--- title: Dirac Seesaw Mechanism in Neutrino Models url: https://www.emergentmind.com/topics/dirac-seesaw-mechanism type: topic --- # Dirac Seesaw Mechanism in Neutrino Models Searching arXiv for relevant papers on Dirac seesaw mechanisms and closely related constructions. arXiv search query: "Dirac seesaw mechanism neutrino masses type-II Dirac inverse seesaw mini-seesaw" Dirac seesaw mechanisms are classes of neutrino-mass constructions in which the smallness of neutrino masses is obtained through a seesaw suppression while the light neutrinos remain Dirac fermions rather than Majorana fermions. In these frameworks, the suppression may arise from heavy intermediary fermions, induced small vacuum expectation values, warped localization effects, radiative generation of Dirac submatrices, or inverse-seesaw-like chains with small symmetry-breaking parameters. A defining structural feature is that lepton number is either exactly conserved or broken in a way that does not induce light Majorana masses, often through residual discrete symmetries or charge assignments that forbid the Weinberg operator and Majorana bilinears. The literature contains several non-equivalent realizations, including warped “mini-seesaw” constructions [1010.2659], type-II Dirac implementations with extended scalar sectors [1710.06498; 2209.14246; 2502.01760], type-I-like Dirac constructions with extra right-handed states [1501.02625; 2501.18181], inverse-seesaw analogues [2011.06609], and radiative double-seesaw scenarios in left-right models [2405.12283]. ## 1. Conceptual definition and distinguishing criteria The term “Dirac seesaw” refers to a suppression mechanism in which the effective light-neutrino mass arises from integrating out heavy states or from a parametrically small induced vev, but the resulting light eigenstates are Dirac rather than Majorana. In contrast with the conventional type-I Majorana seesaw, the low-energy spectrum does not contain light Majorana masses and therefore does not predict neutrinoless double-beta decay as a generic consequence [1501.02625; 2502.01760]. A minimal algebraic template appears in Dirac inverse-seesaw models, where the chiral basis \((\nu_L, N_L)\) versus \((\nu_R, N_R)\) yields \[ \mathcal{M}= \begin{pmatrix} 0 & m_D\\ \mu & M_S \end{pmatrix}, \qquad m_\nu \simeq \frac{m_D\,\mu}{M_S}, \] with \(\mu \ll m_D \ll M_S\) [2011.06609]. Here the smallness of \(m_\nu\) is controlled by a small symmetry-breaking parameter \(\mu\), so the seesaw suppression is linear in the small breaking term rather than quadratic in a heavy Majorana scale. A different but equally characteristic pattern appears in type-I-like Dirac constructions with extra right-handed neutrinos. In the model with one “ordinary” and one “adulterant” right-handed neutrino per family, the full mass matrix in the basis \(\Psi^T=(\nu_L,V_R^c,U_R^{\prime\,c})\) is \[ \begin{pmatrix} 0 & m_D & m_D'\\ m_D & M_R & \mu'\\ m_D' & \mu' & M_R' \end{pmatrix}, \] and after integrating out the heavy \(V_R\) state one obtains an almost Dirac light pair with \[ m_{\rm light}\simeq m_D' - \frac{m_D\,\mu'}{M_R}, \] while the heavy eigenstate sits at \(m_{\rm heavy}\simeq M_R\) [1501.02625]. In the \(M_R\to\infty\) limit the surviving light mass is effectively Dirac: \[ m_\nu^{\rm Dirac}\simeq m_D' = y_\nu' \frac{v}{\sqrt2}. \] Across the model classes, the operative distinction from Majorana seesaws is structural rather than merely numerical. The