[Paper Review] A Radiative Linear Seesaw, Dark Matter and $U(1)_{B-L}$

Weijian Wang, Zhi-Long Han|arXiv (Cornell University)|Jan 1, 2015

Particle physics theoretical and experimental studies13 citations

TL;DR

This paper proposes a radiative linear seesaw model within a U(1)_{B-L} gauge symmetry framework, where the small lepton number-violating term μ_L is generated at one-loop level, leading to spontaneous B-L symmetry breaking. The residual Z₂ × Z₂′ symmetry stabilizes two distinct inert fermion and scalar components as viable two-component dark matter candidates, while also enabling lepton flavor violation, relic density, direct detection, and collider phenomenology to be studied consistently.

ABSTRACT

In this paper we propose a radiated linear seesaw model where the naturally small term $\mu_{L}$ are generated at one-loop level and its soft-breaking of lepton number symmetry attributes to the spontaneous breaking(SSB) of B-L gauge symmetry. The value of $B-L$ charges for new particles are assigned to satisfy the anomalies cancelation. It is founded that some new particles may have exotic values of $B-L$ charge such that there exists residual $Z_{2} imes Z_{2}^{\prime}$ symmetry even after SSB of $B-L$ gauge symmetry. The $Z_{2} imes Z_{2}^{\prime}$ discrete symmetry stabilizes the these particles as dark matter candidates. In the model, two no-interplay classes of inert fermions and scalars are introduced, leading to two-component dark matter candidates. The lepton flavor violation processes, the relic density of dark matter, the direct detection of dark matter and the phenomenology on collider machine are investigated.

Motivation & Objective

• To construct a radiative linear seesaw model that naturally generates small μ_L terms via one-loop dynamics.
• To achieve spontaneous B-L symmetry breaking through soft-breaking of lepton number, consistent with anomaly cancellation.
• To identify residual discrete symmetries (Z₂ × Z₂′) after B-L breaking that stabilize inert fermions and scalars as dark matter candidates.
• To investigate the phenomenology of lepton flavor violation, dark matter relic density, direct detection, and collider signals in the model.
• To ensure anomaly cancellation by assigning appropriate B-L charges to new particles, including exotic values that preserve residual symmetries.

Proposed method

• Introduce a radiative linear seesaw mechanism where the small μ_L term is generated at one-loop level through loop diagrams involving new heavy fermions and scalars.
• Implement a U(1)_{B-L} gauge symmetry with soft-breaking of lepton number to trigger spontaneous B-L symmetry breaking.
• Assign B-L charges to new particles, including exotic values, to ensure anomaly cancellation and to preserve a residual Z₂ × Z₂′ discrete symmetry after symmetry breaking.
• Utilize the residual Z₂ × Z₂′ symmetry to stabilize two distinct inert sectors: one fermionic and one scalar, both contributing to dark matter.
• Construct the full Lagrangian including kinetic, gauge, Yukawa, and scalar potential terms, ensuring consistency with gauge invariance and anomaly cancellation.
• Perform analytical and numerical studies of lepton flavor violation processes, dark matter relic density via thermal freeze-out, direct detection cross-sections, and collider signatures.

Experimental results

Research questions

• RQ1 How can the small μ_L term in the linear seesaw be generated naturally at one-loop level within a U(1)_{B-L} gauge model?
• RQ2 What residual discrete symmetries emerge after spontaneous B-L symmetry breaking, and how do they stabilize dark matter?
• RQ3 What are the implications for lepton flavor violation processes in this model, and are they within current experimental bounds?
• RQ4 What is the predicted relic density of the two-component dark matter, and does it match the observed cosmological value?
• RQ5 What are the prospects for direct detection and collider signals of the inert fermion and scalar dark matter components?

Key findings

• The μ_L term is generated at one-loop level through the radiative seesaw mechanism, providing a natural explanation for its smallness.
• Spontaneous B-L symmetry breaking occurs via soft-breaking of lepton number, with the residual Z₂ × Z₂′ symmetry stabilizing both inert fermions and scalars as dark matter candidates.
• The model features two distinct dark matter components—one fermionic and one scalar—both stabilized by the residual discrete symmetry.
• Lepton flavor violation processes are induced at one-loop level and are constrained by current experimental limits, depending on the model parameters.
• The two-component dark matter scenario can reproduce the observed relic density of dark matter through thermal freeze-out, with viable parameter space satisfying cosmological constraints.
• Direct detection cross-sections for both dark matter components are predicted to be below current experimental sensitivity, while collider signals for the inert scalars and fermions remain accessible at high-energy colliders.