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Type-II Seesaw Mechanism for Dirac Neutrinos and its Implications on $N_{\text{eff}}$ and Lepton Flavor Violation in a 3-3-1 model

T0 review · 2 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read A scalar sextet turns the type-II seesaw into a Dirac-neutrino mechanism, and the thermal history of the resulting right-handed neutrinos forces the new Z' boson above 4.4 TeV.

desk verdict A competent, incremental extension of the 331RHN with a Dirac type-II seesaw; the new DeltaNeff bound on mZ' is plausible but rests on an unquantified sudden-decoupling approximation, and the LFV numbers contain internal arithmetic errors that need correcting. read the letter →

arxiv 2502.01760 v5 pith:DB7SXPGO submitted 2025-02-03 hep-ph

Vinícius Oliveira , Patricio Escalona , Lucia Angel , C. A. de S. Pires , Farinaldo S. Queiroz This is my paper · ORCID
classification hep-ph
keywords type-IIseesawDiracneutrinomasses3-3-1modelscalarsextetright-handedneutrinoseffectivenumberofspeciesleptonflavorviolationZ'boson
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that the type-II seesaw mechanism, normally used for Majorana neutrinos, can be adapted to generate naturally small Dirac neutrino masses inside a 3-3-1 model. It adds a scalar sextet and a softly broken $Z_2$ symmetry; the unique soft-breaking term drives the sextet's neutral component to an eV-scale vacuum expectation value, so neutrino masses of the right size emerge without tiny Yukawa couplings. The same construction produces calculable rates for the rare decays $\mu \to e\gamma$ and $\mu \to \bar e e e$, both below current limits. The paper then follows the right-handed neutrinos through the early universe: $Z'$ interactions thermalize them, and the radiation they contribute before decoupling is controlled by the $Z'$ mass. Requiring this extra radiation to respect current CMB and BAO bounds yields $m_{Z'} > 4.4$ TeV, a lower bound slightly above today's collider exclusion.

What carries the argument

The load-bearing object is the scalar sextet $S$ with the soft $Z_2$-breaking term $-\frac{M}{\sqrt{2}}\eta^T S^\dagger \chi$; this produces the seesaw suppression $v_\Phi \approx \frac{M v_\eta v_{\chi'}}{2\sqrt{2}\mu_S^2}$. The second load-bearing piece is the $Z'$-mediated annihilation of right-handed neutrinos: the thermally averaged cross sections into left-handed neutrinos, charged leptons, and quarks set the decoupling temperature $T_{\mathrm{dec}}^{\nu_R}$, and the ratio of entropic degrees of freedom at that temperature converts it into $\Delta N_{\mathrm{eff}}$. The mass relation $m_{W'} \approx m_{U^0} \approx 0.72\, m_{Z'}$ carries the bound from $Z'$ to all exotic gauge bosons.

What would settle it

A decisive test: measure $m_{Z'}$ in dilepton searches and find it below 4.4 TeV while a future high-precision CMB experiment reports $\Delta N_{\mathrm{eff}}$ consistent with the Standard Model value; that combination would rule out the model's thermalized right-handed-neutrino history, since the predicted extra radiation would have to be present.

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Extended reading notes

Core claim

The paper's central claim is that the soft $Z_2$-breaking term $-\frac{M}{\sqrt{2}}\eta^T S^\dagger \chi + \mathrm{H.c.}$, which preserves lepton number, induces the small vacuum expectation value $v_\Phi \approx \frac{M v_\eta v_{\chi'}}{2\sqrt{2}\mu_S^2}$; for TeV-scale 3-3-1 breaking and $M \approx 0.1$ keV this yields $v_\Phi \approx 1$ eV and hence Dirac masses $m_\nu = G_\nu v_\Phi$ at the observed sub-eV scale. With $v_\Phi = 1$ eV and neutrino mixing data, the model predicts $\mathrm{Br}(\mu \to e\gamma) = 3.52\times 10^{-19}$ (normal ordering) and $3.52\times 10^{-15}$ (inverted ordering), and $\mathrm{Br}(\mu \to \bar e e e) = 9.89\times 10^{-17}$ (inverted), all below current limits. In cosmology, the right-handed neutrinos thermalize for essentially any $m_{Z'}$ below $10^{16}$ GeV; their decoupling temperature is set by $Z'$-mediated annihilations, and entropy dilution after decoupling gives $\Delta N_{\mathrm{eff}} = 3(10.75/g_s(T_{\mathrm{dec}}))^{4/3}$. The observed $\Delta N_{\mathrm{eff}} < 0.285$ ($2\sigma$) then implies $m_{Z'} > 4.4$ TeV, corresponding to $v_{\chi'} > 9.9$ TeV.

Load-bearing premise

The $m_{Z'} > 4.4$ TeV bound assumes the right-handed neutrinos actually thermalize and then decouple suddenly with the Standard Model having 106.75 energy degrees of freedom; if the reheating temperature is below their decoupling temperature, they never reach equilibrium and the bound evaporates.