suppressions may look “type-I-like,” “type-II-like,” “inverse-seesaw-like,” or “double-seesaw-like,” but the symmetries are arranged so that the light neutrino mass term is of Dirac type. This suggests that “Dirac seesaw” is best viewed as a family of mechanisms rather than a single canonical construction. ## 2. Canonical mass structures and symmetry protection A recurring requirement is the absence of allowed Majorana mass terms for the light neutrino sector. Different papers realize this in different ways. In the flavour-symmetric type-II Dirac model, the symmetry group is \(A_4\otimes Z_3\otimes Z_2\), where a residual \(Z_3\) forbids all Majorana mass terms and ensures that neutrinos remain Dirac [1710.06498]. The only renormalisable neutrino-mass operator is then the Dirac Yukawa coupling to a new scalar doublet \(\phi\), whose vev is itself seesaw-suppressed. In the mirror-sector type-II Dirac construction, the gauge group \(SU(2)_L \times SU(2)' \times U(1)_X\) contains no gauge-singlet right-handed neutrinos; instead, the mirror neutrino in \(l'\) plays that role [2209.14246]. Lepton number remains an exact global symmetry, and the small Dirac mass is induced through a bidoublet scalar \(\Phi\) with a tiny vev: \[ v_\Phi \simeq -\frac{\kappa\,v\,v'}{\sqrt2\,\mu_\Phi^2}, \qquad m_\nu = Y_\nu \frac{v_\Phi}{\sqrt2} \simeq Y_\nu \frac{\kappa\,v\,v'}{2\mu_\Phi^2}. \] This is explicitly presented as the Dirac analogue of the type-II seesaw relation [2209.14246]. In the \(3\text{-}3\text{-}1\) realization, exact lepton number conservation and a discrete \(Z_2\) are imposed. The unique soft \(Z_2\)-breaking term \[ \Delta V = -\,\frac{M}{\sqrt2}\;\eta^T\,S^\dagger\,\chi + \mathrm{H.c.} \] preserves total lepton number but induces a tiny sextet vev \[ v_\Phi \simeq \frac{M\,v_\eta\,v_\chi}{2\sqrt2\,\mu_S^2}, \] which then gives \[ M_\nu = G^\nu v_\Phi, \qquad m_\nu \simeq G^\nu\,\frac{M\,v_\eta\,v_\chi}{2\sqrt2\,\mu_S^2} \] [2502.01760]. In \(U(1)_{B-L}\) models with exotic right-handed neutrino charges \(+5,-4,-4\), anomaly freedom is maintained while singlet scalars with \(B-L=+3\) break the gauge symmetry in a way that forbids Majorana masses for \(\nu_R\). The effective light Dirac mass then arises from the off-diagonal block structure \[ \mathcal{M}= \begin{pmatrix} 0_{3\times3} & m_{LN}\\ m_{NR} & M_N \end{pmatrix}, \qquad M_{\rm eff}\simeq -m_{LN}M_N^{-1}m_{NR}, \] which is the direct Dirac analogue of a type-I seesaw formula [1411.5042]. The inverse-seesaw family provides a particularly transparent symmetry logic: the small \(\mu\) parameter is the only source of \(U(1)_{B-L}\) breaking to \(\mathbb{Z}_3\), so \(\mu\to0\) restores the symmetry and makes neutrinos strictly massless Diracs. The smallness of \(\mu\) is therefore technically natural in the sense emphasized in that construction [2011.06609]. ## 3. Type-I, inverse, and extended Dirac seesaw realizations Type-I-like Dirac constructions use heavy fermions to suppress the effective Dirac mass while retaining a Dirac light spectrum. Several distinct realizations exist. A direct extension of the Standard Model with two right-handed neutrinos per family separates roles between a high-scale “ordinary” right-handed neutrino \(V_R\) and a low-scale “adulterant” right-handed neutrino \(U'_R\). The assumed hierarchy \[ M_R \gg m_D \gg m_D',\,\mu',\,M_R' \] leads, after block diagonalization, to a heavy decoupled state at \(M_R\) and an almost Dirac light pair