U(1)A symmetry in two-doublet models, U bosons or light scalars, and ψ and ϒ decays

The pseudoscalar a (possibly traded for a light gauge boson, or scalar particle) should then be, for invisible decays of the new boson, for >96% singlet and <4% doublet, for tanβ>1. Or, more generally, <4%/(tan2βBinv) doublet, which implies a very small rate for the corresponding ψ decay, B(ψ→γ+neutral)Binv≲10−6/tan4β. Similar results are obtained for new spin-1 or spin-0 neutral bosons decaying into μ+μ−.