Anatomy of RHN DM relic in the vanilla scotogenic neutrino mass model

arXiv:2601.00436 · hep-ph, astro-ph.CO, hep-ex · Submitted 2026-01-01 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Hi, I'm Vera.

Jocelyn: And I'm Jocelyn, here with Subrahmanyan.

Vera: We're looking at the paper: "Anatomy of RHN DM relic in the vanilla scotogenic neutrino mass model".

Jocelyn: Here's the gist of the paper. The gist: The lightest right-handed neutrino (RHN) can be a viable dark matter candidate in the minimal scotogenic neutrino mass model within specific mass ranges and parameter spaces, while displaced vertex signatures offer complementary collider probes for this scenario.

Vera: The Model and Neutrino Mass Generation The scotogenic model generates light neutrino masses radiatively at the one-loop level by incorporating three right-handed neutrinos (N1,2,3) and a scalar doublet η which belong to a Z2-odd dark sector <ref:2601.00436#pg5>.

Jocelyn: The lightest particle running in the loop can naturally serve as a viable dark matter (DM) candidate <ref:2601.00436#pg4>.

Vera: The neutrino mass matrix is given by an expression involving the masses of the particles in the model, structured as (mν)αβ = X3 i=1 yαiy∗ iβ 16π2 MNi

M2 ηR M2 ηR − M2 Ni log (M2 ηR M2 Ni) − M2 ηI M2 ηI − M2 Ni log (M2 ηI M Ni): <ref:2601.00436#pg7>.

Title and authors: Vera: We’ve just gone over the setup of this paper, and now we need to unpack what they actually found about the model itself.

Jocelyn: This section summarizes the core findings regarding how they handle that neutrino mass generation mechanism and what it implies for the dark matter candidate.

Subrahmanyan: Essentially, it confirms that by using three right-handed neutrinos and a scalar doublet eta in a Z2 odd dark sector <ref:2601.00436#pg1>.

Vera: The paper focuses on how they manage the complexity of calculating the relic density, which involves multiple channels like self-annihilation, co-annihilation, and those conversion processes we talked about.

Jocelyn: They show that getting the correct thermal relic density is possible by including all these channels in coupled Boltzmann equations <ref:2601.00436#pg10>.

Subrahmanyan: And they also highlight how the dynamics of those abundance evolutions show that the inverse decay rate minus sixteen over Hubble expansion rate becomes comparable to when eta is in equilibrium, bringing the final DM relic abundance to a ballpark consistent with observations <ref:2601.00436#pg33>.

Vera: So, one major finding is that the correct thermal DM relic density can be achieved across a full dark matter mass range once you incorporate all those conversion-driven processes into the Boltzmann equations <ref:2601.00436#pg7>.

Jocelyn: But there are still specific regions where thermal equilibrium with the Standard Model isn't reached, and in those cases, we need to consider the freeze-in mechanism instead <ref:2601.00436#pg19>.

Subrahmanyan: And they point out that this thermal relic is viable for dark matter masses MDM greater than Mh over two <ref:2601.00436#pg18> but they also find regions, especially at low DM masses, where you need the freeze-in mechanism > Page twenty-six > <ref:2601.00436#pg2>.

Vera: They also link the viable mass strongly to the choice of lambda three, four, and five or equivalently lambda R > Page eighteen > <ref:2601.00436#pg2> <ref:2601.00436#pg2>.

Jocelyn: And for those regions that are accessible at colliders, they point to displaced vertex signatures as a way to probe things when there are large lambda five, large MDM, and small lambda four > Page twenty-four > <ref:2601.00436#pg2> <ref:2601.00436#pg2>.

Subrahmanyan: The direct detection searches don't impose new constraints because the relevant interactions only appear at the one-loop level <ref:2601.00436#pg22>.

Vera: They also discuss how the SM Higgs boson h can decay into the neutral components eta R and eta I of that inert doublet > Page twenty-six > <ref:2601.00436#pg2> <ref:2601.00436#pg2>.