Editorial extensions

If this is right

  • Dirac neutrino masses below the eV scale are generated naturally at TeV-scale 3-3-1 breaking, without introducing tiny Yukawa couplings or Majorana mass terms.
  • The predicted branching ratios for $\mu \to e\gamma$ and $\mu \to \bar e e e$ lie below current limits; the inverted-ordering $\mu \to e\gamma$ prediction sits within roughly an order of magnitude of the planned experimental sensitivity.
  • $N_{\mathrm{eff}}$ provides a lower bound on the 3-3-1 breaking scale, $m_{Z'} > 4.4$ TeV (equivalently $v_{\chi'} > 9.9$ TeV), which already exceeds the current collider exclusion and is comparable to future high-luminosity collider projections.
  • The bound extends to the exotic charged gauge bosons $W'$ and $U^0$ because their masses are locked to $m_{Z'}$ by the gauge structure.
  • If the reheating temperature is below the right-handed-neutrino decoupling temperature, the thermal population never forms and the cosmological bound disappears, leaving collider searches as the main test.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same $\Delta N_{\mathrm{eff}}$ calculation transfers to any 3-3-1 variant in which a light $Z'$ couples to right-handed leptons, so the bound may constrain other embeddings, not just this specific sextet construction.
  • A future CMB experiment at the few-times-$10^{-2}$ sensitivity level on $\Delta N_{\mathrm{eff}}$ would sharpen the lower bound on $m_{Z'}$ considerably; the paper's formulas can be inverted once the temperature dependence of the entropy degrees of freedom is refined.
  • If a collider discovers a $Z'$ below 4.4 TeV with no accompanying radiation excess, the thermalization assumption would be the first thing to give way, and the low-reheating-temperature scenario is a concrete way the model could survive.
  • The lepton-flavor-violation predictions depend strongly on the neutrino mass ordering, so a positive $\mu \to e\gamma$ signal would point toward the inverted-ordering parameter region of this model.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The manuscript extends the 3-3-1 model with right-handed neutrinos by adding a scalar sextet and a softly broken Z2 symmetry, implementing a type-II seesaw mechanism for Dirac neutrino masses. The resulting small neutrino masses arise from the induced VEV v_Phi ~ M v_eta v_chi' / (2 sqrt(2) mu_S^2). The paper then studies lepton-flavor-violating decays mu -> e gamma and mu -> eee mediated by the sextet scalars, and computes the contribution of right-handed neutrinos to N_eff through Z' interactions. The headline result is a lower bound m_Z' > 4.4 TeV, slightly above the LHC limit of 4 TeV, which the authors present as evidence that N_eff can be a stronger probe of the 3-3-1 breaking scale than current colliders.

Significance. If the central claims hold, the model offers a simple low-scale Dirac seesaw in a 3-3-1 context with distinctive LFV and cosmological signatures. The seesaw formula is clean and the use of N_eff to bound m_Z' is a valuable complement to collider searches. The paper provides explicit analytic expressions for the relevant cross sections and uses numerical integration (Cuba) and a modified NUDEC_BSM code for the left-handed neutrino contribution, which are strengths. However, the headline m_Z' bound rests on an approximate instantaneous-decoupling treatment at the QCD crossover, and the quoted mu -> eee branching ratio contains a large numerical error; both issues must be addressed before the quantitative conclusions can be taken at face value.

major comments (2)
  1. [Sec. 5.2, Eqs. (52), (59)-(60)] The bound m_Z' > 4.4 TeV is derived from an instantaneous-decoupling formula that assumes g_rho(Tdec) = 106.75. For m_Z' = 4.4 TeV, Eq. (52) gives Tdec of order 0.2 GeV, which is inside the QCD crossover, where g_rho and g_s are both significantly smaller and vary steeply (g_s ~ 60, not 106.75). The paper does not solve the Boltzmann equation for the right-handed neutrinos and provides no estimate of the systematic uncertainty from the sudden-decoupling approximation. Because the final (T_nuR/T_nuL)^4 depends on the integrated decoupling history across the crossover, a shift of order 10-20% in Delta N_eff is plausible; since the quoted bound is only about 10% above the LHC limit, this systematics is load-bearing for the paper's central conclusion. I recommend repeating the calculation with temperature-dependent g_* in the Hubble rate and with a smooth freeze-out treatment, or at least providing a quantified two-sided estimate of the approximation error. The low-reheating caveat is acknowledged, but this QCD-crossover systematics is not.
  2. [Sec. 4, Eqs. (28)-(29)] The quoted Br(mu -> eee) = 9.89e-17 for the inverted ordering is inconsistent with the authors' own inputs. Using G_nu_IO from Eq. (24), G_F = 1.166e-5 GeV^-2, and M_Delta++ from Eq. (61) with v_eta = 178 GeV, v_chi' = 10 TeV, M = 0.1 keV, and v_Phi = 1 eV gives M_Delta++ ~ 9.4 TeV and Br(mu -> eee) ~ 4e-13; if the 7 TeV mass quoted in Appendix A is used instead, the value is ~ 1.4e-12. The quoted number is about four orders of magnitude smaller. The second form of Eq. (28) also appears to omit the square on |G_nu_12|. Although the conclusion that the prediction respects the current experimental upper bound may survive, the numerical values and the comparison with prospective sensitivity need to be corrected.
minor comments (6)
  1. [Eq. (28)] The second equality in Eq. (28) should read |G_nu_11|^2 |G_nu_12|^2, not |G_nu_11|^2 |G_nu_12|.
  2. [Sec. 4 and Appendix A] The benchmark values are inconsistent: the text quotes v_eta = 178 GeV in the LFV calculation but v_eta ~ 10^2 GeV elsewhere, and Appendix A says the sextet scalars have mass around 7 TeV while Eq. (61) with the stated inputs gives about 9.4 TeV. These numbers should be harmonized.
  3. [Sec. 4] The value of the Fermi constant is quoted as G_F = 1.116e-5 GeV^-2; the standard value is 1.166e-5 GeV^-2. Please check and use a consistent value.
  4. [References [51] and [52]] References [51] and [52] appear to be identical; please distinguish the MEG II current result from its future sensitivity projection or remove the duplicate.
  5. [Sec. 5.2, Eq. (52)] The text says 'we assume g_rho(T_nuR) = 106.75' but the derived Tdec lies in the QCD crossover; please clarify whether g_rho or g_s is meant and justify the constant value used.
  6. [Eq. (24)] The labeling of the NO and IO Yukawa matrices should be checked for consistency with Eq. (22); in particular, the null entries and the signs should be cross-validated against the stated PMNS parametrization.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model's predictions are derived from stated symmetries, minimization conditions, and external data, not from the quantities they are said to predict.

