= Solution
A bare <Dirac mass> couples left and right <chirality>, so the distinct electroweak representations prevent writing it as a gauge-invariant term before symmetry breaking. Instead the <Yukawa interactions> are
$$
\mathcal L_Y=-\bar Q_LY_dd_R\Phi-\bar Q_LY_uu_R\widetilde\Phi
-\bar L_LY_ee_R\Phi+\text{Hermitian conjugate},\qquad
\widetilde\Phi=i\tau_2\Phi^*.
$$
Weak indices are contracted to singlets. Substituting the vacuum value gives <mass> matrices $M_f=Y_fv/\sqrt2$ and a physical Higgs coupling $-\bar f_LM_ff_R\sigma/v$ plus its conjugate. Biunitary diagonalization defines <mass> eigenstates; a mismatch between the up- and down-quark left rotations appears in the <CKM matrix>. Gauge-boson masses arise from the Higgs <kinetic term>, whereas these <fermion> masses arise from the Yukawa term.
With only the minimal field content there is no <right-handed neutrino>, so no renormalizable neutrino Yukawa term. Adding a gauge-singlet $N_R$ permits both a Dirac scale $m_D=y_\nu v/\sqrt2$ and a Majorana scale $M_R$. For one family the symmetric <mass> matrix in a left-chiral basis is
$$
\begin{pmatrix}0&m_D\\m_D&M_R\end{pmatrix}.
$$
Its signed <eigenvalues> are $(M_R\pm\sqrt{M_R^2+4m_D^2})/2$. Rephasing gives positive physical masses, and for $|M_R|\gg|m_D|$ the <seesaw mechanism> yields
$$
\boxed{m_{\rm light}\simeq |m_D|^2/|M_R|,\qquad m_{\rm heavy}\simeq |M_R|.}
$$
For $m_D\sim100\,\mathrm{GeV}$ and $M_R\sim10^{14}\,\mathrm{GeV}$, the light scale is about $0.1\,\mathrm{eV}$. Integrating out the heavy state generates the dimension-five <Weinberg operator>, whose Higgs vacuum insertion gives the same suppression. Alternatively a Dirac neutrino can have a very small <Yukawa coupling> with <lepton> number conserved. A tiny observed neutrino <mass> does not by itself distinguish these mechanisms.
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