# Strong and electromagnetic amplitudes of the $J/\psi$ decays into baryons and their relative phase

## TL;DR

This paper analyzes the decay of the $J/ar{J}$ meson into baryon pairs, calculating the phase difference between strong and electromagnetic amplitudes, and determining their individual contributions to decay and production processes.

## Contribution

It provides the first calculation of the mixed strong-electromagnetic amplitude and demonstrates its importance in modeling $J/ar{J}$ decays.

## Key findings

- The relative phase between strong and electromagnetic amplitudes is $(73\u00b0 \u00b1 80)$.
- The mixed strong-electromagnetic contribution is crucial for accurate decay descriptions.
- The study estimates the non-resonant cross section for $e^+ e^- o ext{aryonar{aryon}}$ at the $J/ar{J}$ mass.

## Abstract

The Feynman amplitude for the decay of the $J/\psi$ meson into baryon-antibaryon can be written as a sum of three sub-amplitudes: a purely strong, a purely electromagnetic and a mixed strong-electromagnetic. Assuming that the strong and mixed strong-electromagnetic sub-amplitudes have the same phase, the branching ratio of the decay contains an interference term that depends on the relative phase $\varphi$ between strong and electromagnetic sub-amplitudes. In this work we calculate this phase, by using an effective strong Lagrangian density and considering, as final states, pairs of baryons, $\mathcal{B}\overline{\mathcal{B}}$, belonging to the spin-1/2 SU(3) octet. Moreover, we obtain the purely strong, purely electromagnetic and mixed strong-electromagnetic contributions to the total branching ratio and hence the moduli of the corresponding sub-amplitudes, for each pair of baryons. Of particular interest is the mixed strong-electromagnetic contribution that, not only is determined for the first time, but it is proven to be crucial, in the framework of our model, for the correct description of the decay mechanism. Finally we use the purely electromagnetic branching ratio to calculate the Born non-resonant cross section of the annihilation processes $e^+ e^- \to \mathcal{B}\overline{\mathcal{B}}$ at the $J/\psi$ mass. By taking advantage from all available data, we obtain the relative phase between strong and electromagnetic sub-amplitudes: $\varphi = (73\pm 8)^\circ$.