[Paper Review] Gauged $L_\mu$-$L_ au$ Model with an Inverse Seesaw Mechanism for Neutrino Masses

Abhish Dev|arXiv (Cornell University)|Oct 8, 2017

Particle physics theoretical and experimental studies10 references3 citations

TL;DR

This paper proposes a GL−R × U(1)Lμ−Lτ gauge-symmetric model that simultaneously explains the muon anomalous magnetic moment and the small masses of left-handed neutrinos via an inverse seesaw mechanism. By spontaneously breaking U(1)Lμ−Lτ, the model generates a heavy Zμτ gauge boson that contributes to ∆aμ and a Type-C two-zero texture in the neutrino mass matrix, leading to precise predictions for CP-violating phases and neutrino masses consistent with current experimental data.

ABSTRACT

In this paper, we propose a $G_{L-R} imes U(1)_{L_\mu-L_ au}$ gauge-symmetric model where $G_{L-R}$ is the left-right gauge symmetry and $L_i$ is the $i-$flavor lepton number. We use the spontaneous breaking (SSB) of $U(1)_{L_\mu-L_ au}$ to explain two discrepancies in the standard model: muon anomalous magnetic moment and light neutrinos and its oscillations. The massive neutral gauge boson, $Z_{\mu au}$, arising from the SSB can provide additional contributions to the muon anomalous magnetic moment. In order to explain neutrino masses, we employ the low-energy inverse seesaw mechanism by adding three $G_{L-R}$ singlet fermions, $S_{e,\mu, au}$. The light neutrino mass matrix from the inverse seesaw formula has a specific two-zero texture pattern referred in the literature as the Type-C two-zero texture due to the $U(1)_{L_\mu-L_ au}$ symmetry. This allows us to predict the values of the CP-violating Dirac phase, Majorana phases, and the absolute value of light neutrino masses in terms of the precisely measured mixing angles and mass squared differences. The model accommodates a quasi-degenerate spectrum of neutrino masses with inverted ordering. The calculated best-fit value of $\delta_{CP}$ surprisingly matches with the current experimentally measured best-fit value of $\delta_{CP}$. At $1\sigma$, the measured value of $\delta_{CP}$ favors a $ heta_{23}>\pi/4$. At $1\sigma$, most of the parameter space is within the cosmological bound on the sum of neutrino mass and the bound on the effective Majorana mass from neutrinoless beta decay.

Motivation & Objective

• To resolve the long-standing discrepancy in the muon anomalous magnetic moment (∆aμ) beyond the Standard Model.
• To explain the small masses of left-handed neutrinos and their oscillation parameters using a low-energy seesaw mechanism.
• To unify the explanation of µ−τ symmetry breaking and neutrino mass generation within a single gauge-symmetric framework.
• To predict CP-violating phases and absolute neutrino masses with minimal free parameters using symmetry-imposed texture patterns.
• To test the model’s viability against cosmological bounds on the sum of neutrino masses and effective Majorana mass from neutrinoless double beta decay.

Proposed method

• Introduces a left-right symmetric gauge group GL−R × U(1)Lμ−Lτ, where U(1)Lμ−Lτ is spontaneously broken by a Higgs field with Lμ−Lτ charge.
• The spontaneous breaking of U(1)Lμ−Lτ generates a massive neutral gauge boson Zμτ, which contributes to the muon anomalous magnetic moment.
• Implements the inverse seesaw mechanism by adding three GL−R singlet fermions (Se,µ,τ), leading to a light neutrino mass matrix of the form mν ≈ mT_D (mT_N)^{-1} μ mN mD.
• The U(1)Lμ−Lτ symmetry enforces a specific two-zero texture (Type-C) in the neutrino mass matrix, restricting the structure of mixing parameters.
• Uses the measured mixing angles and mass-squared differences as inputs to derive predictions for δCP, Majorana phases, and absolute neutrino masses.
• Performs a global fit to experimental data, including ∆aμ, neutrino oscillation parameters, and cosmological bounds, to constrain the parameter space.

Experimental results

Research questions

• RQ1 Can a U(1)Lμ−Lτ gauge model with an inverse seesaw mechanism simultaneously explain the muon g−2 anomaly and the small neutrino masses?
• RQ2 What are the implications of the U(1)Lμ−Lτ symmetry for the texture of the neutrino mass matrix, and how does it constrain CP-violating phases?
• RQ3 Does the model predict a specific neutrino mass ordering, and is it consistent with cosmological and neutrinoless double beta decay bounds?
• RQ4 How sensitive are the predictions for δCP to the octant of θ23, and do they align with current experimental best-fit values?
• RQ5 Can the model accommodate a Zμτ boson within the 12–800 GeV mass range required to explain the muon g−2 discrepancy?

Key findings

• The model predicts a best-fit value of the CP-violating Dirac phase δCP ≈ −1.2, which remarkably matches the current experimental best-fit value from global fits.
• At 1σ confidence level, the model favors θ23 > π/4, indicating a preference for the higher octant of the atmospheric mixing angle.
• The neutrino mass spectrum is constrained to be quasi-degenerate with inverted ordering, consistent with the Type-C two-zero texture enforced by U(1)Lμ−Lτ symmetry.
• The absolute neutrino mass scale is predicted to be in the range of 0.05–0.1 eV, which is within the cosmological bound on the sum of neutrino masses.
• The effective Majorana mass for neutrinoless double beta decay is predicted to be below 0.02 eV, consistent with current experimental limits.
• The Zμτ gauge boson mass is constrained to the 12–800 GeV range to explain the muon g−2 anomaly, with couplings that evade constraints from lepton and hadron colliders.