# Analytical two-loop amplitudes of $e^{+} e^{-} \longrightarrow \boldsymbol{J} / \boldsymbol{\psi}+\boldsymbol{\eta}_c$ at $B$ factories

## TL;DR

This paper presents an analytical NNLO calculation of two-loop amplitudes for $e^{+} e^{-} o J/\psi + \eta_c$ at B factories, improving theoretical predictions and aligning them with experimental data.

## Contribution

The authors perform the first analytical NNLO calculation of these amplitudes, revealing the factorization structure and providing accurate cross section predictions.

## Key findings

- Numerical predictions agree with experimental measurements.
- Analysis of leading logarithms clarifies factorization in the process.
- Extension to $Upsilon+eta_b$ production is discussed.

## Abstract

In double charmonium production, a long-standing challenge is that the theoretical predictions are not consistent with the measurements at B factories. Within the NRQCD framework, the next-to-leading order (NLO) calculation has proved its power to cut down the discrepancy between theory and experiments. To further clarify this puzzle, we have performed the next-to-next-to-leading order (NNLO) calculation. The amplitude is obtained as an analytical asymptotic expansion in the ratio of the squared charm-quark mass over the squared center-of-mass energy, $m_c^2/s$. We investigate the origin of the leading logarithms by performing a region analysis, revealing the intricate factorization structure in this process. We provide numerical predictions on the total cross sections of $J/\psi+\eta_c$ production, which agree with the experimental results. Extension of our computation to $\Upsilon+\eta_b$ production is also discussed.