The resonances ($\eta_c,\chi_{ c0,c2}$) contribution to two-photon exchange (TPE) effects in $e^+ e^- \leftrightarrow p \bar{ p}$ is calculated in a simple hadronic model. The calculation shows the TPE contributions by resonance $\chi_{ c2}$, which are dependent on the unknown phases $\phi_{ E,M}$ of proton's time-like form factors $G_{ E,M}$, are much larger than the TPE contributions by non-resonance and are comparable with measurement precision of coming PANDA detector at $\sqrt{ s} \sim M_{ \chi_{ c2}}$ for most $\phi_{ E,M}$.
Categories: hep-ph