Jocelyn: And they note that a specific choice for lambda four, namely lambda four Meta R, satisfies the LEP constraint on charged scalars and avoids contributions to the invisible decay width of the Z boson provided that Meta R plus Meta I is greater than MZ > Page twenty-six > <ref:2601.00436#pg2> <ref:2601.00436#pg2>.

Subrahmanyan: The constraints from Higgs invisible decay are shown in a parameter space defined by Meta R minus lambda R > Page twenty-seven > <ref:2601.00436#pg2> <ref:2601.00436#pg2>.

Vera: They also discuss the effect of co-scattering on the relic density, showing that it’s subdominant compared to the decay and inverse-decay processes within that conversion framework <ref:2601.00436#pg30>.

Jocelyn: The results show that co-scattering contributes non-negligibly to the final relic density only when there are deviations from unity in the rho parameter > Page twenty-five > <ref:2601.00436#pg2> <ref:2601.00436#pg2>.

Subrahmanyan: To summarize, the paper "Anatomy of RHN DM relic in the vanilla scotogenic neutrino mass model" shows how to handle a complex dark matter candidate, mapping out thermal viability across different mass ranges and pointing towards experimental signatures for those regions where thermal equilibrium is not achieved <ref:2601.00436#pg18>.

Vera: It's a lot of parameter space being mapped out, from the initial model setup through all the relic density mechanisms and the experimental constraints they have to deal with.

Jocelyn: It gives us concrete ways to look for this particle at colliders, like those displaced vertex signatures that depend on mass splitting and DM mass > Page fifty-one > <ref:2601.00436#pg2>.

Subrahmanyan: For cosmology, it tells us that the viability of this dark matter candidate is strongly tied to specific choices in the parameters lambda three, four, and five > Page twenty-six > <ref:2601.00436#pg2> <ref:2601.00436#pg2>.

The paper's summary: Tom: So we're looking at how they suggest improving this paper now, and what that means for us later on.

Vera: They are suggesting adding more detail to the relic density calculation by explicitly showing how self-annihilation and co-annihilation fit into those coupled Boltzmann equations <ref:2601.00436#pg11>.

Jocelyn: That's good because it takes the conversion term, Gamma two into one, and breaks down exactly what co-scattering versus decay and inverse decay are doing to the DM abundance <ref:2601.00436#pg11>.

Subrahmanyan: It’s a necessary step because we can’t just assume those conversion processes happen perfectly; we need to see if they actually balance out the depletion of dark matter over time <ref:2601.00436#pg33>.

Vera: Then there's this focus on mapping out the parameter space, specifically MDM versus Delta MR, incorporating all those constraints from S and T parameters and flavor violation data <ref:2601.00436#pg18>.

Jocelyn: That helps us narrow down where this model actually lives in reality; it moves beyond just finding a number to actually drawing a map of the allowed physics <ref:2601.00436#pg26>.

Subrahmanyan: If we can map that space, then we know which combinations of those Yukawa couplings lambda three, four, and five are physically possible for this neutrino mass generation mechanism <ref:2601.00436#pg18>.

Vera: And they’re also looking at the Higgs invisible decay constraints more closely by exploring the M eta R minus lambda R parameter plane > Page twenty-seven > <ref:2601.00436#pg2> <ref:2601.00436#pg2>.

Jocelyn: That gives us a clearer picture of how tightly constrained that scalar doublet is, especially concerning those LEP bounds on charged scalars and Z boson invisible decays <ref:2601.00436#pg26>.

Subrahmanyan: So, the implication here is we’re getting tighter constraints on the new physics scale dictated by these couplings > Page eighteen > <ref:2601.00436#pg2> <ref:2601.00436#pg2>.

Vera: The real improvement for us is seeing how this refined parameter space interacts with what we observe from direct detection experiments that are looking for those loop-level interactions <ref:2601.00436#pg22>.

