[Paper Review] Radiative neutrino mass in an alternative $U(1)_{B-L}$ gauge symmetry

Takaaki Nomura, Hiroshi Okada|arXiv (Cornell University)|May 23, 2017

Neutrino Physics Research10 citations

TL;DR

This paper proposes a radiative neutrino mass model based on an alternative $U(1)_{B-L}$ gauge symmetry with non-trivial right-handed neutrino charges, where neutrino masses arise at one loop via exotic scalar and fermion loops. A remnant $Z_2$ symmetry ensures dark matter stability, and the model successfully fits neutrino oscillation data, lepton flavor violation constraints, and the observed dark matter relic density through $Z'$ and Goldstone boson-mediated annihilation channels.

ABSTRACT

We propose a neutrino model in which neutrino masses are generated at one loop level and three right-handed fermions have non-trivial charges under $U(1)_{B-L}$ gauge symmetry in no conflict with anomaly cancellation. After the spontaneously symmetry breaking, a remnant $Z_2$ symmetry is induced and plays an role in assuring the stability of dark matter candidate.

Motivation & Objective

• To construct a radiative neutrino mass model based on an alternative $U(1)_{B-L}$ charge assignment for right-handed neutrinos.
• To ensure neutrino mass generation at one loop while canceling anomalies and preserving gauge invariance.
• To stabilize a fermionic dark matter candidate via a remnant $Z_2$ symmetry after $U(1)_{B-L}$ spontaneous breaking.
• To fit neutrino oscillation data, lepton flavor violation constraints, and the observed dark matter relic density through $Z'$ and Goldstone boson-mediated annihilation.

Proposed method

• Introduce three right-handed neutrinos with $U(1)_{B-L}$ charges $-4, -4, 5$ to cancel anomalies and allow one-loop neutrino mass generation.
• Postulate two SM singlet scalar fields $\varphi_1, \varphi_2$ with non-zero $U(1)_{B-L}$ charges to break the symmetry and produce a physical Goldstone boson (GB).
• Implement inert doublet and singlet scalars ($\eta$, $s$) to mediate one-loop neutrino mass generation via a loop diagram involving $N_{R_i}$ and scalar states.
• Derive the neutrino mass matrix using one-loop self-energy diagrams with $N_{R_i}$ and scalar propagators, ensuring $\mu$-term suppression.
• Compute the relic density of the dark matter fermion $X$ via $XX \to Z'$ and $XX \to 2\text{GB}$, using cross-section formulas involving $M'_{11}$, $v'_{\varphi_2}$, and $M_X$.
• Perform global and benchmark analyses to constrain Yukawa couplings, $Z'$ mass, and $M_X$ to satisfy neutrino data, LFV bounds, and $\Omega h^2$.

Experimental results

Research questions

• RQ1 Can a radiative neutrino mass model be constructed with a non-trivial $U(1)_{B-L}$ charge assignment for right-handed neutrinos that avoids tree-level mass generation?
• RQ2 How does the spontaneous breaking of $U(1)_{B-L}$ induce a remnant $Z_2$ symmetry that stabilizes a fermionic dark matter candidate?
• RQ3 What are the viable parameter regions where the model reproduces neutrino oscillation data, satisfies lepton flavor violation constraints, and achieves the correct dark matter relic density?
• RQ4 How do $Z'$ and Goldstone boson-mediated annihilation processes contribute to the dark matter relic density, and what mass ranges are allowed?

Key findings

• The model achieves one-loop neutrino mass generation via a loop involving $N_{R_i}$, $\eta$, and $s$, with Yukawa couplings of order $\mathcal{O}(0.01)$ to fit neutrino oscillation data.
• The remnant $Z_2$ symmetry after $U(1)_{B-L}$ breaking stabilizes the lightest neutral fermion $X$ as a viable dark matter candidate.
• The observed dark matter relic density is reproduced through $Z'$-mediated annihilation when $m_{Z'} \sim 2M_X$, indicating resonance enhancement.
• The Goldstone boson (GB) mode contributes significantly to relic density at lower $M_X$, especially when $M_X \lesssim 100$ GeV and $|M'_{11}| \gtrsim 150$ GeV.
• Yukawa couplings to the dark matter are negligible, so the dominant relic density contribution comes from $Z'$ and GB-mediated annihilation, not from direct Yukawa interactions.
• The model satisfies the LEP bound on $g_{BL}/m_{Z'} \leq 1/(7\,\text{TeV})$ with $v'_1 \sim 66\,\text{TeV}$ and $v'_2 = 500\,\text{GeV}$, consistent with $v'_2 \ll v'_1$.