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arxiv: 2606.17827 · v1 · pith:AQ7RSRQRnew · submitted 2026-06-16 · ✦ hep-ph · hep-ex

Semi-analytical results for e^+e^-to J/psi + X_{{rm non\,}cbar{c}} up to mathcal{O}(α_s v²) at B factories

Cong Li , Hao-Yang Liu , Xu-Dong Huang , Wen-Long Sang This is my paper

Pith reviewed 2026-06-27 00:17 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords NRQCD factorizationJ/ψ productionB factoriescolor-singlethigher-order correctionsangular distributionfeeddown
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The pith

The O(α_s v²) correction to color-singlet J/ψ production in e⁺e⁻ collisions is obtained for the first time, verifying NRQCD factorization at B factories.

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

The paper calculates the strong-coupling, velocity, and mixed corrections up to O(α_s v²) for the color-singlet part of e⁺e⁻ → J/ψ + X without charm quarks. Short-distance coefficients are extracted as high-order asymptotic series in the mass ratio r = m_c/√s. The new mixed term turns out small, the factorization structure holds, and after adding ψ(2S) feeddown the total rate matches the Belle measurement while the predicted angular shape does not.

Core claim

Within NRQCD factorization the O(α_s), O(v²) and O(α_s v²) corrections to both the unpolarized cross section and the J/ψ angular distribution are computed for the color-singlet channel. The O(α_s v²) short-distance coefficients are obtained for the first time via the differential equation method as expansions in r = m_c/√s up to r^40; these reproduce exact results to relative precision 10^{-14} for the rate and 10^{-7} for the angular parameter at B-factory energies. With the scale choice μ_R = √s/2 the O(α_s) term reaches roughly 50 % of the leading-order rate while the two velocity corrections remain accidentally small. After including feeddown from ψ(2S) the predicted cross section is 0.5

What carries the argument

Short-distance coefficients for color-singlet J/ψ production computed to O(α_s v²) as asymptotic expansions in r = m_c/√s up to order r^40 via the differential equation method.

If this is right

  • The O(α_s) correction is large (~50 % of LO) while O(v²) and O(α_s v²) are small, so the perturbative and velocity expansions can be kept separate at present precision.
  • Feeddown from ψ(2S) is required to bring the predicted cross section into agreement with Belle data.
  • The angular-distribution parameter remains discrepant with experiment by >2σ, indicating that further contributions or measurements are needed.
  • The asymptotic expansions reproduce exact results to 10^{-14} relative accuracy for the rate at B-factory energies.

Where Pith is reading between the lines

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

  • The same expansion technique could be used for other charmonium states or different production channels to test factorization at this order.
  • The persistent angular-distribution mismatch may point to the importance of color-octet channels or still-higher-order terms once the LDMEs are allowed to adjust at O(α_s v²).
  • Re-extracting the LDMEs from data that now includes the new coefficients would provide a direct test of whether the present scale choice and matrix-element values stay stable.

Load-bearing premise

The long-distance matrix elements and renormalization-scale choice taken from earlier lower-order fits remain appropriate once the new O(α_s v²) coefficients are added.

What would settle it

An exact (non-asymptotic) evaluation of any O(α_s v²) short-distance coefficient at √s ≈ 10.6 GeV that differs from the r^40 expansion result by more than the stated 10^{-14} relative error on the cross section.

read the original abstract

Within the NRQCD factorization framework, we investigate the color-singlet contribution to $e^+e^- \to J/\psi + X_{{\rm non\,}c\bar{c}}$ at B factories, computing the $\mathcal{O}(\alpha_s)$, $\mathcal{O}(v^2)$, and $\mathcal{O}(\alpha_s v^2)$ corrections to both the unpolarized cross section and the $J/\psi$ angular distribution. The $\mathcal{O}(\alpha_s v^2)$ correction is obtained for the first time, and the validity of NRQCD factorization at this order is explicitly verified. Using the differential equation method, the short-distance coefficients are obtained as asymptotic expansions in $r = m_c/\sqrt{s}$ up to $r^{40}$, which reproduce exact results with high precision at B factory energies, achieving relative errors around $10^{-14}$ for the cross section and around $10^{-7}$ for the angular distribution. Notably, with the same input parameters, our $\mathcal{O}(\alpha_s)$ and $\mathcal{O}(v^2)$ corrections are consistent with those reported in the literature. Phenomenologically, the $\mathcal{O}(\alpha_s)$ correction (with $\mu_R=\sqrt{s}/2$) reaches about $50\%$ of the leading-order cross section, while the $\mathcal{O}(v^2)$ and $\mathcal{O}(\alpha_s v^2)$ corrections are accidentally small. After including feeddown contributions from $\psi(2S)$, the predicted cross section $0.530_{-0.113}^{+0.122}$ pb agrees with the {\tt Belle} measurement within uncertainties. However, the predicted angular distribution parameter $0.120_{-0.019}^{+0.027}$ deviates from the experimental value $5.71\pm 2.51$ by more than $2\sigma$, calling for further experimental and theoretical investigations.

