics to a single form factor F. The authors use the scalar function method: they multiply H by ε^{μναβ} p_β, average over photon directions, and integrate against a spherical Bessel function, obtaining a scalar I(E_γ, Δt) from which F is extracted directly at every photon energy. This avoids the model-dependent interpolation of discrete lattice momenta used previously. The form factor feeds a Monte Carlo phase-space integral for the decay width; the dimensionless ratio Γ/f_J/ψ is then continuum-extrapolated in a^2 and rescaled with the lattice decay constant and the wo

Load-bearing premise

The load-bearing assumption is that the charm-quark vector-axial hadronic matrix element in the J/ψ → γ transition is insensitive to the light-quark sea mass at the ~7% level, so using N_f=2 ensembles with pion masses of 300–365 MeV — without any chiral extrapolation or corresponding systematic error — is safe; if the sea-quark effect is larger than that, the central value moves outside the quoted error budget.

What would settle it

A concrete check: compute the same decay width on a lattice ensemble with a physical pion mass (or with N_f=2+1 dynamical quarks) and see whether the central value moves by more than the quoted total uncertainty of ±0.16×10^-10. Alternatively, include the OZI-suppressed disconnected diagrams and compare; if either change exceeds the error budget, the central claim is falsified. A direct experimental measurement at a future charm-tau factory reaching 10^-10 sensitivity that excludes 1.0×10^-10 would also settle it.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Searches for invisible new particles in J/ψ → γ + invisible can now subtract a known Standard Model background, so any remaining excess is attributable to new physics.
  • Next-generation charm-tau facilities with roughly 10^5 times more J/ψ events, targeting 10^-10 sensitivity, will land on this neutrino floor; the lattice value tells them exactly where that floor is.
  • The same method transfers directly to Υ and φ radiative invisible decays, providing ab initio background estimates for those channels.
  • The result, 1.00×10^-10, is about 1.4 times larger than the earlier nonrelativistic color-singlet estimate of 0.7×10^-10, demonstrating that phenomenological models can be off by tens of percent.
  • The full-q^2 scalar function method removes a source of model dependence, so the quoted precision is directly testable by finer lattice calculations rather than depending on fitting assumptions.

Where Pith is reading between the lines

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

  • The quoted 7% systematic uncertainty does not include any estimate for the unphysical sea-quark mass, since the ensembles use pion masses of 300–365 MeV with no chiral extrapolation; if the charm axial matrix element varies by more than ~7% when extrapolated to the physical pion mass, the central value would shift outside the stated error budget.
  • Using the ratio Γ/f_J/ψ before continuum extrapolation likely cancels some common renormalization and discretization effects; a direct computation without this ratio would clarify how much of the precision comes from that cancellation.
  • A natural test of the claim is a repeat calculation with N_f=2+1 or physical-mass sea quarks, or one that includes the disconnected diagrams currently dropped via OZI suppression; either could move the central value beyond the quoted uncertainty.
  • If a next-generation experiment directly measures J/ψ → γ ν ν̄, the comparison with this lattice prediction would double as a low-energy test of the Standard Model's neutrino couplings in charmonium decays.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper presents the first lattice QCD calculation of the Standard Model decay J/ψ → γνν̄, which constitutes an irreducible neutrino background to searches for J/ψ → γ + invisible. Using three N_f=2 twisted-mass ensembles with lattice spacings a ≃ 0.067, 0.085, 0.098 fm and pion masses 300–365 MeV, the authors compute the hadronic function via a scalar-function method, extract Γ(J/ψ→γνν̄)/f_{J/ψ} with a two-state excited-state fit, extrapolate linearly in a², and rescale by the continuum J/ψ decay constant. The final result is Br = 1.00(9)(7)×10⁻¹⁰ (Eq. 17), with the systematic error estimated from dropping the coarsest ensemble. The paper argues that this ab initio prediction is needed for upcoming STCF and other searches.

