TeV-scale leptogenesis in a parity symmetric neutrino mass model

Abstract: We study leptogenesis via out-of-equilibrium decays of right-handed neutrinos in a parity symmetric extension of the Standard Model with gauge group $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$, spontaneously broken to the Standard Model gauge group at a scale $v_R$. We focus on the minimal Higgs realization, in which the strong CP problem is resolved without invoking additional symmetries. In this framework, lepton number is violated through Yukawa interactions, while neutrino masses arise only at higher loop order, a feature that permits the CP-violating quantum corrections to right-handed neutrino decays to be parametrically large. For thermal production of right-handed neutrinos, we find that successful leptogenesis requires $v_R \gtrsim 6\times 10<sup>{12}$ GeV. Non-thermal production, however, relaxes this bound dramatically, requiring only $v_R \gtrsim 10$ TeV, a scale accessible to collider searches for new particles and searches for rare processes.

• The paper demonstrates that leptogenesis in a parity-symmetric extension of the Standard Model, leveraging the minimal Higgs realization. The model allows leptogenesis without needing heavy Majorana neutrinos or suppressed Yukawa couplings.
• The steady generation of the neutrino mass at 5 loops allows a decoupling of the size of the CP-violating couplings from the light-neutrino mass scale, permitting significant $\mathcal{O}(1)$ Yukawa couplings for $v_R$ near 10 TeV under specific non-thermal production conditions.
• Thermally and non-thermally produced lepton asymmetries demonstrate a sharp dichotomy, with the thermal scenario necessitating $v_R \gtrsim 6\times 10^{12}$ GeV and the non-thermal scenario yielding a viable solution down to $v_R \gtrsim 10\text{ TeV}$ accessible by current and future collider experiments.

Leptogenesis is typically tied to heavy Majorana neutrinos whose Yukawa couplings must be small enough to keep the decays out of equilibrium, which pushes the new-physics scale far above experimental reach. This paper by Harigaya and Leone (2608.19367) shows that a parity-symmetric extension of the Standard Model — the minimal Higgs realization that solves the strong CP problem — admits leptogenesis at scales as low as $v_R \sim 10$ TeV, provided the right-handed neutrinos are produced non-thermally. The mechanism exploits a radiative neutrino mass model in which lepton number is violated by Dirac Yukawa interactions while observed neutrino masses arise only at five loops, decoupling the size of the CP-violating couplings from the light-neutrino mass scale.

Model and decay structure

The framework has gauge group $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$, broken to the Standard Model gauge group when an $SU(2)_R$ doublet $H_R$, the parity partner of the SM Higgs, acquires a vacuum expectation value $v_R$. Parity forbids the parity-odd QCD $\Theta$ term, resolving strong CP without additional symmetries, and the $H_L \leftrightarrow H_R$ symmetry ensures that fine-tuning at $v_R$ costs no more than electroweak fine-tuning.

Gauge-singlet fermions $S_i$ couple to both $H_L\ell$ and $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$0. After $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$1 breaking they form heavy Dirac fermions $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$2 with masses $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$3 (in the singular-value basis), while left-handed neutrino masses are generated radiatively through a small Majorana mass $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$4 [Harigaya:2025zru]. Because $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$5, the Yukawa coupling may be $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$6 even for $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$7 TeV. The coexistence of the two Yukawa terms violates $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$8: the channels $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$9 (gauge-mediated) and $SU(2)_R$0 (Yukawa-mediated) carry opposite $SU(2)_R$1, so their interference generates a lepton asymmetry converted to baryon number by sphalerons with the standard factor $SU(2)_R$2.

A crucial structural point concerns the charged-lepton sector. If all right-handed charged leptons originated purely from $SU(2)_R$3, one could diagonalize the $SU(2)_R$4–$SU(2)_R$5–$SU(2)_R$6 coupling and the one-loop CP-violating interference would vanish. In the minimal Higgs model, however, $SU(2)_R$7 generically mixes charged components of $SU(2)_R$8 with vector-like states from other $SU(2)_R$9 representations via couplings of the form $H_R$0. The resulting non-unitary mixing matrix $H_R$1 enables a nonzero CP asymmetry at one loop, controlled by the invariant $H_R$2 with $H_R$3.

Two constraints shape the analysis. First, if the heavy charged-lepton combination $H_R$4 were lighter than $H_R$5, unitarity would cancel the inclusive CP asymmetry; hence $H_R$6 is required, which suppresses the source by the non-unitarity factor $H_R$7. Second, the mass splitting of the resonant pair cannot be arbitrarily small: radiative corrections from singlet wavefunction renormalization and charged-lepton wavefunction renormalization impose a floor $H_R$8 for $H_R$9 GeV.

Resonant enhancement and flavor alignment

The self-energy contribution to the per-channel CP asymmetry, computed with Breit–Wigner-resummed propagators following Pilaftsis-style resummation, takes the form

$v_R$0

with the loop factor $v_R$1, regulated against divergence at exact degeneracy.