Jocelyn: And they’re also setting up the roadmap for collider searches, specifically showing how to predict the decay length c tau as a function of DM mass and mass splitting Delta M plus > Page fifty-one > <ref:2601.00436#pg2>.

Subrahmanyan: That prediction is useful because it tells us exactly what kind of displaced vertex signature we should look for at facilities like CMS or ATLAS when searching for this particle <ref:2601.00436#pg51>.

Vera: So, they’re taking a model that was complex and showing how to refine the math so we can actually test it against real data from the sky and the lab.

Jocelyn: It’s moving us from just theoretical possibility to concrete experimental targets based on specific mass splittings <ref:2601.00436#pg51>.

Subrahmanyan: This refinement connects cosmology directly to high-energy physics searches, which is exactly where we need to be looking right now <ref:2601.00436#pg51>.

The paper's improvements: Vera: So, to wrap up this look at "Anatomy of RHN DM relic in the vanilla scotogenic neutrino mass model," we’ve seen how they nail down viable regions for this right-handed neutrino dark matter candidate.

Jocelyn: It’s clear that achieving the correct thermal relic density isn't just a theoretical exercise; it depends on these specific choices you have to make in the couplings, like lambda four and lambda five <ref:2601.00436#pg18>.

Subrahmanyan: And for me, what this means is that we need observational data that can constrain those coupling parameters because right now they are quite broad across the mass range <ref:2601.00436#pg18>.

Vera: Exactly; these constraints from flavor violation and the muon magnetic moment are really helping us narrow down where this whole model might be physically real > Page twenty-six > <ref:2601.00436#pg2> <ref:2601.00436#pg2>.

Jocelyn: And for those specific regions where thermal equilibrium doesn't happen, we’ve got the freeze-in mechanism as a way to generate the dark matter density instead of relying on standard annihilation <ref:2601.00436#pg19> > <ref:2601.00436#pg19>.

Subrahmanyan: That freeze-in scenario is intriguing because it opens up a whole new production channel that might be testable with very different experimental setups than what we usually run <ref:2601.00436#pg19> > <ref:2601.00436#pg19>.

Vera: And for us, the observational astronomer side, it points us toward looking for those displaced vertex signatures at colliders when lambda five is large and delta M plus is small enough to make sense > Page fifty-one > <ref:2601.00436#pg2>.

Jocelyn: I think that’s the big payoff because it gives us a clear signature to hunt for if we build those future searches correctly <ref:2601.00436#pg51> > <ref:2601.00436#pg51>.

Subrahmanyan: It really shows how cosmology and structure formation connect with these particle physics models through the relic density calculation of this RHN DM candidate <ref:2601.00436#pg51> > <ref:2601.00436#pg51>.

Vera: So, this paper gives us a solid framework for where to look in the parameter space and what kind of signals to expect from future experiments on both the ground and in space > Page fifty-one > <ref:2601.00436#pg2>.

Jocelyn: It's a good roadmap for us as we plan what follow-up observations are needed to settle these uncertainties about the DM abundance <ref:2601.00436#pg51> > <ref:2601.00436#pg51>.

Subrahmanyan: I'm still waiting for those direct detection results to come in, because that’s the ultimate confirmation or rejection of whether this model has any footing in reality <ref:2601.00436#pg51> > <ref:2601.00436#pg51>.

Conclusion: Vera: So we've covered the full scope of "Anatomy of RHN DM relic in the vanilla scotogenic neutrino mass model," focusing on how this right-handed neutrino acts as dark matter.

Jocelyn: It really boils down to how you get that correct thermal relic density, which depends heavily on those specific choices in the couplings like lambda four and lambda five.

Subrahmanyan: And for me, what this means is that we need observational data to constrain those coupling parameters because right now they are quite broad across the mass range for this fermionic candidate.

Vera: Exactly; these constraints from flavor violation and the muon magnetic moment are really helping us narrow down where this whole model might be physically real.

Subrahmanyan: That freeze-in scenario is intriguing because it opens up a whole new production channel that might be testable with very different experimental setups than what we usually run.