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

1 major / 0 minor

Summary. The manuscript computes the color-singlet contributions to e⁺e⁻ → J/ψ + X_non-c c̄ at B-factory energies in NRQCD factorization, obtaining the O(α_s), O(v²), and first-time O(α_s v²) corrections to both the unpolarized cross section and the J/ψ angular distribution. Short-distance coefficients are derived via the differential-equation method as asymptotic expansions in r = m_c/√s up to r⁴⁰, reproducing exact results to relative precision ~10^{-14} (cross section) and ~10^{-7} (angular). Lower-order terms match literature values with the same inputs; after ψ(2S) feeddown the predicted cross section is 0.530 pb (agreeing with Belle within uncertainties) while the angular parameter 0.120 deviates by >2σ.

Significance. If the results hold, the work supplies the first O(α_s v²) short-distance coefficients for this process together with high-order semi-analytical expansions that serve as a practical tool at B-factory energies. Explicit verification of NRQCD factorization at the new order and consistency of the O(α_s) and O(v²) pieces with prior literature are concrete strengths. The phenomenological section illustrates both the size of perturbative corrections and a tension in the angular observable that warrants further study.

major comments (1)
  1. [Abstract] Abstract and phenomenological discussion: the quoted agreement of the total cross section (0.530 pb) with Belle data and the assessment that O(v²) and O(α_s v²) corrections are “accidentally small” both rest on LDMEs and the choice μ_R = √s/2 taken unchanged from lower-order literature; because the O(α_s) term already reaches ~50 % of LO with this scale, the numerical impact of the new O(α_s v²) coefficient on the final prediction is not independently tested by a refit or by a scale-variation study at the enlarged perturbative order.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation and the detailed comment. We respond to the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and phenomenological discussion: the quoted agreement of the total cross section (0.530 pb) with Belle data and the assessment that O(v²) and O(α_s v²) corrections are “accidentally small” both rest on LDMEs and the choice μ_R = √s/2 taken unchanged from lower-order literature; because the O(α_s) term already reaches ~50 % of LO with this scale, the numerical impact of the new O(α_s v²) coefficient on the final prediction is not independently tested by a refit or by a scale-variation study at the enlarged perturbative order.

    Authors: We agree that the quoted numerical results and the characterization of the higher-order corrections as accidentally small are obtained with the LDMEs and scale choice μ_R=√s/2 taken from the existing literature. These inputs were deliberately retained to permit a direct, apples-to-apples comparison of the newly computed O(α_s v²) short-distance coefficients with the lower-order terms already published. A global refit of the LDMEs that incorporates the O(α_s v²) corrections, or a dedicated scale-variation study at the enlarged perturbative order, would constitute a separate phenomenological analysis and lies outside the scope of the present work, whose primary goal is the derivation and verification of the perturbative coefficients themselves. We will add a brief clarifying sentence in the abstract and in the phenomenological discussion to make this choice of inputs explicit. revision: partial

Circularity Check

0 steps flagged

No circularity; short-distance coefficients derived independently via differential equations

full rationale

The paper computes the new O(α_s v²) short-distance coefficients from first principles using the differential equation method with asymptotic expansions in r = m_c/√s up to r^40. Lower-order results are reproduced for consistency with external literature but are not used to define or fit the new term. LDMEs and μ_R = √s/2 are adopted as standard external inputs for phenomenology without refitting or redefinition at the new order; the factorization verification applies only to the independently computed coefficients. No step reduces the central result to a fitted quantity, self-citation chain, or input by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The calculation rests on the NRQCD factorization framework with standard inputs (LDMEs, m_c, α_s) taken from prior literature; the new content is the short-distance coefficients at O(α_s v²).

free parameters (2)
  • renormalization scale μ_R = √s/2
    Chosen as √s/2 so that the O(α_s) correction reaches ~50% of the leading-order cross section.
  • long-distance matrix elements
    Standard NRQCD inputs; values taken from literature or previous fits and not re-determined at the new order.
axioms (1)
  • domain assumption NRQCD factorization remains valid at O(α_s v²)
    The paper states that this validity is explicitly verified, yet the separation of short- and long-distance physics is the foundational premise of the entire framework.

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discussion (0)

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Reference graph

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