The flavor dynamics contain a subtle obstruction: in a strict two-generation theory, $v_R$2, so the off-diagonal element needed for resonance vanishes precisely where $v_R$3 peaks. With three generations this degeneracy is lifted: a non-degenerate spectator $v_R$4 ($v_R$5) renders $v_R$6 misaligned with the identity even within the quasi-degenerate subspace,

$v_R$7

Since this second term is positive semi-definite, $v_R$8. The baryon yield is maximized by taking $v_R$9 near this lower bound (larger values increase washout without enhancing the resonance peak) and choosing $\Theta$0 subject to the radiative floor. In the basis where only $\Theta$1 couples directly to $\Theta$2 and $\Theta$3, the maximal asymmetry scales as

$\Theta$4

and the signs of $\Theta$5 and $\Theta$6 coincide, so the pair's contributions do not cancel. Notably, a two-singlet model suffices for neutrino masses but eliminates the resonant enhancement entirely, since $\Theta$7 for small splittings; the paper also analyzes the non-resonant case $\Theta$8 applicable there.

Thermal production

For thermally produced $\Theta$9, the Boltzmann system tracks yields of $H_L \leftrightarrow H_R$0, $H_L \leftrightarrow H_R$1, $H_L \leftrightarrow H_R$2, and $H_L \leftrightarrow H_R$3 with real-intermediate-state subtraction to avoid double counting near resonance. Analytic upper bounds on the efficiency matrix are constructed in weak washout ($H_L \leftrightarrow H_R$4) and strong washout regimes, interpolated continuously. The tension is fundamental: the same $H_L \leftrightarrow H_R$5 interaction that sources CP violation keeps $H_L \leftrightarrow H_R$6 in equilibrium, with $H_L \leftrightarrow H_R$7 growing rapidly at low scales.

The result is stark. Even with resonant enhancement, successful thermal leptogenesis requires

$H_L \leftrightarrow H_R$8

with the non-resonant benchmark more constrained still. The implication is that thermal leptogenesis in this model is untestable by colliders, though it is consistent with the scale $H_L \leftrightarrow H_R$9–$v_R$0 GeV at which the SM Higgs quartic coupling runs toward zero — a prediction of the Higgs parity mechanism itself, testable through improved determinations of the top quark mass and $v_R$1.

Non-thermal production and collider access

If the inflaton (or any field dominating the energy density) decays into $v_R$2 with branching number $v_R$3 and $v_R$4, the singlet abundance decouples from thermal equilibrium. The required reheating temperature follows from $v_R$5, with $v_R$6 when reheating completes after sphaleron freeze-out. Three exclusions are imposed: inverse-decay washout (requiring both $v_R$7- and $v_R$8-mediated inverse chains to be inefficient), doubly off-shell scattering $v_R$9 through a dimension-seven operator whose rate scales as $S_i$0 (relevant only at low $S_i$1), and consistency of the assumption $S_i$2.

The outcome is a viable window down to

$S_i$3

achieved around $S_i$4 where the $S_i$5 channel remains open and unsuppressed. This region overlaps existing LHC bounds ($S_i$6 TeV from $S_i$7 excludes the lowest corner), lies partly within HL-LHC reach ($S_i$8 TeV), and extends into the projected sensitivity of the same-sign muon collider $S_i$9TRISTAN via $H_L\ell$0 at $H_L\ell$1 TeV, with complementary heavy-neutral-lepton probes at 3 and 10 TeV $H_L\ell$2 colliders exploiting active-heavy mixing $H_L\ell$3.

One model dependence is acknowledged: if the inflaton couples as $H_L\ell$4 and $H_L\ell$5, CP-violating inflaton decays generate additional lepton asymmetry not suppressed by the small $H_L\ell$6 branching ratio, potentially lowering the viable $H_L\ell$7 for $H_L\ell$8 — but not below the minimum already attained at $H_L\ell$9, where the direct $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$00-decay asymmetry is unsuppressed.

Limitations and open questions

The authors state several caveats explicitly. The Boltzmann treatment uses Maxwell–Boltzmann statistics, leading-order expansion in $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$01 and chemical potentials, and neglects $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$02 scatterings (justified for $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$03); off-shell $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$04 widths use a contact-interaction approximation neglecting finite-width and threshold effects. A fully flavor-dependent finite-temperature calculation could shift boundaries by $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$05 factors. The scattering-washout bound assumes an unsuppressed flavor factor $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$06; destructive interference among virtual singlet contributions could relax it. The smallness of $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$07 is technically natural but its dynamical origin is deferred to a spontaneously broken gauge symmetry studied elsewhere. Detailed predictions for connected observables — neutrinoless double beta decay and $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$08 mediated by light right-handed neutrinos and $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$09 — depend on the unspecified lepton flavor texture and remain open.

Conclusion

The paper establishes that in the minimal Higgs realization of the parity solution to strong CP, leptogenesis does not require heavy Majorana neutrinos or suppressed Yukawa couplings. Radiative neutrino masses permit $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$10 lepton-number-violating Yukawas at $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$11 near the TeV scale, and the generic charged-lepton mixing supplies the one-loop CP violation absent in simpler embeddings. The dichotomy between production mechanisms is sharp: thermal initial conditions force $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$12 GeV, while inflaton-generated abundances leave a cosmologically viable window at $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$13 TeV overlapping current and projected collider sensitivity. The model thereby connects baryogenesis to concrete experimental targets — $$SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_X$$14 bosons, heavy neutral leptons, and rare lepton-flavor-violating processes — within a framework whose low-scale consistency is independently tied to the running of the SM Higgs quartic coupling.