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We compare precision $e^+e^-$ to $\mu^+\mu^-$ cross section measurements byBESIII in the E_cm =3.8-4.6 GeV range, to predictions based on measured R_haddata. The consistency is poor (p-value <0.012). Allowing for resonancecontributions not seen in R_had gives an excellent fit, with the state at 4421MeV ( 4.6 sigma) giving insight into the psi(4415) and the 3.1 sigma structureat 4211 MeV, if confirmed, being a new, very narrow resonance. This analysisshows the power of precision $e^+e^-$ to $\mu^+\mu^-$ measurements to uncoveror probe otherwise difficult to access states.

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