Dutta and Narendra (Phys. Rev. D 112, 115043 (2025)) proposed a framework in which the baryon asymmetry of the universe and an asymmetric, self-interacting dark matter relic arise together from the CP-violating out-of-equilibrium decays of heavy scalar doublets, with neutrinos kept Dirac by an exact global U(1)B−LU(1)_{B-L} symmetry. Quantum-gravity arguments imply that global symmetries are generically violated, so Planck-suppressed operators could reintroduce Majorana neutrino masses and lepton-number violation; the robust safeguard is to gauge B−LB-L. The paper argues only qualitatively that its charge assignments admit a gauged B−LB-L embedding whose heavy gauge boson decouples, leaving the cosmological analysis — performed entirely in the global-B−LB-L theory — unchanged. The open problem is to construct this gauged U(1)B−LU(1)_{B-L} completion explicitly and to determine quantitatively whether the framework survives it: a consistent B−LB-L-breaking scalar sector (or unbroken realization) that forbids the renormalizable ϕB−LνRνR\phi_{B-L}\nu_R\nu_R, bounded residual lepton-number-violating operators, a thermal history including the B−LB-L gauge sector that preserves the framework's required delayed νL−νR\nu_L-\nu_R equilibration and asymmetry preservation, and the resulting viable parameter space and new observables.

Background

The observed baryon asymmetry of the universe (BAU) and the dark matter (DM) abundance stand in the striking ratio ΩDM≈5 ΩB\Omega_{\rm DM} \approx 5\,\Omega_{\rm B}. This coincidence motivates asymmetric dark matter (ADM), in which DM carries a particle-antiparticle asymmetry generated by the same dynamics as the baryon asymmetry, so that its present relic density tracks the baryon's. Independently, whether neutrinos are Dirac fermions (distinct particle and antiparticle, with lepton number conserved) or Majorana fermions (their own antiparticles, with lepton-number violation) remains undecided experimentally. Dick, Lindner, Ratz and Wright (Phys. Rev. Lett. 84, 4039 (2000)) showed that leptogenesis — baryogenesis via CP-violating out-of-equilibrium decays of heavy particles producing a lepton asymmetry that electroweak sphaleron transitions (thermal transitions that violate B+LB+L but conserve B−LB-L, active above the electroweak phase transition) partially convert into baryon number — can work with Dirac neutrinos: the decays create equal and opposite lepton asymmetries in the left-handed (νL\nu_L) and right-handed (νR\nu_R) neutrino sectors, sphalerons convert only the left-handed part into baryon asymmetry, and total B−LB-L remains zero. The mechanism requires that interactions equilibrating νL\nu_L and νR\nu_R stay slower than the Hubble expansion until after sphaleron freeze-out, which tiny Dirac Yukawa couplings achieve.

Dutta and Narendra (Phys. Rev. D 112, 115043 (2025); building on Dutta, Narendra, Sahu and Shil, Phys. Rev. D 106, 095017 (2022)) combined this Dirac leptogenesis with ADM and self-interacting dark matter (SIDM). SIDM addresses small-scale structure problems of cold DM by letting dark particles scatter off each other through a light MeV-scale mediator, here the Z′Z' gauge boson of a gauged dark symmetry U(1)DU(1)_D; a kinetic mixing parameter ϵ\epsilon between Z′Z' and the Standard Model ZZ boson (a gauge-invariant mixing of the two field-strength terms) provides the portal for direct detection. Their model adds to the Standard Model three right-handed neutrinos νRi\nu_{R_i}, a singlet fermion χ\chi (the DM candidate), a vectorlike SU(2)LSU(2)_L doublet fermion ψ\psi (vectorlike meaning both chiralities are present with equal gauge charges, so they contribute no gauge anomalies), and heavy scalar doublets ηi\eta_i, with a discrete Z2\mathcal{Z}_2 symmetry under which χ\chi, νR\nu_R and η\eta are odd. The Z2\mathcal{Z}_2 is broken softly by a term μ2H†η\mu^2 H^\dagger\eta, which together with a Yukawa coupling f ℓˉη~νRf\,\bar{\ell}\tilde{\eta}\nu_R generates small Dirac neutrino masses Mν∼f⟨H⟩μ2/Mη2M_\nu \sim f\langle H\rangle\mu^2/M_\eta^2 radiatively, through one-loop heavy-scalar exchange; the CP-violating out-of-equilibrium decays of η\eta feed asymmetries simultaneously into the visible sector (η→νRℓ\eta \to \nu_R \ell) and the dark sector (η→χψ\eta \to \chi\psi). A phenomenologically viable slice requires an extremely small kinetic mixing ϵ≲10−8\epsilon \lesssim 10^{-8} (so the effective Z′Z' coupling to Standard Model matter is geff′=ϵg′∼10−9g'_{\rm eff} = \epsilon g' \sim 10^{-9}), consistent with CRESST-III and XENON1T direct-search limits.

