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arxiv: 2604.15256 · v1 · submitted 2026-04-16 · ✦ hep-lat · hep-ph

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Charmonium radiative transitions to dileptons from lattice QCD: The case of h_c to η_c ell^+ell^- and chi_{c1} to J/psi\,ell^+ell^-

D. Be\v{c}irevi\'c , R. Di Palma , R. Frezzotti , G. Gagliardi , V. Lubicz , F. Sanfilippo , N. Tantalo
Authors on Pith no claims yet

Pith reviewed 2026-05-10 08:26 UTC · model grok-4.3

classification ✦ hep-lat hep-ph
keywords lattice QCDcharmoniumdilepton decaysradiative transitionscontinuum extrapolationdecay ratestransition form factors
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The pith

Lattice QCD yields first dynamical predictions of 5.45 keV and 2.87 keV for two charmonium dilepton decay rates.

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

The paper computes the hadronic matrix elements that govern the production of electron-positron or muon pairs in the decays h_c to eta_c and chi_c1 to J/psi. Using gauge configurations with four lattice spacings and N_f=2+1+1 dynamical quarks at physical masses, the authors perform a controlled continuum extrapolation of the relevant transition form factors. From these they extract the full decay widths, the differential distributions in dilepton invariant mass, and angular observables that cannot be accessed with real-photon emission. The results supply benchmark numbers that experiments can test and that can be compared with existing BESIII data for the chi_c1 channel.

Core claim

In the continuum limit the calculation gives Γ(h_c → η_c e⁺e⁻) = 5.45(19) keV and Γ(χ_c1 → J/ψ e⁺e⁻) = 2.869(90) keV, together with the corresponding muon modes and the q²-dependent differential widths; these are the first fully dynamical lattice QCD predictions for these dilepton channels.

What carries the argument

Lattice computation and continuum extrapolation of the vector-current transition matrix elements between the initial and final charmonium states at four lattice spacings.

If this is right

  • The predicted rates and differential distributions can be compared directly with future experimental measurements of these rare decays.
  • The angular observables provide access to the longitudinal transition form factors that are invisible in real-photon radiative decays.
  • The good agreement found for the χ_c1 channel and the 3σ tension found for the h_c channel can be used to assess the reliability of the lattice method.
  • The same framework supplies a template for computing dilepton rates in other charmonium or bottomonium transitions.

Where Pith is reading between the lines

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

  • Extending the calculation to bottomonium states would test whether the same lattice techniques remain controlled at heavier quark masses.
  • The observed tension with BESIII data for the h_c channel could motivate higher-statistics experiments or refined lattice studies that include electromagnetic corrections.
  • Differential distributions in q² could be folded with experimental acceptances to produce more precise comparisons than integrated rates alone.

Load-bearing premise

That the continuum extrapolation from four lattice spacings, one of which has a slightly heavier pion, fully controls discretization and finite-volume effects in the transition matrix elements.

What would settle it

A precision measurement of Γ(h_c → η_c e⁺e⁻) that lies well outside the interval 5.45 ± 0.19 keV would show the extrapolated lattice result to be incorrect.

Figures

Figures reproduced from arXiv: 2604.15256 by D. Be\v{c}irevi\'c, F. Sanfilippo, G. Gagliardi, N. Tantalo, R. Di Palma, R. Frezzotti, V. Lubicz.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The estimators [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The estimators [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Lattice spacing dependence of the form factors [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The three form factors [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The estimators [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The estimators [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Lattice spacing dependence of the ratios [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: The two form factors [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: The form factor [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Our results for the [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Our results for the [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Comparison between our lattice QCD predictions for the decay rates Γ( [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Number of bin-per-bin events measured by BESIII in Ref. [12] before (orange data points) and after (magenta data [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Relative difference ∆( [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Our results for the [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: Our results for the [PITH_FULL_IMAGE:figures/full_fig_p025_17.png] view at source ↗
read the original abstract

We present a lattice QCD study of dilepton production in charmonium transitions, specifically focusing on the $1^{+-} \to 0^{-+}$ and $1^{++} \to 1^{--}$ processes: $h_c \to \eta_c \ell^+ \ell^-$ and $\chi_{c1} \to J/\psi \ell^+ \ell^-$, where $\ell = e, \mu$. The relevant hadronic matrix elements are computed using gauge field configurations generated by the Extended Twisted Mass Collaboration with $N_f = 2+1+1$ dynamical Wilson--Clover twisted-mass fermions at four lattice spacings. Simulations are performed at physical dynamical $u$, $d$, $s$, and $c$ quark masses, except for the coarsest lattice, where the lightest sea quark mass corresponds to a slightly heavier pion mass. A controlled continuum extrapolation is carried out. In the continuum limit for the $h_c$ decays, we obtain $\Gamma(h_c \to \eta_c e^+ e^-) = 5.45(19)~\mathrm{keV}$, and $\Gamma(h_c \to \eta_c \mu^+ \mu^-) = 0.635(22)~\mathrm{keV}$. For the $\chi_{c1}$ decays, we find: $\Gamma(\chi_{c1} \to J/\psi e^+ e^-)= 2.869(90)~\mathrm{keV}$, and $\Gamma(\chi_{c1} \to J/\psi \mu^+ \mu^-) = 0.1993(72)~\mathrm{keV}$. Our results for the $\chi_{c1}$ decays show good compatibility with experimental data. However, our prediction for the $h_c \to \eta_c e^+ e^- $ decay rate is approximately $3\sigma$ larger than the BESIII result. We also present predictions for the differential decay widths as functions of the dilepton invariant mass, $q^2$, and for angular observables sensitive to longitudinal transition form factors, which are inaccessible in radiative decays with real photon emission. These results constitute the first fully dynamical lattice QCD predictions for dilepton decay rates in $h_c$ and $\chi_{c1}$ charmonium transitions, including their differential distributions and angular observables. They provide benchmark predictions for future experimental studies.

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.

Circularity Check

0 steps flagged

No circularity: direct lattice QCD computation of matrix elements

full rationale

The derivation consists of evaluating QCD correlation functions on dynamical ETMC ensembles at four lattice spacings, extracting the relevant hadronic matrix elements for the transitions, performing a controlled continuum extrapolation, and converting the resulting form factors into decay rates and differential distributions. None of these steps reduces the target observables to fitted parameters of themselves or to self-citations by construction; the numerical results are independent outputs of the lattice action and simulation. Minor self-citations for ensemble generation or methodology are not load-bearing for the central claims.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; ledger is therefore minimal. No free parameters beyond standard lattice tuning are mentioned. No invented entities. Axioms are the usual ones of lattice QCD.

axioms (1)
  • standard math Locality and unitarity of the lattice action allow extraction of physical matrix elements after continuum extrapolation.
    Implicit in any lattice QCD calculation of hadronic matrix elements.

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Reference graph

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