Significance. If the central result is correct, this is a valuable first non-perturbative benchmark for a background process that will soon be experimentally relevant. The scalar-function method, the explicit finite-volume check via spatial truncation, and the multi-state treatment of excited states are genuine strengths, and the comparison with the phenomenological NRQCD estimate is useful. The calculation is independent of the experimental bound and does not use the target branching fraction as input. However, the reliability of the quoted precision rests on systematic assumptions that are not quantitatively supported in the manuscript, so the result cannot currently be taken as a robust 10% benchmark.

major comments (3)
  1. [Numerical Setup / Table I; Eq. (17)] The calculation uses only three N_f=2 ensembles with pion masses 300, 315, 365 MeV and performs no chiral extrapolation or sea-quark-mass systematics. The continuum extrapolation in a² is necessarily correlated with m_π because all three ensembles lie on a single trajectory in (a², m_π) space. The claim that the heavy-charm matrix element is insensitive to the light sea quark at the 7% level is unsupported. Since a 7% shift would move the central value outside the quoted systematic, this is a load-bearing gap. The authors should either provide an estimate of the sea-quark dependence (e.g., from a partially quenched comparison, heavy-quark scaling, or a dedicated ensemble at a different m_π) or explicitly enlarge the systematic error.
  2. [Numerical Results, Fig. 4 and Table II] The continuum extrapolation rests on three points, and the a85 point is poorly described by the linear a² fit. From Table II, the values are 1.852(44), 1.503(34), 1.371(25) for a67, a85, a98. A straight line through a67 and a98 predicts ≈1.59 at the a85 lattice spacing, about 2.6σ above the measured 1.503(34). This contradicts the statement that 'the fitting curves ... describe the lattice data well.' The systematic error is estimated only from the difference between the three-point fit and the two-point fit (1.00 vs 1.07), which does not capture the poor internal consistency of the three-point fit. The a² extrapolation needs a more careful treatment or a larger uncertainty, especially because the central value is directly read off this fit.
  3. [Numerical Results, final paragraph; Br formula (Eq. 16)] The neglect of disconnected diagrams is justified only by OZI suppression, with references to other charmonium studies, but no estimate of the size of this effect in the present observable is provided. The weak current in Eq. (6) contains light-quark contributions, and the J/ψ state can couple to disconnected light-quark loops; OZI suppression is qualitative. The same applies to the connected sea-quark effects noted above. Since the paper claims a parameter-free, precision benchmark, these unquantified systematics should be bounded by a numerical check or explicitly folded into the second error.
minor comments (4)
  1. [Abstract vs. Eq. (17)] The abstract quotes Br = 1.04(7)(8)×10⁻¹⁰, while the main text and conclusion quote 1.00(9)(7)×10⁻¹⁰ (Eq. 17). These are inconsistent in both central value and errors; the manuscript must use one consistent set of numbers.
  2. [Fig. 4 caption] The caption refers to 'Γ_{η_c γγ}/f_{J/ψ}', but the plotted quantity is Γ(J/ψ→γνν̄)/f_{J/ψ}. Please correct the typo.
  3. [Introduction] The phrase 'futural experiments' should be 'future experiments'.
  4. [Supplementary, Eq. (S7)] The definition of Z_{0i} involves the point-source operator O_i = Z_A ar c γ_i c; it would be clearer to state explicitly that the renormalization constant Z_A is the same as that used for the weak current, and how the statistical correlation between f_{J/ψ} and R_f is handled in the ratio rescaled to the physical width.

Circularity Check

0 steps flagged

No significant circularity: the J/psi->gamma+invisible branching fraction is an independent lattice calculation, with only non-load-bearing self-citations.

full rationale

The central result Br = 1.00(9)(7)e-10 is produced by a direct lattice computation: the hadronic tensor is measured via three-point functions, the form factor is extracted through the scalar-function construction in Eqs. (12)-(13), and the width is obtained by phase-space integration (Eq. 14) after continuum extrapolation of R_f and f_J/psi (Eqs. 15-16). The target branching fraction never appears as an input; the only external inputs are standard electroweak couplings, the PDG total width, and renormalization constants Z_V (from previous work) and Z_A (from ETMC/RI-MOM), each with independent determinations. The ratio R_f = Gamma/f_J/psi is a standard variance-reduction device: R_f is measured on the lattice, and f_J/psi is measured and separately cross-checked against the PDG and HPQCD values, so rescaling R_f by f_J/psi is not fitting the answer. Self-citations [22-27] supply the scalar-function method and finite-volume checks, but the paper includes a self-contained derivation and a direct R-truncation check (Fig. 6), so these citations are not load-bearing. No uniqueness theorem is imported from the authors, no fitted quantity is renamed as a prediction, and no quantity is defined in terms of the target. The abstract/main-text numerical mismatch (1.04(7)(8) vs 1.00(9)(7)) and the unquantified N_f=2 sea-quark-mass dependence are correctness risks, not circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 4 axioms · 0 invented entities