of mass \(m_D' - m_D\mu'/M_R\) [1501.02625]. Numerically, the model quotes \[ M_R\sim10^{14}\,\mathrm{GeV},\quad m_D\sim1\,\mathrm{MeV}, \quad \frac{m_D^2}{M_R}\sim10^{-11}\,\mathrm{eV}, \] and \[ m_D'\sim10^{-1}\,\mathrm{eV} \quad\Rightarrow\quad y_\nu'\sim 6\times10^{-13} \] [1501.02625]. The resulting low-energy theory contains effectively pure Dirac neutrinos, negligible active-sterile mixing of order \(m_D/M_R\sim10^{-20}\), and no neutrinoless double-beta decay [1501.02625]. A related flavour-model realization uses the group \[ SU(2)_L\times U(1)_Y\times A_4\times Z_3\times Z_{10} \] with heavy vector-like singlets \(N_L,N_R\) and a Dirac-seesaw mass matrix \[ \mathcal{M}= \begin{pmatrix} 0 & B\\ D & M_N \end{pmatrix}, \qquad M_\nu = B\,M_N^{-1}\,D. \] The paper develops the consequences of permutations in the charged-lepton diagonalization matrix \(U_L\), leading to 18 inequivalent \(U_L\) choices and six column-permuted neutrino solutions, of which only \(U_{\nu1}\) and \(U_{\nu3}\) survive the oscillation-data constraints [2501.18181]. The model predicts a tightly restricted solar angle, \[ \sin^2\theta_{12}\in[0.340,0.341], \] for both hierarchies, and specific ranges for the masses in the \(m_1=0\) or \(m_3=0\) limits [2501.18181]. The Dirac inverse-seesaw family abstracts the essential suppression into the product \(m_D\mu/M_S\). One notable feature is that large Yukawas \(Y\sim\mathcal{O}(0.1\!-\!1)\) and TeV-scale \(M_S\) remain compatible with \(m_\nu\sim0.1\) eV if \(\mu\) is in the eV–10 eV range [2011.06609]. The same framework generalizes to “double” and “triple” Dirac inverse seesaws: \[ m_\nu \simeq m_D\,\frac{\mu_1\mu_2}{M_N M_S}, \qquad m_\nu \simeq m_D\prod_i \frac{\mu_i}{M_i}, \] respectively [2011.06609]. A distinct “dynamical seesaw” realization in an \(SU(3)_c\times SU(3)_L\times U(1)_X\) model obtains Dirac masses from a \(2\times2\) block in the \((\nu_L,N_L)\) versus \((S_R,\tilde S_R)\) basis, \[ \mathcal{M}_\nu = \frac1{\sqrt2} \begin{pmatrix} a & b\\ c & d \end{pmatrix}, \] with the light mass controlled by \[ m_{\rm light}\simeq \frac{\bigl|(k_1n_2-k_2n_1)(y_1\tilde y_2-y_2\tilde y_1)\bigr|} {\sqrt{(k_1^2+n_1^2)(y_1^2+y_2^2)+\dots}}. \] Its suppression is dynamical because the small combination \((k_1n_2-k_2n_1)\) follows from a softly lepton-number-breaking trilinear \(f[\phi_0\phi_1\phi_2+\mathrm{h.c.}]_{\rm antisymm.}\) in the scalar potential [1601.05237]. The paper emphasizes three simultaneous suppressions: the hierarchy \(k_0/n\), the small soft parameter \(f\), and a determinant-like Yukawa alignment \((y_1\tilde y_2-y_2\tilde y_1)\) [1601.05237]. ## 4. Type-II Dirac seesaw and induced small vacuum expectation values Type-II Dirac seesaws are the closest analogues of the conventional Majorana type-II mechanism. Their central object is a scalar whose induced tiny vev directly generates a Dirac mass. The flavour-symmetric model with \(A_4\otimes Z_3\otimes Z_2\) introduces a new scalar doublet \(\phi\) and singlet \(\sigma\), with the crucial trilinear scalar-potential term \[ V \supset \mu\,(\sigma\cdot\phi\cdot\hat H^d)+\mathrm{h.c.