Jocelyn: I think that’s the big payoff because it gives us a clear signature to hunt for if we build those future searches correctly.

Subrahmanyan: It really shows how cosmology and structure formation connect with these particle physics models through the relic density calculation of this RHN DM candidate.

Vera: So, this paper gives us a solid framework for where to look in the parameter space and what kind of signals to expect from future experiments on both the ground and in space.

Jocelyn: It's a good roadmap for us as we plan what follow-up observations are needed to settle these uncertainties about the DM abundance.

Subrahmanyan: I'm still waiting for those direct detection results to come in, because that’s the ultimate confirmation or rejection of whether this model has any footing in reality.

Sujit Kumar Sahoo, Narendra Sahu, Vicky Singh Thounaojam a

Department of Physics, Indian Institute of Technology Hyderabad

hep-ph, astro-ph.CO, hep-ex

Submitted: 2026-01-01

Updated: 2026-10-21

Comments: Accepted for publication in JCAP

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 78/100

The gist: The gist: The lightest right-handed neutrino (RHN) can be a viable dark matter candidate in the minimal scotogenic neutrino mass model within specific mass ranges and parameter spaces, while

Key concepts

Scotogenic Neutrino Mass Model: This model generates light neutrino masses at the one-loop level using three right-handed neutrinos and a scalar doublet. The lightest particle in this loop can naturally serve as the dark matter candidate, linking neutrino mass generation to dark matter physics.
Relic Density Mechanisms: The paper investigates how the dark matter's abundance is set by various processes. These include self-annihilation, co-annihilation with scalar components, and conversion-driven processes like decay and inverse decay. Coupled Boltzmann equations track how these densities evolve over time.
Displaced Vertex Signatures: This signature arises from the charged component of the scalar doublet decaying into a right-handed neutrino and a charged lepton. The distance traveled by this particle ($ au$) depends on its mass and the mass splitting between particles, providing a unique observable at colliders.
Electroweak Precision Tests (S and T Parameters): These tests constrain the model by looking at deviations in electroweak interactions. The presence of the additional scalar doublet ($\eta$) affects these parameters, imposing limits on its mass and couplings to ensure consistency with experimental data.

Summary

The gist: The lightest right-handed neutrino (RHN) can be a viable dark matter candidate in the minimal scotogenic neutrino mass model within specific mass ranges and parameter spaces, while displaced vertex signatures offer complementary collider probes for this scenario.

The Model and Neutrino Mass Generation

The scotogenic model generates light neutrino masses radiatively at the one-loop level by incorporating three right-handed neutrinos (N1,2,3) and a scalar doublet η which belong to a Z2-odd dark sector <ref:2601.00436#pg5>. The lightest particle running in the loop can naturally serve as a viable dark matter (DM) candidate <ref:2601.00436#pg4>. The neutrino mass matrix is given by an expression involving the masses of the particles in the model, structured as (mν)αβ = X3 i=1 yαiy∗ iβ 16π2 MNi [M2 ηR M2 ηR − M2 Ni log (M2 ηR M2 Ni) − M2 ηI M2 ηI − M2 Ni log (M2 ηI M Ni)] <ref:2601.00436#pg7>. This structure takes the form of (mν)αβ = y TΛy αβ, where Λ is a diagonal matrix with elements Λi defined by complex expressions involving the masses <ref:2601.00436#pg7>. The Yukawa coupling can be expressed as y = √Λ−1R p mˆ νUPMNS <ref:2601.00436#pg7>.

Phenomenological Constraints

The lightest RHN faces challenges in achieving the correct relic density across a wide region of parameter space due to constraints from several phenomena <ref:2601.00436#pg4>. These constraints include charged lepton flavor violation (cLFV) and neutrino oscillation data <ref:2601.00436#pg4>. The muon anomalous magnetic moment, (g − 2)µ, also imposes restrictions on the model parameters <ref:2601.00436#pg4>. Electroweak precision tests are constrained by the oblique S and T parameters, which are sensitive to the presence of the additional scalar doublet η <ref:2601.00436#pg6>. Furthermore, vacuum stability conditions impose constraints on quartic couplings [31, 32] <ref:2601.00436#pg6>.

