Optimized QCD two-loop correction to exclusive double $J/\ddot{I}ˆ$ production at B factories

Abstract

We report the calculation of the process $e^{+}{e}^{-}\to J/\ddot{I}ˆJ/\ddot{I}ˆ$ 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 $J/\ddot{I}ˆ$ decay constant, while the interference and non-fragmentation parts are computed at NNLO in $\hat{I}{\pm }_s$ and lowest order in velocity. In this optimized scheme, both $\mathcal{O}(\hat{I}{\pm }_s)$ and $\mathcal{O}(\hat{I}{\pm }_s^2)$ 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 ${\mathrm{ab}}^{-1}$ dataset at \texttt{Belle 2}, the prospects for observing exclusive double $J/\ddot{I}ˆ$ production are very promising.

8 pages, 4 figures, 1 table. Proceedings of the XVIth Quark Confinement and the Hadron Spectrum Conference (QCHSC24), PoS(QCHSC24)132