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Constraining dark matter from strong phase transitions in a $U(1)_{L_{\mu}-L_{\tau}}$ model: Implications for neutrino masses and muon $g-2$
High Energy Physics - Phenomenology · Submitted 24 Jun 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show the allowed range of the model parameters that can address all the beyond SM issues targeted in this study.
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The abstract, sentence by sentence
In this paper, we study a non-minimal gauged $U(1)_{L_{\mu}-L_{\tau}}$ model, where we add two complex singlet scalars, three right-handed Majorana neutrinos (RHN), and a vector-like dark fermion to the Standard Model (SM), all non-trivially charged under the extra gauge symmetry. The model offers an easy resolution to the muon $(g-2)$ anomaly, which fixes the scale of spontaneous symmetry breaking. Furthermore, the two-zero minor structure in the RHN mass matrix provides successful predictions for neutrino oscillation parameters, including the Dirac phase. The extended scalar sector can easily induce first-order phase transitions. We identify all possible phase transition patterns in the three-dimensional field space. We quantify the associated gravitational waves from the sound wave source and demonstrate that the signatures can be observed in future space-based experiments. We find that strong first-order phase transitions require large values of scalar quartic couplings which constrain the scalar dark matter (DM) relic density to a maximum of $10^{-2}$ and $10^{-5}$ when we consider the DM direct detection bound. Nonetheless, the model successfully explains the DM relic density via contribution from the vector-like dark fermion. We show the allowed range of the model parameters that can address all the beyond SM issues targeted in this study.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper, we study a non-minimal gauged $U(1)_{L_{\mu}-L_{\tau}}$ model, where we add two complex singlet scalars, three right-handed Majorana neutrinos (RHN), and a vector-like dark fermion to the Standard Model (SM), all non-trivially charged under the extra gauge symmetry. | contribution 0.76 | 0.75 | 0.04 | asserted 0.99 |
| s1 | The model offers an easy resolution to the muon $(g-2)$ anomaly, which fixes the scale of spontaneous symmetry breaking. | result 0.88 | 0.58 | 0.10 | asserted 0.94 |
| s2 | Furthermore, the two-zero minor structure in the RHN mass matrix provides successful predictions for neutrino oscillation parameters, including the Dirac phase. | result 0.96 | 0.74 | 0.08 | asserted 1.00 |
| s3 | The extended scalar sector can easily induce first-order phase transitions. | result 0.53 | 0.33 | 0.05 | hedged possibility 0.69 |
| s4 | We identify all possible phase transition patterns in the three-dimensional field space. | contribution 0.78 | 0.96 | 0.04 | asserted 1.00 |
| s5 | We quantify the associated gravitational waves from the sound wave source and demonstrate that the signatures can be observed in future space-based experiments. | result 0.80 | 0.96 | 0.17 | asserted 0.96 |
| s6 | We find that strong first-order phase transitions require large values of scalar quartic couplings which constrain the scalar dark matter (DM) relic density to a maximum of $10^{-2}$ and $10^{-5}$ when we consider the DM direct detection bound. | result 0.98 | 0.95 | 0.30 | asserted 1.00 |
| s7 | Nonetheless, the model successfully explains the DM relic density via contribution from the vector-like dark fermion. | result 0.90 | 0.79 | 0.15 | asserted 1.00 |
| s8 | We show the allowed range of the model parameters that can address all the beyond SM issues targeted in this study. | contribution 0.55 | 0.94 | 0.20 | asserted 1.00 |
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The paper
Original abstract
In this paper, we study a non-minimal gauged $U(1)_{L_{\mu}-L_{\tau}}$ model, where we add two complex singlet scalars, three right-handed Majorana neutrinos (RHN), and a vector-like dark fermion to the Standard Model (SM), all non-trivially charged under the extra gauge symmetry. The model offers an easy resolution to the muon $(g-2)$ anomaly, which fixes the scale of spontaneous symmetry breaking. Furthermore, the two-zero minor structure in the RHN mass matrix provides successful predictions for neutrino oscillation parameters, including the Dirac phase. The extended scalar sector can easily induce first-order phase transitions. We identify all possible phase transition patterns in the three-dimensional field space. We quantify the associated gravitational waves from the sound wave source and demonstrate that the signatures can be observed in future space-based experiments. We find that strong first-order phase transitions require large values of scalar quartic couplings which constrain the scalar dark matter (DM) relic density to a maximum of $10^{-2}$ and $10^{-5}$ when we consider the DM direct detection bound. Nonetheless, the model successfully explains the DM relic density via contribution from the vector-like dark fermion. We show the allowed range of the model parameters that can address all the beyond SM issues targeted in this study.