} \] After \(\sigma\) acquires a vev, the minimization conditions induce \[ v_\phi \sim \mu\,\langle\sigma\rangle\,v_{h^d}/M_\phi^2, \] and the neutrino Dirac mass matrix becomes \[ m_\nu = Y_\nu v_\phi, \] with explicit \(A_4\)-dictated texture \[ m_\nu= \begin{pmatrix} 0 & a_\nu\alpha_\nu & b_\nu e^{i\theta_\nu}\\ b_\nu\alpha_\nu e^{i\theta_\nu} & 0 & a_\nu\rho_\nu\\ a_\nu & b_\nu\rho_\nu e^{i\theta_\nu} & 0 \end{pmatrix}. \] The same flavour structure also yields the “golden” mass relation \[ \frac{m_\tau}{\sqrt{m_e m_\mu}}=\frac{m_b}{\sqrt{m_d m_s}}, \] and the oscillation analysis selects only inverted ordering, non-maximal atmospheric mixing, and a correlation between \(\delta_{CP}\) and the lightest mass \(m_3\) [1710.06498]. A conceptually different type-II Dirac seesaw arises in the mirror-sector portal model. There the bidoublet \[ \Phi= \begin{pmatrix} \varphi_1^0 & \varphi_2^-\\ \varphi_1^- & \varphi_2^{--} \end{pmatrix} \sim (1,2,2,-1) \] contains one neutral, two singly charged, and one doubly charged scalar. The trilinear term \[ \kappa(H\Phi^\dagger H' + H'^\dagger \Phi H) \] induces \[ v_\Phi \simeq -\frac{\kappa\,v\,v'}{\sqrt2\,\mu_\Phi^2}, \qquad m_\nu \simeq Y_\nu\,\frac{\kappa\,v\,v'}{2\mu_\Phi^2}. \] The construction further embeds a generalized parity, “Higgs-parity,” under which \[ \psi(t,\mathbf x)\longrightarrow i\,\sigma_2\,\psi'{}^*(t,-\mathbf x), \] forcing \(\theta_{\rm QCD}=0\) and \(Y_q'=Y_q^*\), with the tree-level quark mass matrices satisfying \(\arg\det M_uM_d=0\) [2209.14246]. Loop corrections generate only \(\bar\theta\lesssim10^{-16}\), below the bound \(\bar\theta<10^{-10}\) [2209.14246]. This model therefore uses the type-II Dirac seesaw not only for neutrino masses but also as a portal to a mirror sector and to a solution of the strong CP problem. The \(3\text{-}3\text{-}1\) model implements the type-II Dirac seesaw with a scalar sextet \[ S = \frac1{\sqrt2} \begin{pmatrix} \sqrt2\,\Delta^0 & \Delta^- & \Phi^0\\ \Delta^- & \sqrt2\,\Delta^{--} & \Phi^-\\ \Phi^0 & \Phi^- & \sqrt2\,\sigma^0 \end{pmatrix}, \] where \(\Phi^0\) is the neutral component whose small vev controls the Dirac mass [2502.01760]. The mechanism is explicitly described as “exactly analogous to the Majorana type-II result but here generating a Dirac VEV” through \[ v_\Phi \simeq \frac{M\,v_\eta\,v_\chi}{2\sqrt2\,\mu_S^2}. \] For \(M\sim10^{-1}\) keV, \(\mu_S\sim v_\chi\sim10\) TeV, and \(v_\eta\sim10^2\) GeV, the paper states that one obtains \(m_\nu\sim\mathrm{eV}\) [2502.01760]. Finally, the “double type-II Dirac seesaw” in a \(U(1)_{B-L}\) framework uses a TeV-scale Higgs doublet \(\eta\) with a tiny induced vev. Heavy scalar doublets \(\sigma_a\) and \(\omega_b\) generate the mixing \[ \mu_{\eta\phi}^2 \simeq \sum_a \rho_{\sigma a}\langle\sigma_a\rangle \quad\text{or}\quad \mu_{\eta\phi}^2 \simeq \sum_b \kappa_{\omega b}\langle\omega_b\rangle\langle\xi\rangle, \] leading to \[ v_2\equiv \langle\eta\rangle \simeq -\mu_{\eta\phi}^2\,v_1/m_{\eta^0}^2, \qquad m_\nu = f\,v_2 = f\,\frac{\mu^2 v_1}{M_\eta^2}. \] The numerical example gives \[ \langle\xi\rangle\sim10^2\,\mathrm{TeV},\quad M_{\sigma,\omega}\sim10^{16}\,\mathrm{GeV},\quad \mu_{\eta\phi}^2\sim10^{-5}\,\mathrm{GeV}^2, \] hence \[ v_2\sim0.01\text{--}1\,\mathrm{eV}, \qquad m_\nu\sim0.01\text{--}0.1\,\mathrm{eV}\ \text{for}\ f\sim0.1\text{--}1 \] [1907.11557]. ## 5. Warped, radiative, and composite-sector variants Not all Dirac seesaw ideas rely on conventional weakly coupled heavy singlets or triplets. Some use warped geometry, radiative generation, or hidden strong sectors. In a warped slice of \(AdS_5\), the model of light neutrinos from a mini-seesaw mechanism employs a bulk singlet 5D Dirac fermion \(N_R(x,y)\) with action \[ S_{\rm bulk} =\int d^5x\sqrt{-G}\left\{ \frac{i}{2}\bar