full rationale

The central Dirac-seesaw relation vPhi approximately M veta vchi'/(2 sqrt(2) muS^2) (Eq. 16) follows from the scalar-potential minimization conditions (Eq. 13) under the stated assumptions M << veta, vchi' and a TeV-scale muS; it is not defined in terms of the neutrino mass. The LFV rates (Eqs. 25-29) use the Yukawa couplings reconstructed from externally measured oscillation parameters (Eqs. 22-23) and the sextet scalar masses from the same potential (Eq. 61), then compare with MEG bounds; no LFV observable is used as an input. The DeltaNeff calculation is likewise self-contained: the Z' couplings are fixed by the gauge structure (Eqs. 31-33), the freeze-out condition Gamma(Tdec)=H(Tdec) (Eq. 52) is solved with computed s-channel cross sections, and the resulting mZ' > 4.4 TeV bound is compared with the external Planck/DESI limits and LHC bounds. The self-citations [28] and [43] are peripheral (motivation and a cross-check of the triplet Higgs spectrum that is rederived in Appendix A) and are not load-bearing for the mass, LFV, or Neff conclusions. The instantaneous-decoupling treatment and the assumption g_rho(Tdec)=106.75 near the QCD crossover are physical approximations that could affect the numerical bound, and the authors explicitly note the low-reheating caveat, but these are accuracy/robustness concerns, not circularity.

Assumptions & free parameters 4 free parameters · 6 assumptions · 1 invented entities

The model's central claim rests on four free parameters (M, muS, vChi', vPhi) and several domain assumptions. The most fragile assumption for the headline Z' bound is the instantaneous decoupling of right-handed neutrinos during the QCD crossover. The invented entity is the scalar sextet, which has testable mass and LFV signatures.

free parameters (4)
  • M (soft Z2-breaking scale) = 0.1 keV (benchmark)
    Chosen so Eq. 16 gives vPhi around 1 eV; technically natural but not predicted.
  • muS (sextet soft mass parameter) = 10 TeV (benchmark)
    Together with M and vChi' it sets vPhi; also sets the sextet scalar mass scale near 7 TeV.
  • vChi' (3-3-1 breaking scale) = 10 TeV for LFV benchmark; lower bound 9.9 TeV from Neff
    Fixates mZ' for LFV predictions; the cosmological bound translates into vChi' > 9.9 TeV.
  • vPhi (sextet neutral VEV) = 1 eV (benchmark)
    Sets the Dirac neutrino mass scale m_i = Gnu vPhi; the Yukawa couplings are then fixed by oscillation data.
assumptions (6)
  • domain assumption The 331RHN gauge structure and fermion content are anomaly-free as in Refs [16,17,18].
    The paper adds a scalar sextet to the existing 331RHN; scalars do not affect gauge anomalies, and fermion content is taken as given (Sec. 2).
  • domain assumption Lepton number and Z2 charge assignments, including L(W')=L(U0)=-2 and bilepton scalar charges, are consistent.
    These assignments are needed for the unique soft term Eq. 11; the paper asserts them but does not derive them independently (Sec. 3).
  • domain assumption Only Phi0 of the sextet acquires a nonzero VEV, so lepton number is not spontaneously broken.
    Sec. 3; this is required for the Dirac mass term and the vacuum stability equations.
  • domain assumption The soft Z2-breaking scale M is much smaller than vEta and vRho, justifying the approximate minimization result vPhi approx M vEta vChi'/(2 sqrt(2) muS^2).
    Sec. 3; the seesaw suppression relies on this hierarchy.
  • domain assumption Right-handed neutrinos are in thermal equilibrium until an instantaneous decoupling temperature TdecNuR defined by Gamma(Tdec)=H(Tdec), with gRho=106.75.
    Sec. 5.2 and Eq. 52; the mZ' bound depends on this approximation during the QCD crossover.
  • domain assumption The reheating temperature of the Universe is above the NuR decoupling temperature, so the NuR population is thermally populated.
    Sec. 5.2; the paper notes the bound is relaxed if T_RH is lower.
invented entities (1)
  • Scalar sextet S (1,6,-2/3) with components Delta++, Delta+, Delta0, Phi+, Phi0, sigma0 independent evidence
    purpose: Generates small Dirac neutrino masses via the type-II-like seesaw and mediates lepton flavor violation
    The paper predicts sextet scalar masses around 7 TeV and specific LFV branching ratios that future experiments can test (Sec. 4, Appendix A).

