 Solution

Using c and omitting ${\partial }_{\mu }\Phi$, the covariant derivative isThe two components are orthogonal, so their squared magnitudes add; $(W_{\mu }^{+}{)}^{†}=W_{\mu }^{-}$. Thus the Higgs field kinetic contribution to the Lagrangian density isThe two $v^2$ terms are gauge boson mass terms. Comparing with $m_W^2{W}^{+}{W}^{-}+\frac{1}{2}{m}_Z^2{Z}^2$ gives $\boxed{m_W=gv/2,m_Z=Gv/2}$ and $m_W/m_Z=\cos {\theta }_W$. The factor $1/2$ for the real Z boson field is essential.

The two $2vh$ terms are the cubic Higgs boson coupling to W bosons and Higgs boson coupling to Z bosons. They produce the three-leg $h{W}^{+}{W}^{-}$ and $hZZ$ Feynman vertices, allowing Higgs decay to two W bosons, Higgs decay to two Z bosons when kinematically available, and the corresponding production mechanisms with virtual gauge bosons. The two $h^2$ terms are quartic $hh{W}^{+}{W}^{-}$ and $hhZZ$ interactions, including vector-boson scattering into a Higgs boson pair. Written in terms of the masses,The corresponding Feynman vertex factors are $2i{m}_V^2{g}_{\mu \nu }/v$ for one $h$ and $2i{m}_V^2{g}_{\mu \nu }/v^2$ for two $h$, for $V=W,Z$, after differentiating with respect to identical fields. These six contributions contain no photon mass or direct $hAA$ interaction because $Q\Phi =0$.