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How the literature uses it
3 arXiv papers cite this in 3 sentences
What it cites · 46 sentences without a confident label
Uses the method or tool of 13 papers
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We use the sound wave source template from Ref. [ref] , which reads [equation] where the peak amplitude is obtained as [equation] Here the subscript $*$ indicates that quantities are evaluated at the production time.
Gravitational waves from first-order phase transitions in LISA: reconstruction pipeline and physics interpretation · Gravitational waves · 0.97
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The thermally-corrected masses of the scalars are the eigenvalues of the thermally-corrected Hessian matrix [equation] This corresponds to a resummation of a large number of daisy diagrams which enhance the perturbative control at large temperatures [ref] .
Resummation in a Hot Scalar Field Theory · Daisy resummation · 0.90
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The thermally-corrected masses of the scalars are the eigenvalues of the thermally-corrected Hessian matrix [equation] This corresponds to a resummation of a large number of daisy diagrams which enhance the perturbative control at large temperatures [ref] .
Thermal Resummation and Phase Transitions · Daisy resummation · 0.90
Uses data or values from 12 papers
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In particular, we have considered $7σ$ variation in DM relic density as shown below [ref] , [equation] We consider a wide range for DM relic density around its central value $Ω_DMh^2 = 0.12$ to get a large number of points in reasonable time while satisfying the DM relic density.
Planck 2015 results. XIII. Cosmological parameters · Dark matter bounds · 1.00
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In particular, we have considered $7σ$ variation in DM relic density as shown below [ref] , [equation] We consider a wide range for DM relic density around its central value $Ω_DMh^2 = 0.12$ to get a large number of points in reasonable time while satisfying the DM relic density.
Planck 2018 results. VI. Cosmological parameters · Dark matter bounds · 1.00
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In this context, we undertake a major revision of the neutrino sector by using the most recent data [ref] and provide the scale of the fundamental parameters for which the predicted neutrino oscillation parameters fall within their experimental limits.
The fate of hints: updated global analysis of three-flavor neutrino oscillations · Introduction · 0.96
Compares with 2 papers
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We finally checked that our results are in agreement with the sum rules that were discussed in Ref. [ref] .
Predictions for the neutrino parameters in the minimal gauged U(1)$_{L_\mu-L_\tau}$ model · Neutrino mass · 0.95
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We display the associated GW signals in Fig. [ref] and we superimpose the projected sensitivities of LISA and AEDGE [ref] .
AEDGE: Atomic Experiment for Dark Matter and Gravity Exploration in Space · Gravitational waves · 0.81
Cites as background 31 papers
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The model with this particle content has been dubbed the minimal gauged $U(1)_L_μ -L_τ$ in Refs. [ref] and has been studied in the context of the baryon asymmetry via leptogenesis [ref] , particle DM phenomenology [ref] and $(g-2)_μ$ anomaly [ref] , to name the most common.
Gauged L_mu - L_tau Symmetry at the Electroweak Scale · Introduction · 0.96
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The model with this particle content has been dubbed the minimal gauged $U(1)_L_μ -L_τ$ in Refs. [ref] and has been studied in the context of the baryon asymmetry via leptogenesis [ref] , particle DM phenomenology [ref] and $(g-2)_μ$ anomaly [ref] , to name the most common.
Thermal Leptogenesis in the Minimal Gauged $U(1)_{L_\mu-L_\tau}$ Model · Introduction · 0.96
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The model with this particle content has been dubbed the minimal gauged $U(1)_L_μ -L_τ$ in Refs. [ref] and has been studied in the context of the baryon asymmetry via leptogenesis [ref] , particle DM phenomenology [ref] and $(g-2)_μ$ anomaly [ref] , to name the most common.
Neutrino Mass, Dark Matter and Anomalous Magnetic Moment of Muon in a $U(1)_{L_{\mu}-L_{\tau}}$ Model · Introduction · 0.96
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