Relic Density Mechanisms

The relic density of DM can be investigated through several mechanisms <ref:2601.00436#pg9>. The channels contributing to DM depletion include self-annihilation (SA) into leptons, co-annihilation (CA) with the scalar doublet components, and conversion-driven processes <ref:2601.00436#pg9>. The evolution of the comoving number densities is governed by coupled Boltzmann equations (BEs) <ref:2601.00436#pg11>. The conversion term Γ2→1 in these BEs includes both the interaction rate of co-scattering processes as well as the decay/inverse-decay and is given by a complex expression <ref:2601.00436#pg11>.

Direct Detection and Collider Signatures

Direct detection arises only at the one-loop level, mediated by either gauge bosons or the Higgs boson <ref:2601.00436#pg22>. The spin-dependent cross section per nucleon N is given by a formula involving the Yukawa coupling yα1 and loop functions <ref:2601.00436#pg23>. For larger values of quartic couplings λ3,4,λ5, the spin-independent direct detection interaction becomes relevant via an effective operator <ref:2601.00436#pg24>. The presence of displaced vertex signatures provides a complementary probe, as the charged component of the scalar doublet can decay into N1 and charged lepton <ref:2601.00436#pg25>. The decay width for η+→N1l+α is given by an expression involving the Yukawa coupling and mass splittings <ref:2601.00436#pg25>.

Conclusion on Viable Regions

The correct thermal DM relic density can be achieved across the full dark matter mass range once all conversion-driven processes are incorporated in the Boltzmann equations <ref:2601.00436#pg7>. The conversion-driven mechanism is realized through co-scattering as well as decay and inverse decay processes <ref:2601.00436#pg16>. The viable mass being strongly correlated with the choice of λ3,4,5 or, equivalently, λR <ref:2601.00436#pg26>. Sizable regions remain accessible at colliders through displaced vertex signatures for large λ5, large MDM, and small λ4 <ref:2601.00436#pg24>. The current direct detection searches do not impose additional constraints as the relevant interactions arise only at the loop level <ref:2601.00436#pg22>.

Higgs Invisible Decay Constraints

The SM Higgs boson h can decay into the neutral components ηR and ηI of the inert doublet <ref:2601.00436#pg26>. The decay h → η +η− is kinematically forbidden because values Mη+. The choice of λ4 MηR, which automatically satisfies the LEP constraint on charged scalars and avoids contributions to the invisible decay width of the Z boson provided that MηR + MηI > MZ <ref:2601.00436#pg26>. This choice also allows MηR to remain relatively small while eliminating the decay h → ηIηI when kinematically inaccessible <ref:2601.00436#pg26>. The constraints from Higgs invisible decay are illustrated in the MηR − λR parameter plane <ref:2601.00436#pg27>.

Freeze-in Mechanism

The relic density of DM (N1) can be generated via the freeze-in mechanism, where production is dominated by the decay of Z2 odd scalars <ref:2601.00436#pg21>. The equation governing the evolution of the DM from the scalar decay is given by dYN1 dx = 1 xH(T) X i=R,I,± ⟨Γηi⟩Yeq ηi, where x = MN1 /T <ref:2601.00436#pg21>. In this scenario, the Boltzmann suppression is significant in the region of ∆M/MDM > 1, while it becomes milder when the same ratio is less than 1 <ref:2601.00436#pg21>. The final DM yield is decided by the production rate Γη in the small ∆M/MDM region <ref:2601.00436#pg21>.

Co-scattering Effect

The impact of co-scattering on DM relic density is subdominant compared to the decay and inverse-decay processes within the conversion-driven framework <ref:2601.00436#pg30>. The resulting values of the ρ parameter are displayed in Fig. 24, where ρ remains approximately equal to 1 across the entire DM mass range considered <ref:2601.00436#pg25>. This indicates that co-scattering contributes non-negligibly to the final relic density only when deviations from unity occur <ref:2601.00436#pg25>.

