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Naturally small Dirac neutrino mass and $B-L$ dark matter
High Energy Physics - Phenomenology · Submitted 9 Jan 2026 · Published version
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In both cases, spontaneous $B-L$ breaking can induce a strong first-order phase transition, producing stochastic gravitational waves (GW) which can be tested at GW experiments.
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The abstract, sentence by sentence
In the conventional gauged ${B-L}$ extension of the standard model, the $B-L$ charge of the singlet scalar $\chi$, responsible for the breaking of $U(1)_{B-L}$ symmetry, is taken to be 2 such that it can anchor type-I seesaw by giving Majorana masses to the right-handed neutrinos, $\nu_R$. In this paper, we consider instead the cases $\chi \sim 3$ or 4 under $B-L$, so that $\nu_R$ may not acquire any Majorana mass and neutrinos are Dirac fermions. We then consider a vector-like fermion $S$ with 2 units of $B-L$ charge, which becomes a good candidate for dark matter, either Dirac for $\chi \sim 3$ or Majorana for $\chi \sim 4$. In both cases, spontaneous $B-L$ breaking can induce a strong first-order phase transition, producing stochastic gravitational waves (GW) which can be tested at GW experiments. Moreover, the presence of light $\nu_R$s gives rise to an additional contribution to the effective number of relativistic degrees of freedom, $\Delta{N}_{\rm eff}$, providing complementary constraints from current and upcoming CMB observations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In the conventional gauged ${B-L}$ extension of the standard model, the $B-L$ charge of the singlet scalar $\chi$, responsible for the breaking of $U(1)_{B-L}$ symmetry, is taken to be 2 such that it can anchor type-I seesaw by giving Majorana masses to the right-handed neutrinos, $\nu_R$. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s1 | In this paper, we consider instead the cases $\chi \sim 3$ or 4 under $B-L$, so that $\nu_R$ may not acquire any Majorana mass and neutrinos are Dirac fermions. | contribution 0.96 | 0.68 | 0.14 | hedged possibility 0.81 |
| s2 | We then consider a vector-like fermion $S$ with 2 units of $B-L$ charge, which becomes a good candidate for dark matter, either Dirac for $\chi \sim 3$ or Majorana for $\chi \sim 4$. | contribution 0.93 | 0.70 | 0.11 | hedged possibility 0.65 |
| s3 | In both cases, spontaneous $B-L$ breaking can induce a strong first-order phase transition, producing stochastic gravitational waves (GW) which can be tested at GW experiments. | result 0.87 | 0.68 | 0.25 | asserted 0.54 |
| s4 | Moreover, the presence of light $\nu_R$s gives rise to an additional contribution to the effective number of relativistic degrees of freedom, $\Delta{N}_{\rm eff}$, providing complementary constraints from current and upcoming CMB observations. | result 0.54 | 0.40 | 0.08 | asserted 0.96 |
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The paper
Original abstract
In the conventional gauged ${B-L}$ extension of the standard model, the $B-L$ charge of the singlet scalar $\chi$, responsible for the breaking of $U(1)_{B-L}$ symmetry, is taken to be 2 such that it can anchor type-I seesaw by giving Majorana masses to the right-handed neutrinos, $\nu_R$. In this paper, we consider instead the cases $\chi \sim 3$ or 4 under $B-L$, so that $\nu_R$ may not acquire any Majorana mass and neutrinos are Dirac fermions. We then consider a vector-like fermion $S$ with 2 units of $B-L$ charge, which becomes a good candidate for dark matter, either Dirac for $\chi \sim 3$ or Majorana for $\chi \sim 4$. In both cases, spontaneous $B-L$ breaking can induce a strong first-order phase transition, producing stochastic gravitational waves (GW) which can be tested at GW experiments. Moreover, the presence of light $\nu_R$s gives rise to an additional contribution to the effective number of relativistic degrees of freedom, $\Delta{N}_{\rm eff}$, providing complementary constraints from current and upcoming CMB observations.
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How the literature uses it
5 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 1 paper
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Another possibility involves extending the gauge sector with a $U(1)_B-L$ symmetry and an additional $Z'$ boson [ref] .
Sterile neutrino Dark Matter in the minimal Dirac Seesaw · Summary and outlook · 0.98
What it cites · 28 sentences without a confident label
Uses the method or tool of 12 papers
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We then compute the key parameters required to estimate the stochastic gravitational wave (GW) spectrum originating from bubble collisions [ref] , sound waves in the plasma [ref] , and plasma turbulence [ref] .
Gravitational Radiation From Cosmological Turbulence · Introduction · 0.89
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We then compute the key parameters required to estimate the stochastic gravitational wave (GW) spectrum originating from bubble collisions [ref] , sound waves in the plasma [ref] , and plasma turbulence [ref] .
Gravitational waves from stochastic relativistic sources: primordial turbulence and magnetic fields · Introduction · 0.89
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We then compute the key parameters required to estimate the stochastic gravitational wave (GW) spectrum originating from bubble collisions [ref] , sound waves in the plasma [ref] , and plasma turbulence [ref] .
Gravitational Radiation from Colliding Vacuum Bubbles: Envelope Approximation to Many-Bubble Collisions · Introduction · 0.89
Uses data or values from 6 papers
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From this analysis, we find that DESI [ref] excludes the region with $m_η<240$ GeV.
DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations · Introduction · 0.88
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The ACT [ref] data exclude $m_η<250$ GeV, while the combined Planck+ACT [ref] analysis excludes $m_η<300$ GeV.
The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models · Introduction · 0.88
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The Planck [ref] data exclude $m_η<260$ GeV.
Planck 2018 results. VI. Cosmological parameters · Introduction · 0.86
Cites as background 1 paper
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Hence $ν_R$ acquires a large Majorana mass, and the type-I seesaw mechanism prevails [ref] .
Complex Spinors and Unified Theories · Introduction · 0.90
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