Electroweak doublet with negative hypercharge (${\varphi }_0=(v,0{)}^T/\sqrt{2},Y=-I/2$)

An electroweak doublet with $Y=-1/2$ has component charges $(0,-1)$ under $Q=T^3+Y$. Its upper-component vacuum therefore preserves electromagnetism. The canonical covariant-derivative term gives $m_W=g_{2}v/2$, $m_Z=v\sqrt{g_1^2+g_2^2}/2$ and a massless photon. Neutral eigenvectors are proportional to $(g_2,-g_1)$ for $Z$ and $(g_1,g_2)$ for the photon. This is the conjugate-doublet convention to the usual positive-hypercharge Higgs doublet and gives the same mass ratio and electric coupling.