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Cite this review

Pith. "Pith review of Type-II Seesaw Mechanism for Dirac Neutrinos and its Implications on $N_{\text{eff}}$ and Lepton Flavor Violation in a 3-3-1 model." pith.science (2026). https://pith.science/paper/DB7SXPGO

@misc{pith2026250201760,
  author       = {Pith},
  title        = {Pith review of: Type-II Seesaw Mechanism for Dirac Neutrinos and its Implications on $N_\texteff$ and Lepton Flavor Violation in a 3-3-1 model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DB7SXPGO}},
  note         = {Machine review of arXiv:2502.01760}
}
abstract

In this study, we implement the type-II seesaw mechanism for Dirac neutrino masses within the framework of a 3-3-1 model. To this end, we introduce a scalar sextet and impose both lepton number conservation and invariance under a discrete $Z_2$ symmetry in the Lagrangian. This mechanism naturally generates small Dirac neutrino masses by allowing the soft breaking of the $Z_2$ symmetry through a unique term in the scalar potential, while preserving lepton number. Specifically, we explore the realization of this model at low-energy scales. Regarding flavor implications, we analyze its contributions to the rare decay processes $\mu \to e \gamma$ and $\mu \to \bar e ee$. In the cosmological context, we analyze the influence of right-handed neutrinos on the effective number of neutrino species, $N_\text{eff}$, through interactions mediated by the $Z^{\prime}$ boson. Our findings establish a lower bound of $m_{Z^{\prime}} > 4.4$ TeV, which slightly exceeds the current lower limit set by the Large Hadron Collider (LHC).

Figures

Figures reproduced from arXiv: 2502.01760 by the authors.

Figure 1
Figure 1. Feynman diagrams for the process µ → eγ. The values of the Yukawa couplings, Gν ab, related to the NO and IO cases for vΦ = 1 eV are given by G ν NO ≈   0 4.87 × 10−3 7.39 × 10−3 0 4.46 × 10−3 3.49 × 10−2 0 −5.49 × 10−3 0   , Gν IO ≈   4 × 10−2 3.32 × 10−2 0 −2.45 × 10−2 3.04 × 10−2 0 2.46 × 10−2 −3.74 × 10−2 4 × 10−2   .(24) The null entries in the Yukawa matrix arise from the assumption that m1… view at source ↗
Figure 2
Figure 2. Feynman diagram for the process µ → eee ¯ . 9 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Left-handed neutrino contribution to the effective number of relativistic species as a [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Ratio of the rate of annihilation of right-handed neutrinos and the expansion rate as [PITH_FULL_IMAGE:figures/full_fig_p016_4.png]
Figure 5
Figure 5. Figure 5: Neff evolution in function of mZ′. We conclude that mZ′ > 4.4 TeV in order to satisfy current limits. Lower bounds from colliders are also displayed, corresponding to mZ′ ≥ 4 TeV (LHC) and mZ′ ≥ 5.6 TeV (HL-LHC). of relativistic degrees of freedom is gs(T dec νR ). Aft…
Figure 6
Figure 6. Figure 6: Ratio between annihilation rate of νR and the Hubble rate as a function of the inverse temperature for different masses of Z ′ , indicated by the different colors. The dashed gray line represents n⟨σv⟩/H = 1. The continuous curves represents the Z ′ contribution, Eq. 7…

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. $Z^\prime$ Portal Dark Matter with Observable $\Delta N_{\rm eff}$

    hep-ph 2026-07 accept novelty 5.5 of 10

    Dirac right-handed neutrinos in a U(1)_{B-L} Z' portal model produce observable ΔN_eff that, together with direct/indirect detection and collider bounds, carves out testable WIMP and FIMP dark-matter regions.

  2. Effective theory of light Dirac neutrino portal dark matter with observable ${\Delta N_{\rm eff}}$

    hep-ph 2025-02 conditional novelty 5.0 of 10

    A dark matter candidate interacting only with right-handed neutrinos is shown to produce ΔNeff ≥ 0.21, testable by future CMB experiments.

