[Paper Review] An $SU(2)_L imes U(1)_Y$ model with reflection symmetry in view of recent neutrino experimental result

Ambar Ghosal|ArXiv.org|Apr 9, 2003

Neutrino Physics Research3 citations

TL;DR

This paper proposes an $SU(2)_L \times U(1)_Y$ model with reflection symmetry between the second and third lepton generations, generating neutrino masses via dimension-5 operators with explicit lepton number violation. The model successfully accommodates solar, atmospheric, CHOOZ, WMAP, and neutrinoless double-beta decay data, predicting a small $|U_{13}| \simeq 3.5 \times 10^{-3}$ and $\langle m_{ee} \rangle \simeq 0.0519$ eV, which is at the lower edge of current experimental bounds.

ABSTRACT

We demonstrate that an $SU(2)_L imes U(1)_Y$ model with the same particle content as Standard Model(SM) and discrete reflection symmetry between second and third generation of leptons give rise to charged lepton and neutrino mass matrices which can accommodate the present solar, atmospheric, WMAP neutrino experimental results.The model predicts the value of $|U_{13}|$ which could be tested in neutrino factories and the value of the effectiv Majorana neutrino mass $$ comes out at the lower end of the present experimental limit. Neutrino masses are generated through dim = 5 operators and the scale of which is constrained by the value of $$. If, in future neutrino less double beta decay experiments, namely, MOON, EXO, GENIUS etc. shifts the lower bound on $}$ by one order the present model will fail to accommodate the solar neutrino mixing angle due to LMA solution.

Motivation & Objective

• To construct a minimal $SU(2)_L \times U(1)_Y$ model with the Standard Model particle content that explains recent neutrino oscillation data.
• To incorporate a discrete reflection symmetry between the second and third generations of leptons to constrain the lepton mass matrix texture.
• To generate neutrino masses through dimension-5 operators with explicit lepton number violation, avoiding the seesaw mechanism.
• To predict $|U_{13}|$ and $\langle m_{ee} \rangle$ consistent with current experimental bounds and testable in future experiments.
• To assess the model's viability under future improvements in neutrinoless double-beta decay sensitivity, particularly from MOON, EXO, and GENIUS experiments.

Proposed method

• Introduce a discrete reflection symmetry $l_{2L} \leftrightarrow l_{3L}, \mu_R \leftrightarrow \tau_R$ to constrain the structure of charged lepton and neutrino mass matrices.
• Assume neutrino masses arise from dimension-5 effective operators violating lepton number, with the mass scale $M$ set by the vacuum expectation value of a scalar singlet.
• Construct the charged lepton mass matrix as non-diagonal, with eigenvalues matching the muon and tau lepton masses.
• Derive the neutrino mass matrix from the same scalar sector, ensuring the structure respects the reflection symmetry and leads to a specific texture.
• Use the Maki-Nakagawa-Sakata-Pontecorvo (MNSP) mixing matrix to relate the flavor eigenstates to mass eigenstates, with parameters constrained by solar, atmospheric, and reactor neutrino data.
• Apply perturbative unitarity bounds on Yukawa couplings to constrain the scale $M$, with $M \leq 10^{13}$ GeV for $\langle m_{ee} \rangle \simeq 0.0519$ eV and $\langle \phi \rangle \simeq 200$ GeV.

Experimental results

Research questions

• RQ1 Can a reflection symmetry between the second and third lepton generations in an $SU(2)_L \times U(1)_Y$ model with SM particle content reproduce the observed solar, atmospheric, and reactor neutrino oscillation data?
• RQ2 What is the predicted value of the mixing angle $\theta_{13}$, and is it testable in upcoming neutrino factory experiments?
• RQ3 How does the model predict the effective Majorana neutrino mass $\langle m_{ee} \rangle$, and what is its sensitivity to future improvements in $\beta\beta_{0\nu}$ decay experiments?
• RQ4 What is the scale $M$ of the new physics in the model, and how is it constrained by unitarity and experimental bounds on $\langle m_{ee} \rangle$?
• RQ5 Would the model remain viable if future $\beta\beta_{0\nu}$ experiments (e.g., MOON, EXO, GENIUS) improve the lower bound on $\langle m_{ee} \rangle$ by one order of magnitude?

Key findings

• The model predicts $|U_{13}|^2 \simeq 1.25 \times 10^{-5}$, corresponding to $\sin^2 2\theta_{13} \simeq 4.99 \times 10^{-5}$, which is small but potentially testable in future neutrino factories.
• The effective Majorana neutrino mass is predicted as $\langle m_{ee} \rangle \simeq 0.0519$ eV, placing it at the lower end of the current experimental limit of $0.05 - 0.84$ eV at 95% C.L.
• The solar neutrino mixing angle is predicted as $\sin^2 2\theta_\odot \simeq 0.85$, consistent with the LMA-MSW solution and the KamLAND data.
• The atmospheric neutrino mixing angle is $\sin^2 2\theta_{\text{atm}} \simeq 0.99$, close to maximal mixing, and consistent with Super-K and K2K results.
• The sum of neutrino masses is $\Sigma m_i \simeq 0.1031$ eV, well below the WMAP upper bound of $0.71$ eV at 95% C.L.
• The scale $M$ of the model is constrained to $M \leq 10^{13}$ GeV due to perturbative unitarity of Yukawa couplings, assuming $\langle \phi \rangle \simeq 200$ GeV.