REVIEW
Inclusive weak decays of the $J/\psi$: single-charm decay and weak annihilation
High Energy Physics - Phenomenology · Submitted 22 Oct 2026 · 50 references
Pith's verdict: A useful first inclusive calculation of J/psi weak decays, but the central branching fraction rests on a vacuum-saturation assumption whose uncertainty is not quantitatively justified.
T0 · AI review
Why Pith says this
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Referee report
The paper
The paper claims
The inclusive weak branching fraction of the J/ψ is calculated from first principles to be about 8×10⁻⁸, dominated by weak annihilation, not single-charm decays alone.
The reading
What carries the argument
The optical theorem is applied to the forward-scattering amplitude with two insertions of the weak effective Hamiltonian. The heavy-quark expansion (HQE) organizes the transition operator into two-quark (single-charm) and four-quark (annihilation) operators. The leading four-quark operators are identified through a heavy-pair expansion, which shows that the dominant annihilation structure is pair creation followed by pair annihilation. Hadronic matrix elements are evaluated using vacuum saturation for the color-singlet component, fixed by the physical J/ψ mass and decay constant, and the scale uncertainty is estimated by varying μ between 1 GeV and 3M_{J/ψ}.
Extended reading notes
Core claim
Pair annihilation, not single-charm decay, is the dominant mechanism for J/ψ weak decays. The calculation yields B_weak = (7.96⁺³·⁴³₋₀·⁴³ ± 1.24) × 10⁻⁸, with annihilation providing about 77% of the central value. The neutral-current contribution is the largest single term, and the W–Z interference is destructive at the central scale but changes sign. Previous estimates that summed only the single-charm decays gave B ≈ 1.4 × 10⁻⁸, undershooting the inclusive rate by a factor of about five.
Load-bearing premise
Vacuum saturation for the leading colour-singlet component of the four-charm matrix elements (eq. 4.7), which omits non-vacuum intermediate states, colour-octet contributions, and hard radiative corrections; the authors acknowledge this limitation and assign a 20% hadronic uncertainty based on Λ_QCD/m_c.
Editorial extensions
If this is right
- Existing BESIII upper limits on exclusive J/ψ weak modes (at the few ×10⁻⁸ level) do not yet probe the predicted inclusive rate of ~8×10⁻⁸, but planned super tau-charm facilities with ~10¹² J/ψ events should detect signals.
- The dominance of neutral-current annihilation implies that final states with no open charm (e.g., purely leptonic or hadronic states from Z⁰ exchange) are the largest component, motivating searches for these modes.
- The significant scale sensitivity of the W–Z interference, which changes sign within the 1–9.3 GeV interval, means that next-to-leading order QCD corrections to the hard kernels are needed for a more precise prediction.
- The branching fraction in the |ΔC|=1 sector (1.86×10⁻⁸) arises solely from single-charm decays and confirms the conventional estimate, but the total is dominated by the ΔC=0 sector (6.10×10⁻⁸) from annihilation, so future searches should target ΔC=0 final states.
- The calculation provides a benchmark for testing quark-hadron duality in charm-quarkonium weak decays, complementing similar studies in B-meson systems.
Reading between the lines
- If the predicted inclusive weak width is correct, then the J/ψ is, after the B mesons, the second best laboratory for testing the heavy-quark expansion in weak decays at the charm scale, with pair annihilation replacing the usual spectator effects.
- The vacuum-saturation approximation could be tested with lattice QCD by computing the four-quark matrix elements of the colour-octet operators that are omitted here; a lattice calculation would either confirm the dominance of the colour-singlet component or reveal sizeable corrections.
- The sign-changing W–Z interference offers a rare opportunity to isolate neutral-current effects in a hadronic decay; if future high-statistics data show a branching fraction at the high end of the uncertainty band (≈1.1×10⁻⁷), that would suggest constructive interference at low scales and favour a particular pattern of Wilson-coefficient running.
- A measurement of the J/ψ → ℓ⁺ℓ⁻ (via Z⁰ exchange) would directly test the neutral-current annihilation component, which is the largest single contribution in the calculation.