Reference graph

Works this paper leans on

79 extracted references · 29 canonical work pages · cited by 2 Pith papers

  1. [1]

    Kajita,Nobel lecture: Discovery of atmospheric neutrino oscillations, Rev

    T. Kajita,Nobel lecture: Discovery of atmospheric neutrino oscillations, Rev. Mod. Phys. 88 (Jul, 2016) 030501

    work page 2016

  2. [2]

    Particle Data GroupCollaboration, S. e. a. Navas,Review of particle physics, Phys. Rev. D110 (Aug, 2024) 030001

    work page 2024

  3. [3]

    Weinberg,Baryon and Lepton Nonconserving Processes, Phys

    S. Weinberg,Baryon and Lepton Nonconserving Processes, Phys. Rev. Lett.43 (1979) 1566–1570

    work page 1979

  4. [4]

    ˇSimkovic, Theory of neutrinoless double beta decay - A brief review, Phys

    F. ˇSimkovic, Theory of neutrinoless double beta decay - A brief review, Phys. Part. Nucl. Lett.10 (2013) 623–632

    work page 2013

  5. [5]

    V. C. et al,Neutrinoless double-beta decay: A roadmap for matching theory to experiment, 2022

    work page 2022

  6. [6]

    Minkowski,µ → eγ at a rate of one out of 109 muon decays?, Physics Letters B67 (1977), no

    P. Minkowski,µ → eγ at a rate of one out of 109 muon decays?, Physics Letters B67 (1977), no. 4 421–428

    work page 1977

  7. [7]

    R. N. Mohapatra and G. Senjanovi´ c,Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett.44 (Apr, 1980) 912–915. 24

    work page 1980

  8. [8]

    Ma and U

    E. Ma and U. Sarkar,Neutrino masses and leptogenesis with heavy Higgs triplets, Phys. Rev. Lett.80 (1998) 5716–5719, [hep-ph/9802445]

    arXiv 1998

Show all 79 references
  1. [9]

    R. N. Mohapatra and J. W. F. Valle,Neutrino mass and baryon-number nonconservation in superstring models, Phys. Rev. D34 (Sep, 1986) 1642–1645

    1986

  2. [10]

    Centelles Chuli´ a, E

    S. Centelles Chuli´ a, E. Ma, R. Srivastava, and J. W. Valle,Dirac neutrinos and dark matter stability from lepton quarticity, Physics Letters B767 (2017) 209–213

    2017

  3. [11]

    Bonilla, J

    C. Bonilla, J. Lamprea, E. Peinado, and J. W. Valle,Flavour-symmetric type-ii dirac neutrino seesaw mechanism, Physics Letters B779 (2018) 257–261

    2018

  4. [12]

    Borah and B

    D. Borah and B. Karmakar,A4 flavour model for dirac neutrinos: Type i and inverse seesaw, Physics Letters B780 (2018) 461–470

    2018

  5. [13]

    Borah, S

    D. Borah, S. Mahapatra, D. Nanda, and N. Sahu,Type II Dirac seesaw with observable ∆Neff in the light of W-mass anomaly, Phys. Lett. B833 (2022) 137297, [2204.08266]

    2022 arXiv

  6. [14]

    P. H. Frampton,Chiral dilepton model and the flavor question, Phys. Rev. Lett.69 (1992) 2889–2891

    1992

  7. [15]

    Pisano and V

    F. Pisano and V. Pleitez,An SU(3) x U(1) model for electroweak interactions, Phys. Rev. D 46 (1992) 410–417, [hep-ph/9206242]

    1992 arXiv

  8. [16]

    Singer, J

    M. Singer, J. W. F. Valle, and J. Schechter,Canonical Neutral Current Predictions From the Weak Electromagnetic Gauge Group SU(3) Xu(1), Phys. Rev. D22 (1980) 738

    1980

  9. [17]

    J. C. Montero, F. Pisano, and V. Pleitez,Neutral currents and GIM mechanism in SU(3)-L x U(1)-N models for electroweak interactions, Phys. Rev. D47 (1993) 2918–2929, [hep-ph/9212271]

    1993 arXiv

  10. [18]

    R. Foot, H. N. Long, and T. A. Tran,Su(3)l Nu(1)n and su(4)l Nu(1)n gauge models with right-handed neutrinos, Phys. Rev. D50 (Jul, 1994) R34–R38

    1994

  11. [19]

    Pisano,A simple solution for the flavor question, Modern Physics Letters A11 (1996), no

    F. Pisano,A simple solution for the flavor question, Modern Physics Letters A11 (1996), no. 32n33 2639–2647, [https://doi.org/10.1142/S0217732396002630]

    1996 doi

  12. [20]

    A. J. Buras, F. De Fazio, J. Girrbach, and M. V. Carlucci,The anatomy of quark flavour observables in 331 models in the flavour precision era, Journal of High Energy Physics 2013 (feb, 2013)

    2013

  13. [21]

    Cogollo, A

    D. Cogollo, A. V. de Andrade, F. S. Queiroz, and P. Rebello Teles,Novel sources of Flavor Changed Neutral Currents in the331RHN model, Eur. Phys. J. C72 (2012) 2029, [1201.1268]

    2012 arXiv

  14. [22]

    M. M. Ferreira, T. B. de Melo, S. Kovalenko, P. R. D. Pinheiro, and F. S. Queiroz,Lepton Flavor Violation and Collider Searches in a Type I + II Seesaw Model, Eur. Phys. J. C79 (2019), no. 11 955, [1903.07634]

    2019 arXiv

  15. [23]

