= Charged-lepton Yukawa matrix diagonalization
{title2=$U_L^\dagger Y_\ell U_R=\operatorname{diag}(y_e,y_\mu,y_\tau)$}
A <singular value decomposition> of the charged-lepton <Yukawa matrix> uses independent unitary rotations of left- and right-handed <leptons>. Their <gauge-covariant kinetic terms> are unchanged because each rotation mixes identical <Standard Model representations>. After <electroweak symmetry breaking>, the nonnegative singular values give <Dirac masses> $m_i=y_iv/\sqrt2$ and diagonal <Higgs boson> couplings $m_i/v$. When the <neutrinos> are massless, rotating their left-handed fields with the charged partners preserves the diagonal <weak charged current>.
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