The calculation rests on standard SM electroweak inputs (G_F, α, sin²θ_W, m_Z), the single-form-factor parameterization of Ref. [21], OZI-suppression of disconnected diagrams, and the unquantified assumption that N_f=2 ensembles at m_π=300–365 MeV are adequate. The valence charm quark mass is tuned to the physical J/ψ mass. No new particles or forces are introduced.

free parameters (1)
  • valence charm quark mass = tuned per ensemble so m_J/ψ matches the physical value (details in Ref. [22])
    The charm quark mass is tuned to reproduce the physical J/ψ mass on each ensemble. This is a standard renormalization condition, but it is an input that affects the matrix element and is not a prediction.
axioms (4)
  • domain assumption Single-form-factor parameterization H^{μνα} = ε^{μναβ} q_β F(q²) (Eq. 7)
    Taken from Ref. [21]; justified by gauge invariance and C-parity, but not derived in this paper. The lattice extraction projects onto this Lorentz structure and would miss any additional form factors.
  • domain assumption Disconnected diagrams are negligible (OZI suppression)
    Section 'Numerical Results': 'Neglected disconnected diagrams are known to yield only small contributions in charmonium system [36–39] due to OZI suppression.' No numerical bound is estimated in this work.
  • domain assumption Wick rotation convergence; η_c(q=0) contamination vanishes (Eqs. S4–S6)
    Supplementary Eqs. (S4)-(S6) argue that the η_c(0) intermediate state decouples from the projected hadronic function. This is load-bearing for extracting the Minkowski form factor from the Euclidean correlator.
  • domain assumption N_f=2 ensembles with m_π=300–365 MeV are sufficient; no chiral extrapolation needed
    Table I lists pion masses well above physical; the paper does not discuss pion-mass dependence or assign an uncertainty for this approximation.

pith-pipeline@v1.3.0-alltime-deepseek · 12020 in / 29658 out tokens · 310494 ms · 2026-08-03T08:04:50.519454+00:00 · methodology

0 comments
read the original abstract

Searching for dark matter is a primary goal of modern astronomy and particle physics. Invisible decays of heavy quarkonia are particularly promising for probing light dark matter, attracting broad interest due to their unique sensitivity. Experiments searching for radiative invisible decays of the $J/\psi$ have steadily improved upper limits, and upcoming facilities will push sensitivity further--making the precise determination and subtraction of the neutrino background indispensable. Here, we present the first lattice QCD calculation of the Standard Model decay $J/\psi \to \gamma\nu\bar{\nu}$, an irreducible background to $J/\psi \rightarrow \gamma + \textrm{invisible}$. Our result for the branching fraction is $\operatorname{Br}(J/\psi \rightarrow \gamma\nu\bar{\nu})=1.04(7)(8)\times 10^{-10}$, where the first uncertainty is statistical and the second is our systematic estimate. This work advances lattice-based determinations of neutrino backgrounds to quarkonium invisible decays, delivering an ab initio benchmark for $J/\psi \rightarrow \gamma + \textrm{invisible}$. Our approach generalizes to other quarkonium channels (e.g., $\Upsilon/\phi \rightarrow \gamma+\textrm{invisible}$) and provides critical theoretical support for dark matter searches at colliders.

Figures

Figures reproduced from arXiv: 2601.18209 by Chuan Liu, Haobo Yan, Ke-Long Zhang, Ning Li, Xue-Ze Zhang, Yu Meng.

Figure 1
Figure 1. Figure 1: FIG. 1. An example of the feynman diagram for the decay [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The lattice results of Γ [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The lattice results of Γ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Lattice values of Γ [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Lattice results of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. For ensemble a67, Γ [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

discussion (0)

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Forward citations

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