$H^{\pm }\to W^{\pm }\gamma$ and $H^{\pm }\to W^{\pm }Z$ in two-Higgs-doublet models: Large-fermion-mass limit

In two-Higgs-doublet models, the $H^{\pm }{W}^{\mp }V$ vertex ($V=Z or \gamma$) does not occur at the tree level, but is generated at one-loop order. We derive explicit formulas for the contribution of a weak doublet of fermions ($t, b$) to the $H^{\pm }\to W^{\pm }Z$ amplitude in the limit of large fermion masses that appear in the internal loop. In this limit, the amplitude grows as the square of the fermion masses for $m_t\ne m_b$, and is constant if $m_t=m_b$. In contrast, the $H^{\pm }\to W^{\pm }\gamma$ amplitude approaches a constant (which depends on $\frac{m_t}{m_b}$) in the large-fermion-mass limit. Asymptotic results for the contribution of a heavy supersymmetric family are also given. The observability of $H^{\pm }\to W^{\pm }Z$ at a future supercollider requires either $m_{H^{\pm }}<m_t$ and a large $t$-quark mass, or the existence of a fourth-generation nondegenerate quark doublet.