= Solution
A Dirac mass term directly pairs a left-handed weak doublet with a right-handed weak singlet and is therefore not electroweak gauge invariant. Introduce the <Higgs doublet> $H:(\mathbf1,\mathbf2)_{1/2}$ and $\widetilde H=i\sigma_2H^*:(\mathbf1,\mathbf2)_{-1/2}$. The gauge-invariant <Yukawa coupling>[Yukawa terms] are
$$
-\bar Q_LY_dHd_R-\bar Q_LY_u\widetilde Hu_R
-\bar L_LY_eHe_R-\bar L_LY_\nu\widetilde H\nu_R+\text{h.c.}
$$
When <electroweak symmetry breaking> gives $\langle H\rangle=(0,v_H/\sqrt2)^T$, these become Dirac mass matrices $M_f=Y_fv_H/\sqrt2$.
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