  We compare precision $e^+e^-$ to $\mu^+\mu^-$ cross section measurements by
BESIII in the E_cm =3.8-4.6 GeV range, to predictions based on measured R_had
data. The consistency is poor (p-value <0.012). Allowing for resonance
contributions not seen in R_had gives an excellent fit, with the state at 4421
MeV ( 4.6 sigma) giving insight into the psi(4415) and the 3.1 sigma structure
at 4211 MeV, if confirmed, being 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.
