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The Feynman amplitude for the decay of the $J/\psi$ meson intobaryon-antibaryon can be written as a sum of three sub-amplitudes: a purelystrong, a purely electromagnetic and a mixed strong-electromagnetic. Assumingthat the strong and mixed strong-electromagnetic sub-amplitudes have the samephase, the branching ratio of the decay contains an interference term thatdepends on the relative phase $\varphi$ between strong and electromagneticsub-amplitudes. In this work we calculate this phase, by using an effectivestrong 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 mixedstrong-electromagnetic contributions to the total branching ratio and hence themoduli of the corresponding sub-amplitudes, for each pair of baryons. Ofparticular interest is the mixed strong-electromagnetic contribution that, notonly is determined for the first time, but it is proven to be crucial, in theframework of our model, for the correct description of the decay mechanism.Finally we use the purely electromagnetic branching ratio to calculate the Bornnon-resonant cross section of the annihilation processes $e^+ e^- \to\mathcal{B}\overline{\mathcal{B}}$ at the $J/\psi$ mass. By taking advantagefrom all available data, we obtain the relative phase between strong andelectromagnetic sub-amplitudes: $\varphi = (73\pm 8)^\circ$.

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