N_R\Gamma^A D_A N_R -\frac{i}{2}(D_A\bar N_R)\Gamma^A N_R +c\,k\,\bar N_R N_R \right\}. \] The right-chiral zero mode has profile \[ f_R^{(0)}(z)= \sqrt{\frac{k(1+2c)}{(kR)^{1+2c}-1}}\,(kz)^c, \] and for \(c>1/2\) it is localized near the IR brane and strongly suppressed on the UV brane. This yields a tiny UV-induced Dirac mass \[ m_D \simeq \lambda \langle H\rangle \sqrt{\frac{k(1+2c)}{M_*}\,(kR)^{-(c+1/2)}}, \] together with an IR-localized Majorana mass \[ M_{00}=\lambda_2\,\frac{1+2c}{R}. \] The light eigenvalue is \[ m_\nu \simeq \frac{m_D^2}{M_{00}} \approx \frac{\lambda^2}{\lambda_2}\, \frac{\langle H\rangle^2}{M_*}\,(kR)^{-2c}, \] which the paper characterizes as a “mini-seesaw” with \(m_D\ll M_R\ll m_W\) [1010.2659]. For \(k\simeq1.5\) TeV, \(M_*\simeq9\) TeV, \(\lambda\sim\lambda_2\sim0.1\), and \(c\approx1.2\), the representative values are \(R^{-1}\sim\mathcal{O}(1\text{--}10)\) GeV, \(m_D\sim10^{-6}\text{--}10^{-4}\) GeV, \(M_{00}\sim\mathcal{O}(1\text{--}10)\) GeV, and \(m_\nu\sim10^{-2}\text{--}1\) eV [1010.2659]. The same paper also gives a 4D dual description via AdS/CFT: the right-handed zero mode is predominantly a CFT composite, the UV overlap explains the tiny effective Dirac coupling, and the IR-brane Majorana term corresponds to explicit lepton-number breaking confined to the hidden CFT sector at scale \(R^{-1}\) [1010.2659]. Although this construction is not a purely Dirac low-energy theory, it is central to the broader Dirac–Majorana seesaw landscape because it shows how suppressed Dirac and Majorana scales can coexist below the weak scale. Radiative Dirac submatrices appear prominently in the left-right model with a radiative double seesaw. The gauge group \[ SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_{B-L} \] is augmented by a global \(U(1)_X\) that breaks to a remnant \(\mathbb{Z}_2\), forbidding tree-level \(\nu_L\)–\(\nu_R\) Yukawa couplings. The Dirac mass arises at one loop: \[ (m_D)_{ij} = \sum_{r=1}^3 \frac{x_{E\,ir}z_{E\,rj}m_{E_r}}{16\pi^2} \Big[ f(m^2_{H_1^+},m^2_{E_r}) - f(m^2_{H_2^+},m^2_{E_r}) \Big] \sin2\theta_H, \] with \[ f(m_1^2,m_2^2)= \frac{m_1^2}{m_1^2-m_2^2}\ln\!\left(\frac{m_1^2}{m_2^2}\right). \] The full neutrino mass matrix in the basis \((\nu_L,\nu_R^C,N_R^C)\) is \[ M_\nu= \begin{pmatrix} 0 & m_D & 0\\ m_D^T & 0 & M\\ 0 & M^T & M_N \end{pmatrix}, \] so that in the seesaw limit \[ M_\nu^{\rm light}=m_D(M^T)^{-1}M_NM^{-1}m_D^T \] [2405.12283]. The article emphasizes that this is the first implementation, to its knowledge, of a radiative double seesaw in which the Dirac submatrix is generated at one loop [2405.12283]. A different use of heavy Dirac mediators appears in the TeV-scale five-plet model. There, a vector-like Dirac five-plet \[ \Sigma_{L,R}\sim(1,5,2) \] and scalar four-plets \(\Phi_1\sim(1,4,-3)\), \(\Phi_2\sim(1,4,-1)\) generate the dimension-nine operator \[ {\cal O}_9= \frac{Y_1Y_2}{M_\Sigma} (\overline{\ell_L}\,\ell_L^c)\Phi_1\Phi_2. \] After induced vevs \[ v_{\Phi_1}\simeq \frac{\lambda_1 v^3}{\mu_{\Phi_1}^2}, \qquad v_{\Phi_2}\simeq \frac{\lambda_2 v^3}{\mu_{\Phi_2}^2}, \] the neutrino mass scales as \[ m_\nu \sim \frac{v^6}{M_\Sigma^5}. \] This mechanism uses Dirac mediators but produces Majorana neutrino masses, so it does not belong to the strict class of Dirac-neutrino seesaws [1105.5561]. Its relevance is taxonomic: it illustrates that “Dirac seesaw” may refer either to Dirac mediators or to Dirac light neutrinos, and the