Learning what the Higgs boson is mixed with

The Standard Model Higgs boson may be mixed with another scalar that does not couple to fermions. The electroweak quantum numbers of such an additional scalar can be determined by measuring the quartic Higgs-Higgs-vector-vector couplings, which contribute---along with the coveted triple Higgs coupling---to double Higgs production in $e^+e^-$ collisions. We show that simultaneous sensitivity to the quartic Higgs-Higgs-vector-vector coupling and the triple Higgs coupling can be obtained using measurements of the double Higgs production cross section at two different e+e- center-of-mass energies. Kinematic distributions of the two Higgs bosons in the final state could provide additional discriminating power.