The framework's Dirac neutrinos are protected only by an exact global U(1)B−LU(1)_{B-L} symmetry (BB minus LL, baryon minus lepton number), imposed at the renormalizable level. However, general arguments in quantum gravity — crystallized by Banks and Seiberg (Phys. Rev. D 83, 084019 (2011)) — hold that exact global symmetries do not exist in a theory of gravity, so Planck-scale-suppressed operators are expected to violate the global B−LB-L and reintroduce Majorana mass terms νRνR\nu_R\nu_R. This would threaten not only the Dirac nature of the neutrino but also the preserved asymmetries, since lepton-number-violating processes can wash out the generated asymmetries. The theoretically robust protection is to gauge U(1)B−LU(1)_{B-L}: gauge invariance then forbids Majorana masses to all orders and constrains the Planck-suppressed operators by charge conservation. Gauged B−LB-L models with Dirac neutrinos are known in other contexts — e.g. Ma and Srivastava (Mod. Phys. Lett. A 30, 1530020 (2015)) and Leite, Morales, Valle and Vaquera-Araujo (Phys. Lett. B 807, 135537 (2020)) — so the generic possibility is established model-building technology. In the version-2 revision of their paper, Dutta and Narendra note that their charge assignments (with η\eta neutral and νR\nu_R, ψ\psi, χ\chi of charge −1-1 under B−LB-L) already render the Lagrangian gauge-invariant, that SM plus three νR\nu_R is anomaly-free with vectorlike ψ\psi, χ\chi adding nothing, that a B−LB-L-breaking scalar ϕB−L\phi_{B-L} can be charged so as to avoid the unwanted operator ϕB−LνRνR\phi_{B-L}\nu_R\nu_R, and that a sufficiently heavy ZB−LZ_{B-L} (mass ≫\gg TeV) decouples without changing the low-energy phenomenology. But this is a qualitative consistency sketch: every quantitative result of the paper — the Boltzmann evolution of the asymmetries, the washout analysis, the SIDM self-interaction cross sections, and the direct-detection and collider phenomenology — is derived in the global-B−LB-L theory, and the phenomenological implications of actually gauging B−LB-L are left unintegrated.

Problem Statement

Construct the explicit gauged U(1)B−LU(1)_{B-L} completion of the Dutta–Narendra common-origin framework and determine, quantitatively, whether the framework survives it. Establish, jointly and for the stated field content (three νR\nu_R, the vectorlike singlet χ\chi and doublet ψ\psi, the heavy scalar doublets ηi\eta_i, and the gauged U(1)DU(1)_D sector with its MeV-scale Z′Z'):