two notions should not be conflated. ## 6. Phenomenology, cosmology, and model-dependent signatures The phenomenology of Dirac seesaw models is highly model-dependent because the suppression can be tied to different sectors: flavour, gauge extensions, warped geometry, hidden strong dynamics, or scalar portals. In flavour-symmetric type-II Dirac models, the most distinctive outputs are oscillation correlations rather than direct collider states. The \(A_4\otimes Z_3\otimes Z_2\) model predicts only inverted ordering, prefers the higher octant \(\sin^2\theta_{23}\gtrsim0.51\), and yields \[ 6.4\times10^{-4}\,\mathrm{eV}\lesssim m_3\lesssim2.7\times10^{-3}\,\mathrm{eV} \] for the lightest neutrino mass [1710.06498]. It also implies that for \(m_3\lesssim2\times10^{-3}\) eV one must have \(\delta_{CP}\neq0\) [1710.06498]. In the \(A_4\times Z_3\times Z_{10}\) type-I Dirac model, charged-lepton flavour violation and dark matter depend on the same structures that control the PMNS matrix. The paper gives \[ {\rm BR}(\mu\to e\gamma)\sim 10^{-29}\text{--}10^{-12}, \qquad {\rm BR}(\tau\to \ell\gamma)\sim 10^{-28}\text{--}10^{-8}, \] depending on the parameters and the permutation choice in \(U_L\) [2501.18181]. Its dark-matter annihilation cross sections span from \(\sim10^{-24}\,\mathrm{cm}^3/\mathrm{s}\) down to \(\sim10^{-46}\,\mathrm{cm}^3/\mathrm{s}\) [2501.18181]. The \(3\text{-}3\text{-}1\) type-II Dirac model links neutrino physics to both lepton-flavour violation and cosmology. For \(\mu\to e\gamma\), the doubly charged scalar \(\Delta^{++}\) gives \[ \mathrm{Br}(\mu\to e\gamma)\sim10^{-19}\ \text{(normal ordering)}, \qquad \sim10^{-15}\ \text{(inverted ordering)}, \] below the present bound \(4.3\times10^{-13}\) [2502.01760]. More stringently, the right-handed neutrinos thermalize through \(Z'\)-mediated interactions, and requiring \(\Delta N_{\rm eff}<0.3\text{--}0.4\) yields \[ m_{Z'}\gtrsim 4.4\ \mathrm{TeV} \quad\Longrightarrow\quad v_\chi\gtrsim 9.9\ \mathrm{TeV} \] [2502.01760]. The double type-II Dirac seesaw with \(U(1)_{B-L}\) adds a stable Dirac fermionic dark matter state \[ \chi\equiv \nu_{R3}+\nu_{R4}^c, \qquad m_\chi = y_{34}\langle\xi\rangle. \] Its relic-density analysis gives \[ 25\,\mathrm{TeV}\lesssim \langle\xi\rangle \lesssim 222\,\mathrm{TeV}, \qquad 0.5\,\mathrm{TeV}\lesssim m_\chi \lesssim 38\,\mathrm{TeV}, \] and direct detection implies \(m_\chi\gtrsim5\) TeV, with \[ \sigma_{\chi N}\simeq 3.5\times10^{-45}\,\mathrm{cm}^2\, \left(\frac{5\,\mathrm{TeV}}{m_\chi}\right)^2 \] [1907.11557]. The same setup supports Dirac leptogenesis through out-of-equilibrium decays of heavy scalar doublets, with \[ B = -\frac{28}{79}A_\eta, \] and a representative asymmetry \(B\sim10^{-10}\) for \(\mathcal{O}(0.1)\) CP phases [1907.11557]. In the mirror type-II Dirac portal, collider-scale signatures are muted because the bidoublet mass scale is typically large, but the scalar spectrum includes singly and doubly charged states analogous to those in Majorana type-II seesaws. Their couplings to SM leptons are, however, restricted by a \(\mathbb Z_3\), and no observable shifts in \(W\), \(Z\), or the \(\rho\)-parameter arise because the \(\Phi\) vev respects custodial symmetry [2209.14246]. Cosmologically, the paper states that dark radiation from mirror neutrinos is negligible, with freeze-in yields \(\Delta N_{\rm eff}\ll10^{-10}\), while avoiding overclosure by stable mirror electrons requires \[ T_{\rm RH}