# Update of hadronic decays of $J/\psi$ and $\psi(2S)$ though virtual photons

## TL;DR

This paper updates the hadronic decay branching ratios of $J/ar{ ext{}}$ and $ar{ ext{}}$psi(2S) via virtual photons using recent measurements, significantly improving their precision.

## Contribution

It provides the most recent and precise updates to the hadronic decay branching ratios of $J/ar{ ext{}}$ and $ar{ ext{}}$psi(2S) through virtual photons, based on new data.

## Key findings

- Precision of branching ratios increased by about 4 and 3 times.
- Updated ratios are based on latest $R$ value and leptonic decay measurements.
- Results enhance the accuracy of charmonium decay data.

## Abstract

The hadronic decay branching ratios of $J/\psi$ and $\psi(2S)$ through virtual photons, $B(J/\psi, \psi(2S) \rightarrow \gamma^*\rightarrow \text{hadrons})$, are updated by using the latest published measurements of the $R$ value and the branching ratios of $J/\psi, \psi(2S) \rightarrow l^+l^-$. Their respective precision increases by about 4 and 3 times.