  1. Consistent gauge completion. The full gauge-invariant Lagrangian including the B−LB-L gauge boson and its mass-generation mechanism — either spontaneous breaking by a scalar ϕB−L\phi_{B-L} whose B−LB-L charge (or an auxiliary symmetry) forbids the renormalizable operator ϕB−LνRνR\phi_{B-L}\nu_R\nu_R, or an unbroken realization in which that operator is absent — so that neutrinos remain exactly Dirac at the renormalizable level, with a verification of anomaly cancellation and consistency with the existing Z2\mathcal{Z}_2 and U(1)DU(1)_D charge structure.
  2. Bounded residual lepton-number violation. An operator analysis of the Majorana-mass terms that remain allowed once B−LB-L is gauged (and, in a broken realization, broken) — including higher-dimensional operators built from the breaking scalars and any Planck-suppressed operators consistent with the gauge charges — with numerical bounds (e.g. against neutrinoless double beta decay limits and the washout requirements of the leptogenesis mechanism), replacing the paper's qualitative statement that gauge invariance 'tightly constrains' such operators.
  3. Integrated thermal history. A re-derivation of the early-universe evolution with the B−LB-L gauge sector included: the Boltzmann system for the η\eta decays and asymmetry sharing, augmented by B−LB-L-mediated processes, must be shown to preserve the two conditions on which the mechanism rests — that νL−νR\nu_L-\nu_R equilibration remains slower than the Hubble rate until sphaleron freeze-out, and that neither the visible nor the dark asymmetry is washed out — for the chosen MZB−LM_{Z_{B-L}} and gauge coupling (including the regime where the leptogenesis temperature is comparable to or below the B−LB-L breaking scale and the gauge boson acts as a heavy virtual mediator), together with cosmological constraints such as ΔNeff\Delta N_{\rm eff} (the deviation in the effective number of light relativistic species probed by Big-Bang nucleosynthesis and the cosmic microwave background) from the light νR\nu_R population.
  4. Viability of the parameter space and new signatures. The resulting viable region along the new B−LB-L directions (MZB−LM_{Z_{B-L}}, gauge coupling, and breaking sector), jointly satisfying the baryon asymmetry, asymmetric SIDM relic density, self-interaction cross sections in the desired range, and direct-detection limits (CRESST-III, XENON1T), together with the new constraints and potential signals of the ZB−LZ_{B-L} sector (collider, electroweak-precision, and cosmological), establishing whether the framework's joint fit survives gauging or fails.

Each part is to be addressed at the analytic or benchmark level of the framework's own analysis, and a non-empty viable region confined to an explicitly identified sub-regime also counts as an affirmative resolution.

An answer that instead demonstrates impossibility — for instance a gauge-invariant operator unavoidably generated by any consistent gauged-B−LB-L realization that drives Majorana masses above existing bounds, or B−LB-L-mediated processes unavoidably in equilibrium before sphaleron freeze-out for all MZB−LM_{Z_{B-L}} and gauge couplings not already excluded by existing laboratory and cosmological constraints in the light window 1 GeV<MZB−L<100 TeV1\,{\rm GeV} < M_{Z_{B-L}} < 100\,{\rm TeV}, with no viable heavy decoupling realization at MZB−L≫M_{Z_{B-L}} \gg TeV remaining — resolves the problem in the negative. The technically small parameters (μ≪Mη\mu \ll M_\eta with μ/Mη≈10−4\mu/M_\eta \approx 10^{-4}, f∼10−4f \sim 10^{-4}, λ∼10−7\lambda \sim 10^{-7}) and the testability of the tiny-kinetic-mixing regime are acknowledged separate limitations of the source framework and are not required for completion, though a completion may incidentally address them.

References

  1. Manoranjan Dutta and Nimmala Narendra, A Common Origin of Asymmetric Self-interacting Dark Matter and Dirac Leptogenesis, Phys. Rev. D 112, 115043 (2025), doi:10.1103/6s66-twc5, arXiv:2506.22388, https://arxiv.org/abs/2506.22388 (source paper)
  2. Karin Dick, Manfred Lindner, Michael Ratz, and David Wright, Leptogenesis with Dirac Neutrinos, Phys. Rev. Lett. 84, 4039 (2000), doi:10.1103/PhysRevLett.84.4039, arXiv:hep-ph/9907562, https://arxiv.org/abs/hep-ph/9907562
  3. Tom Banks and Nathan Seiberg, Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 83, 084019 (2011), doi:10.1103/PhysRevD.83.084019, arXiv:1011.5120, https://arxiv.org/abs/1011.5120
  4. Manoranjan Dutta, Nimmala Narendra, Narendra Sahu, and Sujay Shil, Asymmetric self-interacting dark matter via Dirac leptogenesis, Phys. Rev. D 106, 095017 (2022), doi:10.1103/PhysRevD.106.095017, arXiv:2202.04704, https://arxiv.org/abs/2202.04704
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