Decay and Inverse Decay Dynamics

The abundance evolution of N1 is governed by equations where the inverse decay rate ΓID mimics thermally averaged cross-section for the decay and inverse decay, with its expression given by a formula involving ∆M2R × e −∆MR/T <ref:2601.00436#pg32>. The final DM relic abundance can be lowered if YN1 attains a fixed number, and the ratio YN1/Y eq N1 gets larger than 1, thereby reducing freeze-out abundance of CDM N1 <ref:2601.00436#pg33>. This behavior is explained by comparing the various rates with the Hubble expansion rate as shown in the right panel of Fig. 10 <ref:2601.00436#pg33>. The inverse decay rate – 16 > becomes comparable to the Hubble expansion rate while η is in equilibrium, thereby bringing the final DM relic abundance to the correct ballpark <ref:2601.00436#pg33>.

Final Summary of Viable Regions

The correct thermal DM relic can be achieved for MDM ≳ Mh/2 <ref:2601.00436#pg18>. The viable mass being strongly correlated with the choice of λ3,4,5 or, equivalently, λR <ref:2601.00436#pg18>. Although a thermal relic is viable over a wide dark matter mass range, we identify regions—particularly at low dark matter masses—where thermal equilibrium with the SM is not attained <ref:2601.00436#pg26>. In such cases, the observed relic abundance can instead be generated via the freeze-in mechanism <ref:2601.00436#pg19>. Sizable regions remain accessible at colliders through displaced vertex signatures for large λ5, large MDM, and small λ4 <ref:2601.00436#pg24>. The current direct detection searches do not impose additional constraints as the relevant interactions arise only at the loop level <ref:2601.00436#pg22>.

Acknowledgments

Owing to the scalar couplings λ3,4,5, the SM Higgs boson h can decay into the neutral components ηR and ηI of the inert doublet <ref:2601.00436#pg26>. The corresponding partial decay widths are given by an expression involving λi and mass terms <ref:2601.00436#pg26>. The observed upper limits on the Higgs invisible branching fraction are 18% and 14.5% at the 95% C.L., respectively <ref:2601.00436#pg27>. These bounds are expected to improve to approximately 10% for both experiments <ref:2601.00436#pg27>.

B Functions in Oblique Parameters

The oblique parameters, S and T, are expressed as a complex expression involving loop functions G(zη+, zη+), G(zηR, zηI) and other terms <ref:2601.00436#pg27>. The loop functions are given by a formula involving x and y <ref:2601.00436#pg27>. The function F(x, y) is defined as an expression involving x, y, and logarithms <ref:2601.00436#pg27>.

Feynman Diagrams

The paper presents Feynman diagrams corresponding to Self-Annihilation (SA) of DM in Fig. 19 <ref:2601.00436#pg28>, annihilation and co-annihilation among the sector-2 particles in Fig.

Improvements for AI systems

Improved Dark Matter Relic Density Calculation: The system can accurately predict DM relic density across a wide mass range by incorporating self-annihilation, co-annihilation, and conversion processes into coupled Boltzmann equations described in Equations (3.2) and (3.3).
Direct Detection Cross Section Prediction: The AI can calculate spin independent and spin dependent direct detection cross sections using the effective operator derived in Equation (4.6), allowing for comparison against current experimental limits like XENONnT, LZ, and PandaX-4T data.
Displaced Vertex Signature Identification: The system can predict the decay length c tau as a function of DM mass and mass splitting Delta M plus using Equation (5.1), enabling the identification of displaced vertex signatures at colliders based on CMS and ATLAS search sensitivities.
Parameter Space Mapping: The AI can map out viable parameter space in planes such as MDM versus Delta MR, incorporating constraints from electroweak precision tests (S and T parameters), charged lepton flavor violation, and the anomalous magnetic moment of the muon.