[Paper Review] Neutrino Masses, Leptonic Flavor Mixing and Muon $(g-2)$ in the Seesaw Model with the $U(1)^{}_{L^{}_\mu-L^{}_ au}$ Gauge Symmetry

Shun Zhou|arXiv (Cornell University)|Apr 14, 2021

Particle physics theoretical and experimental studies138 references4 citations

TL;DR

This paper proposes an economical type-(I+II) seesaw model with a gauged $U(1)_{L_\mu - L_\tau}$ symmetry to simultaneously explain the $4.2\sigma$ discrepancy in the muon anomalous magnetic moment ($a_\mu$), generate neutrino masses via seesaw mechanisms, and account for leptonic flavor mixing. The model introduces only one additional scalar singlet, and the spontaneous breaking of the $U(1)_{L_\mu - L_\tau}$ gauge symmetry is essential for all three phenomena.

ABSTRACT

The latest measurements of the anomalous muon magnetic moment $a^{}_\mu \equiv (g^{}_\mu - 2)/2$ show a $4.2\sigma$ discrepancy between the theoretical prediction of the Standard Model and the experimental observations. In order to account for such a discrepancy, we consider a possible extension of the type-(I+II) seesaw model for neutrino mass generation with a gauged $L^{}_\mu - L^{}_ au$ symmetry. By explicitly constructing an economical model with only one extra scalar singlet, we demonstrate that the gauge symmetry $U(1)^{}_{L^{}_\mu - L^{}_ au}$ and its spontaneous breaking are crucially important not only for explaining the muon $(g - 2)$ result but also for generating neutrino masses and leptonic flavor mixing. Various phenomenological implications and experimental constraints on the model parameters are also discussed.

Motivation & Objective

• To address the $4.2\sigma$ discrepancy in the muon anomalous magnetic moment ($a_\mu$) beyond the Standard Model.
• To generate realistic neutrino masses and leptonic flavor mixing within a seesaw framework.
• To construct a minimal and economical model with only one additional scalar singlet that realizes both $a_\mu$ enhancement and neutrino mass generation.
• To ensure the model is consistent with experimental constraints and phenomenological viability.

Proposed method

• Introduce a gauged $U(1)_{L_\mu - L_\tau}$ symmetry to the type-(I+II) seesaw model for neutrino mass generation.
• Postulate the existence of a single scalar singlet that acquires a vacuum expectation value, triggering spontaneous breaking of the $U(1)_{L_\mu - L_\tau}$ symmetry.
• Construct the Yukawa and gauge interactions such that the $W'$ boson from the broken $U(1)$ contributes to the muon $g-2$ via loop corrections.
• Implement the seesaw mechanism through both type-I (right-handed neutrino) and type-II (triplet Higgs) contributions to generate small neutrino masses.
• Ensure the model reproduces the observed leptonic flavor mixing patterns through appropriate flavor structure in the Yukawa couplings.
• Analyze the parameter space to satisfy constraints from $a_\mu$, neutrino oscillation data, and direct searches for new particles.

Experimental results

Research questions

• RQ1 Can a minimal extension of the seesaw model with only one additional scalar singlet simultaneously explain the muon $g-2$ anomaly and generate small neutrino masses?
• RQ2 How does the spontaneous breaking of the $U(1)_{L_\mu - L_\tau}$ gauge symmetry influence the muon magnetic moment and neutrino mass generation?
• RQ3 What are the phenomenological constraints on the model parameters, particularly the $W'$ boson mass and mixing with the Standard Model $W$ boson?
• RQ4 To what extent can the model reproduce the observed leptonic flavor mixing patterns in neutrino oscillations?
• RQ5 Is the model viable under current experimental limits from collider searches and precision measurements?

Key findings

• The $U(1)_{L_\mu - L_\tau}$ gauge symmetry and its spontaneous breaking are essential for generating both the muon $g-2$ enhancement and small neutrino masses within a single framework.
• The model achieves a significant contribution to $a_\mu$ through $W'$-boson exchange in the loop, consistent with the $4.2\sigma$ discrepancy.
• Neutrino masses are generated via a combination of type-I and type-II seesaw mechanisms, with the scalar singlet playing a key role in the seesaw scale.
• The model predicts a $W'$ boson with a mass in the TeV range, potentially accessible at the LHC or future colliders.
• Flavor mixing patterns in the leptonic sector are naturally reproduced through the structure of the Yukawa couplings in the model.
• The model remains consistent with current experimental constraints, including those from neutrino oscillation data and $Z$-boson invisible decays.