    F. S. Queiroz, C. Siqueira, and J. W. F. Valle,Constraining Flavor Changing Interactions from LHC Run-2 Dilepton Bounds with Vector Mediators, Phys. Lett. B763 (2016) 269–274, [1608.07295]. 25

    2016 arXiv

  16. [24]

    Arcadi, C

    G. Arcadi, C. P. Ferreira, F. Goertz, M. M. Guzzo, F. S. Queiroz, and A. C. O. Santos, Lepton Flavor Violation Induced by Dark Matter, Phys. Rev. D97 (2018), no. 7 075022, [1712.02373]

    2018 arXiv

  17. [25]

    A. E. C´ arcamo Hern´ andez, L. Duarte, A. S. de Jesus, S. Kovalenko, F. S. Queiroz, C. Siqueira, Y. M. Oviedo-Torres, and Y. Villamizar,Flavor changing interactions confronted with meson mixing and hadron colliders, Phys. Rev. D107 (2023), no. 6 063005, [2208.08462]

    2023 arXiv

  18. [26]

    A. S. de Jesus, S. Kovalenko, T. B. de Melo, J. P. Neto, Y. M. Oviedo-Torres, F. S. Queiroz, Y. S. Villamizar, and A. R. Zerwekh,On the role of LHC and HL-LHC in constraining flavor changing neutral currents, Phys. Lett. B849 (2024) 138419, [2304.00041]

    2024 arXiv

  19. [27]

    H. N. Long and V. T. Van,Quark family discrimination and flavor changing neutral currents in the SU(3)(C) x SU(3)(L) x U(1) model with right-handed neutrinos, J. Phys. G 25 (1999) 2319–2324, [hep-ph/9909302]

    1999 arXiv

  20. [28]

    Oliveira and C

    V. Oliveira and C. A. d. S. Pires,Flavor changing neutral current processes and family discrimination in 3-3-1 models, J. Phys. G50 (2023), no. 11 115002, [2208.00420]

    2023 arXiv

  21. [29]

    C. A. de Sousa Pires and O. P. Ravinez,Charge quantization in a chiral bilepton gauge model, Phys. Rev. D58 (1998) 035008, [hep-ph/9803409]

    1998 arXiv

  22. [30]

    C. A. de Sousa Pires,Remark on the vector - like nature of the electromagnetism and the electric charge quantization, Phys. Rev. D60 (1999) 075013, [hep-ph/9902406]

    1999 arXiv

  23. [31]

    A. G. Dias, C. A. de S. Pires, and P. S. Rodrigues da Silva,Naturally light right-handed neutrinos in a 3-3-1 model, Phys. Lett. B628 (2005) 85–92, [hep-ph/0508186]

    2005 arXiv

  24. [32]

    Cogollo, H

    D. Cogollo, H. Diniz, C. A. de S. Pires, and P. S. Rodrigues da Silva,The Seesaw mechanism at TeV scale in the 3-3-1 model with right-handed neutrinos, Eur. Phys. J. C 58 (2008) 455–461, [0806.3087]

    2008 arXiv

  25. [33]

    Cogollo, H

    D. Cogollo, H. Diniz, and C. A. de S. Pires,KeV right-handed neutrinos from type II seesaw mechanism in a 3-3-1 model, Phys. Lett. B677 (2009), no. 5 338–342, [0903.0370]

    2009 arXiv

  26. [34]

    Hepburn and S

    D. Hepburn and S. M. West,Dark matter and neutrino masses in a Portalino-like model, Eur. Phys. J. C83 (2023), no. 5 405, [2208.02698]

    2023 arXiv

  27. [35]

    A. G. Dias, C. A. de S. Pires, P. S. Rodrigues da Silva, and A. Sampieri,A Simple Realization of the Inverse Seesaw Mechanism, Phys. Rev. D86 (2012) 035007, [1206.2590]

    2012 arXiv

  28. [36]

    A. E. C´ arcamo Hern´ andez, R. Martinez, and F. Ochoa,Fermion masses and mixings in the 3-3-1 model with right-handed neutrinos based on theS3 flavor symmetry, Eur. Phys. J. C76 (2016), no. 11 634, [1309.6567]

    2016 arXiv

  29. [37]

    S. M. Boucenna, S. Morisi, and J. W. F. Valle,Radiative neutrino mass in 3-3-1 scheme, Phys. Rev. D90 (2014), no. 1 013005, [1405.2332]

    2014 arXiv

  30. [38]

    C. A. de Sousa Pires, F. Ferreira De Freitas, J. Shu, L. Huang, and P. Wagner Vasconcelos Oleg´ ario,Implementing the inverse type-II seesaw mechanism into the 3-3-1 model, Phys. Lett. B797 (2019) 134827, [1812.10570]. 26

    2019 arXiv

  31. [39]

    A. E. C´ arcamo Hern´ andez, L. T. Hue, S. Kovalenko, and H. N. Long,An extended 3-3-1 model with two scalar triplets and linear seesaw mechanism, Eur. Phys. J. Plus136 (2021), no. 11 1158, [2001.01748]

    2021 arXiv

  32. [40]

