Optimized QCD two-loop correction to exclusive double $J/ψ$ production at B factories

TL;DR

This paper addresses the challenge of predicting exclusive double $J/\psi$ production in $e^+e^-$ collisions at B-factory energies by employing an optimized NRQCD factorization that separates photon-fragmentation and non-fragmentation contributions. It computes the $\mathcal{O}(\alpha_s^2)$ corrections to the interference and non-fragmentation components (NNLO in $\alpha_s$), while anchoring the fragmentation part to the measured $f_{J/\psi}$ and NRQCD matrix elements, and ensuring proper scale dependence cancellation. The main result is a robust, positive NNLO cross section of $\sigma(e^+e^-\to J/\psi+J/\psi)=2.13^{+0.30}_{-0.06}$ fb at $\sqrt{s}=10.58$ GeV, with non-fragmentation contributions negligible and higher-order corrections showing good convergence. These findings, together with current and upcoming Belle II data (up to 50 ab$^{-1}$), indicate strong prospects for observing exclusive double $J/\psi$ production and help delineate QCD dynamics in quarkonium production.

Abstract

We report the calculation of the process $e^+ e^- \to J/ψJ/ψ$ up to next-to-next-to-leading order (NNLO) at a center-of-mass (CM) energy of $\sqrt{s}=10.58$ GeV. We employ an improved NRQCD factorization approach, decomposing the amplitude into photon-fragmentation and non-fragmentation components. The fragmentation contribution is determined using the measured $J/ψ$ decay constant, while the interference and non-fragmentation parts are computed at NNLO in $α_s$ and lowest order in velocity. In this optimized scheme, both ${\cal O}(α_s)$ and ${\cal O}(α^2_s)$ corrections in the interference part are positive and exhibit good convergence. The non-fragmentation part is numerically insignificant. Our results indicate that with the projected 50 ${\rm ab}^{-1}$ dataset at \texttt{Belle 2}, the prospects for observing exclusive double $J/ψ$ production are very promising.

Figures (4)

• Figure 1: Illustration of the $e^+e^-\to J/\psi+J/\psi$ process through two photon independent fragmentation.
• Figure 2: Non-fragmentation type of tree-level Feynman diagrams [$a)$ and $b)$], together with some sample one-loop non-fragmentation diagrams [$c)$ through $h)$].
• Figure 3: Some representative two-loop diagrams of non-fragmentation origin for $e^+e^-\to J/\psi+J/\psi$.
• Figure 4: Differential cross sections for $e^+ e^- \to J/\psi J/\psi$ against $\cos \theta$ at various perturbative accuracy from improved NRQCD approach. We have fixed $\mu_{\Lambda} = 1\:\text{GeV}$, and taken the central value of $\mu_{R}$ to be $\sqrt{s}/2$. The error bands of the NLO and NNLO predictions are estimated by sliding $\mu_R$ from $m_c$ to $\sqrt{s}$.