Original abstract
Conventional estimates of $J/\psi$ weak decays, based on independent single-charm decays, suggest a branching fraction of order $10^{-8}$. Searches with samples of approximately $10^{10}$ $J/\psi$ events have so far yielded upper limits on exclusive modes. We calculate the inclusive weak branching fraction using the optical theorem, including single-charm decay, charged- and neutral-current annihilation, and their interference. The heavy-quark expansion identifies the leading pair-annihilation structure and motivates vacuum saturation for the leading color-singlet component. With tree-level hard kernels and leading-logarithmic Wilson coefficients at $\mu_0=M_{J/\psi}$, we obtain $B_{\rm weak}=(7.96^{+3.43}_{-0.43}\pm1.24)\times10^{-8}$. The contribution mediated by the $W$ boson alone, i.e. single-charm decays and $W$-exchange annihilation without the $W$-$Z$ interference, has a branching fraction of $(2.37^{+1.64}_{-0.42}\pm0.13)\times10^{-8}$. For the flavor sectors $(\Delta C,|\Delta S|)=(0,1)$ and $|\Delta C|=1$, the branching fractions are $(4.97^{+16.44}_{-4.97}\pm0.99)\times10^{-10}$ and $(1.86^{+0.20}_{-0.06}\pm0.02)\times10^{-8}$, respectively, including charge-conjugate channels. The first uncertainty estimates missing perturbative corrections through scale variation over $1~\mathrm{GeV}\leq\mu\leq3M_{J/\psi}$. The second is a hadronic uncertainty, obtained by jointly varying each vacuum-saturation and kinetic/chromomagnetic input within relative ranges of $\Lambda_{\rm QCD}/m_c\simeq20\%$. Pair annihilation dominates, with a substantial neutral-current contribution and scale-sensitive $W$-$Z$ interference.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Conventional estimates of $J/\psi$ weak decays, based on independent single-charm decays, suggest a branching fraction of order $10^{-8}$. Searches with samples of approximately $10^{10}$ $J/\psi$ events have so far yielded upper limits on exclusive modes. We calculate the inclusive weak branching fraction using the optical theorem, including single-charm decay, charged- and neutral-current annihilation, and their interference. The heavy-quark expansion identifies the leading pair-annihilation structure and motivates vacuum saturation for the leading color-singlet component. With tree-level hard kernels and leading-logarithmic Wilson coefficients at $\mu_0=M_{J/\psi}$, we obtain $B_{\rm weak}=(7.96^{+3.43}_{-0.43}\pm1.24)\times10^{-8}$. The contribution mediated by the $W$ boson alone, i.e. single-charm decays and $W$-exchange annihilation without the $W$-$Z$ interference, has a branching fraction of $(2.37^{+1.64}_{-0.42}\pm0.13)\times10^{-8}$. For the flavor sectors $(\Delta C,|\Delta S|)=(0,1)$ and $|\Delta C|=1$, the branching fractions are $(4.97^{+16.44}_{-4.97}\pm0.99)\times10^{-10}$ and $(1.86^{+0.20}_{-0.06}\pm0.02)\times10^{-8}$, respectively, including charge-conjugate channels. The first uncertainty estimates missing perturbative corrections through scale variation over $1~\mathrm{GeV}\leq\mu\leq3M_{J/\psi}$. The second is a hadronic uncertainty, obtained by jointly varying each vacuum-saturation and kinetic/chromomagnetic input within relative ranges of $\Lambda_{\rm QCD}/m_c\simeq20\%$. Pair annihilation dominates, with a substantial neutral-current contribution and scale-sensitive $W$-$Z$ interference.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Conventional estimates of $J/\psi$ weak decays, based on independent single-charm decays, suggest a branching fraction of order $10^{-8}$. | background 1.00 | 0.05 | 0.04 | hedged possibility 0.94 |
| s1 | Searches with samples of approximately $10^{10}$ $J/\psi$ events have so far yielded upper limits on exclusive modes. | background 0.88 | 0.07 | 0.02 | asserted 1.00 |
| s2 | We calculate the inclusive weak branching fraction using the optical theorem, including single-charm decay, charged- and neutral-current annihilation, and their interference. | contribution 0.65 | 0.96 | 0.11 | asserted 0.99 |
| s3 | The heavy-quark expansion identifies the leading pair-annihilation structure and motivates vacuum saturation for the leading color-singlet component. | method 0.97 | 0.57 | 0.04 | asserted 0.99 |
| s4 | With tree-level hard kernels and leading-logarithmic Wilson coefficients at $\mu_0=M_{J/\psi}$, we obtain $B_{\rm weak}=(7.96^{+3.43}_{-0.43}\pm1.24)\times10^{-8}$. | result 1.00 | 0.96 | 0.84 | asserted 1.00 |
| s5 | The contribution mediated by the $W$ boson alone, i.e. single-charm decays and $W$-exchange annihilation without the $W$-$Z$ interference, has a branching fraction of $(2.37^{+1.64}_{-0.42}\pm0.13)\times10^{-8}$. | result 1.00 | 0.86 | 0.07 | asserted 1.00 |
| s6 | For the flavor sectors $(\Delta C,|\Delta S|)=(0,1)$ and $|\Delta C|=1$, the branching fractions are $(4.97^{+16.44}_{-4.97}\pm0.99)\times10^{-10}$ and $(1.86^{+0.20}_{-0.06}\pm0.02)\times10^{-8}$, respectively, including charge-conjugate channels. | result 1.00 | 0.91 | 0.06 | asserted 1.00 |
| s7 | The first uncertainty estimates missing perturbative corrections through scale variation over $1~\mathrm{GeV}\leq\mu\leq3M_{J/\psi}$. | limitation 0.84 | 0.78 | 0.03 | asserted 0.94 |
| s8 | The second is a hadronic uncertainty, obtained by jointly varying each vacuum-saturation and kinetic/chromomagnetic input within relative ranges of $\Lambda_{\rm QCD}/m_c\simeq20\%$. | method 0.94 | 0.87 | 0.03 | asserted 0.99 |
| s9 | Pair annihilation dominates, with a substantial neutral-current contribution and scale-sensitive $W$-$Z$ interference. | interpretation 0.90 | 0.88 | 0.59 | asserted 1.00 |
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Figures
Figures reproduced from arXiv:2610.30649 by the authors.
References
Discussion
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