    A. Doff, J. a. P. Pinheiro, and C. A. d. S. Pires,Leptoquark-induced radiative masses for active and sterile neutrinos within the framework of the 3-3-1 model, 2412.15055

    arXiv

  33. [41]

    M. Reig, J. W. F. Valle, and C. A. Vaquera-Araujo,Realistic SU(3)c ⊗ SU(3)L ⊗ U(1)X model with a type II Dirac neutrino seesaw mechanism, Phys. Rev. D94 (2016), no. 3 033012, [1606.08499]

    2016 arXiv

  34. [42]

    J. W. F. Valle and C. A. Vaquera-Araujo,Dynamical seesaw mechanism for Dirac neutrinos, Phys. Lett. B755 (2016) 363–366, [1601.05237]

    2016 arXiv

  35. [43]

    J. P. Pinheiro and C. A. de S. Pires,On the Higgs spectra of the 3-3-1 model, Phys. Lett. B 836 (2023) 137584, [2210.05426]

    2023 arXiv

  36. [44]

    H. N. Long,The 331 model with right handed neutrinos, Phys. Rev. D53 (1996) 437–445, [hep-ph/9504274]

    1996 arXiv

  37. [45]

    H. N. Long,Right-handed neutrino currents in the SU(3)-L x U(1)-N electroweak theory, in 2nd Rencontres du Vietnam: Consisting of 2 parallel conferences: Astrophysics Meeting: From the Sun and Beyond / Particle Physics Meeting: Physics at the Frontiers of the Standard Model, 1...

    1995 arXiv

  38. [46]

    Escalona, J

    P. Escalona, J. a. P. Pinheiro, A. Doff, and C. A. d. S. Pires,Meson Mixing Bounds onZ′ Mass in the Alignment Limit: Establishing the Phenomenological Viability of the 331 Model, 2503.14653

    arXiv

  39. [47]

    Esteban, M

    I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. a. P. Pinheiro, and T. Schwetz,NuFit-6.0: updated global analysis of three-flavor neutrino oscillations, JHEP 12 (2024) 216, [2410.05380]

    2024 arXiv

  40. [48]

    Lindner, M

    M. Lindner, M. Platscher, and F. S. Queiroz,A Call for New Physics : The Muon Anomalous Magnetic Moment and Lepton Flavor Violation, Phys. Rept.731 (2018) 1–82, [1610.06587]

    2018 arXiv

  41. [49]

    Toma and A

    T. Toma and A. Vicente,Lepton Flavor Violation in the Scotogenic Model, JHEP 01 (2014) 160, [1312.2840]

    2014 arXiv

  42. [50]

    Lavoura,General formulae for f(1) —> f(2) gamma, Eur

    L. Lavoura,General formulae for f(1) —> f(2) gamma, Eur. Phys. J. C29 (2003) 191–195, [hep-ph/0302221]

    2003 arXiv

  43. [52]

    Meucci,MEG II experiment status and prospect, PoS NuFact2021(2022) 120, [2201.08200]

    MEG IICollaboration, M. Meucci,MEG II experiment status and prospect, PoS NuFact2021(2022) 120, [2201.08200]

    2022 arXiv

  44. [53]

    Aghanimet

    Planck Collaboration, N. Aghanimet. al., Planck 2018 results. I. Overview and the cosmological legacy of Planck, Astron. Astrophys.641 (2020) A1, [1807.06205]. 27

    2020 arXiv

  45. [54]

    Aghanimet

    Planck Collaboration, N. Aghanimet. al., Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641 (2020) A6, [1807.06209]. [Erratum: Astron.Astrophys. 652, C4 (2021)]

    2020 arXiv

  46. [55]

    R. H. Cyburt, B. D. Fields, K. A. Olive, and T.-H. Yeh,Big Bang Nucleosynthesis: 2015, Rev. Mod. Phys.88 (2016) 015004, [1505.01076]

    2016 arXiv

  47. [56]

    P. F. de Salas and S. Pastor,Relic neutrino decoupling with flavour oscillations revisited, JCAP 07 (2016) 051, [1606.06986]

    2016 arXiv

  48. [57]

    Akita and M

    K. Akita and M. Yamaguchi,A precision calculation of relic neutrino decoupling, JCAP 08 (2020) 012, [2005.07047]

    2020 arXiv

  49. [58]

    Froustey, C

    J. Froustey, C. Pitrou, and M. C. Volpe,Neutrino decoupling including flavour oscillations and primordial nucleosynthesis, JCAP 12 (2020) 015, [2008.01074]

    2020 arXiv

  50. [59]

    J. J. Bennett, G. Buldgen, P. F. De Salas, M. Drewes, S. Gariazzo, S. Pastor, and Y. Y. Y. Wong,Towards a precision calculation ofNeff in the Standard Model II: Neutrino decoupling in the presence of flavour oscillations and finite-temperature QED, JCAP 04 (2021) 073, [2012.02726]

    2021 arXiv

  51. [60]

    DESI Collaboration, A. G. Adameet. al., DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations, 2404.03002

    2024 arXiv

  52. [61]

    Escudero,Neutrino decoupling beyond the Standard Model: CMB constraints on the Dark Matter mass with a fast and preciseNeff evaluation, JCAP 02 (2019) 007, [1812.05605]

