New approach to finding invisible states in $e^{+}{e}^{-}$ annihilation and application to BESIII data

We compare precision $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ cross section measurements by BESIII in the $E_{\mathrm{cm}}=3.8–4.6\mathrm{GeV}$ range, to predictions based on measured $R_{\mathrm{had}}$ data. The consistency is poor (p-value $<0.012$). Allowing for resonance contributions not seen in $R_{\mathrm{had}}$ gives an excellent fit. The $4.6\sigma$ state required at 4421 MeV suggests that a substantial portion of $\psi \left(4415\right)$ decays are not identified, while the $3.2\sigma$ structure at 4211 MeV, if confirmed, points to a new, very narrow resonance. This analysis shows the power of precision $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ measurements to uncover or probe otherwise difficult to access states.