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Absent in the minimal Standard Model. The single charged-lepton Yukawa matrix supplies both the fermion mass matrix and the Higgs coupling, so the same left/right rotations diagonalize both. There is no off-diagonal $h\tau \mu$ vertex. With massless neutrinos, the separate charged-lepton family numbers prevent this transition perturbatively. If neutrino masses and mixing are added, loop-induced charged-lepton flavour violation can occur but is extremely suppressed; a sizeable rate would require an additional source of flavour violation. Part (c) provides one such source.

A larger-than-predicted rate can be described by adding new fields and symmetry-respecting renormalizable interactions, or, when those fields are much heavier than the energy being probed, by an effective field theory. In the latter description, add gauge-invariant operators with Wilson coefficients divided by appropriate powers of a heavy scale. Their interference with existing amplitudes, or their leading contribution to an otherwise forbidden amplitude, can enhance a decay. The operators should respect the Standard Model gauge group and be consistent with other observables; writing an arbitrary flavour-changing term without its electroweak completion is insufficient.

For charged leptons, the proposed operator has mass dimension six: the fermion bilinear contributes three, the scalar doublet one, and ${\varphi }^{†}\varphi$ two. Its hypercharge vanishes by the same calculation as the renormalizable lepton Yukawa interaction, and the extra factor ${\varphi }^{†}\varphi$ is a gauge singlet. Thus its coefficient scales as ${\Lambda }^{-2}$.

In unitary gauge, $\varphi =(0,(v+h)/\sqrt{2}{)}^T$, so the renormalizable and dimension-six terms combine intoThe charged-lepton fermion mass matrix and the single-Higgs Yukawa matrix are thereforeThis is the dimension-six Higgs Yukawa misalignment. Let $U_L^{†}M{U}_R=\mathrm{diag}(m_e,m_{\mu },m_{\tau })$ and ${\hat{\lambda }}^{\prime }=U_L^{†}{\lambda }^{\prime }{U}_R$. In the mass basis,The two matrices need not be aligned. Choosing a nonzero off-diagonal ${\hat{\lambda }}_{\mu \tau }^{\prime }$ or ${\hat{\lambda }}_{\tau \mu }^{\prime }$ produces the required charged-lepton flavour violation while keeping the fermion mass matrix diagonal.

For example, the amplitude for $h\to {\mu }^{-}{\tau }^{+}$ is, up to an overall phase,Neglecting the final lepton masses, summing spins gives $m_h^2(|({\hat{Y}}_h{)}_{\mu \tau }{|}^2+|({\hat{Y}}_h{)}_{\tau \mu }{|}^2)$. The conjugate charge channel has the same rate. The summed width isThis demonstrates an enhancement that is absent in the minimal renormalizable theory. It requires flavour misalignment: an added matrix aligned with the original Yukawa matrix would not generate these decays. The same operator also predicts double-Higgs and triple-Higgs lepton interactions through the remaining powers of $(v+h{)}^3$.