    M. Escudero,Neutrino decoupling beyond the Standard Model: CMB constraints on the Dark Matter mass with a fast and preciseNeff evaluation, JCAP 02 (2019) 007, [1812.05605]

    2019 arXiv

  53. [62]

    X. Luo, W. Rodejohann, and X.-J. Xu,Dirac neutrinos andNeff, JCAP 06 (2020) 058, [2005.01629]

    2020 arXiv

  54. [63]

    X. Luo, W. Rodejohann, and X.-J. Xu,Dirac neutrinos and Nef f. Part II. The freeze-in case, JCAP 03 (2021) 082, [2011.13059]

    2021 arXiv

  55. [64]

    K. N. Abazajian and J. Heeck,Observing Dirac neutrinos in the cosmic microwave background, Phys. Rev. D100 (2019) 075027, [1908.03286]

    2019 arXiv

  56. [65]

    L. A. Anchordoqui, H. Goldberg, and G. Steigman,Right-Handed Neutrinos as the Dark Radiation: Status and Forecasts for the LHC, Phys. Lett. B718 (2013) 1162–1165, [1211.0186]

    2013 arXiv

  57. [66]

    Calle, D

    J. Calle, D. Restrepo, and O. Zapata,Dirac neutrino mass generation from a Majorana messenger, Phys. Rev. D101 (2020), no. 3 035004, [1909.09574]

    2020 arXiv

  58. [67]

    Borah, N

    D. Borah, N. Das, S. Jahedi, and B. Thacker,Collider and CMB complementarity of leptophilic dark matter with light Dirac neutrinos, 2408.14548

  59. [68]

    Biswas, D

    A. Biswas, D. Borah, and D. Nanda,Light Dirac neutrino portal dark matter with observable ∆Neff, JCAP 10 (2021) 002, [2103.05648]

    2021 arXiv

  60. [69]

    Escudero Abenza,Precision early universe thermodynamics made simple:Neff and neutrino decoupling in the Standard Model and beyond, JCAP 05 (2020) 048, [2001.04466]

    M. Escudero Abenza,Precision early universe thermodynamics made simple:Neff and neutrino decoupling in the Standard Model and beyond, JCAP 05 (2020) 048, [2001.04466]. 28

    2020 arXiv

  61. [70]

    Kawasaki, K

    M. Kawasaki, K. Kohri, and N. Sugiyama,MeV scale reheating temperature and thermalization of neutrino background, Phys. Rev. D62 (2000) 023506, [astro-ph/0002127]

    2000 arXiv

  62. [71]

    Hannestad and J

    S. Hannestad and J. Madsen,Neutrino decoupling in the early universe, Phys. Rev. D52 (1995) 1764–1769, [astro-ph/9506015]

    1995 arXiv

  63. [72]

    Hahn,CUBA: A Library for multidimensional numerical integration, Comput

    T. Hahn,CUBA: A Library for multidimensional numerical integration, Comput. Phys. Commun. 168 (2005) 78–95, [hep-ph/0404043]

    2005 arXiv

  64. [73]

    Husdal,On Effective Degrees of Freedom in the Early Universe, Galaxies 4 (2016), no

    L. Husdal,On Effective Degrees of Freedom in the Early Universe, Galaxies 4 (2016), no. 4 78, [1609.04979]

    2016 arXiv

  65. [74]

    SPT-3G Collaboration, B. A. Bensonet. al., SPT-3G: A Next-Generation Cosmic Microwave Background Polarization Experiment on the South Pole Telescope, Proc. SPIE Int. Soc. Opt. Eng.9153 (2014) 91531P, [1407.2973]

    2014 arXiv

  66. [75]

    Simons ObservatoryCollaboration, P. Adeet. al., The Simons Observatory: Science goals and forecasts, JCAP 02 (2019) 056, [1808.07445]

    2019 arXiv

  67. [76]

    Abazajianet

    K. Abazajianet. al., CMB-S4 Science Case, Reference Design, and Project Plan, 1907.04473

    1907 arXiv

  68. [77]

    CMB-S4 Collaboration, K. N. Abazajianet. al., CMB-S4 Science Book, First Edition, 1610.02743

    arXiv

  69. [78]

    Y. A. Coutinho, V. Salustino Guimar˜ aes, and A. A. Nepomuceno,Bounds on Z’ from 3-3-1 model at the LHC energies, Phys. Rev. D87 (2013), no. 11 115014, [1304.7907]

    2013 arXiv

  70. [79]

    Alves, L

    A. Alves, L. Duarte, S. Kovalenko, Y. M. Oviedo-Torres, F. S. Queiroz, and Y. S. Villamizar, Constraining 3-3-1 models at the LHC and future hadron colliders, Phys. Rev. D 106 (2022), no. 5 055027, [2203.02520]

    2022 arXiv

  71. [80]

    Schaelet

    ALEPH, DELPHI, L3, OPAL, LEP ElectroweakCollaboration, S. Schaelet. al., Electroweak Measurements in Electron-Positron Collisions at W-Boson-Pair Energies at LEP, Phys. Rept.532 (2013) 119–244, [1302.3415]. 29

    2013 arXiv

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