begin{align}
left(begin{array}{c}{A_{mu}} \ {rho_{mu}^{*}}end{array}right) &rightarrowleft(begin{array}{cc}{cos theta} & {-sin theta} \ {sin theta} & {cos theta}end{array}right)left(begin{array}{c}{A_{mu}} \ {rho_{mu}^{*}}end{array}right), qquadqquadqquadqquadtan theta&=frac{g_{e l}}{g_{*}}\
left(begin{array}{c}{psi_{L}} \ {chi_{L}}end{array}right) &rightarrowleft(begin{array}{cc}{cos varphi_{psi_{L}}} & {-sin varphi_{psi_{L}}} \ {sin varphi_{psi_{L}}} & {cos varphi_{psi_{L}}}end{array}right)left(begin{array}{c}{psi_{L}} \ {chi_{L}}end{array}right), hfill tan varphi_{psi_{L}}&=frac{Delta}{m}\
left(begin{array}{c}{tilde{psi}_{R}} \ {tilde{chi}_{R}}end{array}right) &rightarrowleft(begin{array}{cc}{cos varphi_{tilde{psi}_{R}}} & {-sin varphi_{tilde{psi}_{R}}} \ {sin varphi_{tilde{psi}_{R}}} & {cos varphi_{tilde{psi}_{R}}}end{array}right)left(begin{array}{c}{tilde{psi}_{R}} \ {tilde{chi}_{R}}end{array}right), quad tan varphi_{tilde{psi}_{R}}&=frac{tilde{Delta}}{tilde{m}}
end{align}