Predictions for the neutrino parameters in the minimal model extended by linear combination of U(1)$$_{L_e-L_\mu }$$, U(1)$$_{L_\mu -L_\tau }$$ and U(1)$$_{B-L}$$ gauge symmetries
Kento Asai
Abstract
Abstract We study the minimal extensions of the Standard Model by a linear combination of U(1) $$_{L_e-L_\mu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow/><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mi>μ</mml:mi></mml:msub></mml:mrow></mml:msub></mml:math> , U(1) $$_{L_\mu -L_\tau }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow/><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mi>τ</mml:mi></mml:msub></mml:mrow></mml:msub></mml:math> and U(1) $$_{B-L}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow/><mml:mrow><mml:mi>B</mml:mi><mml:mo>-</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:math> gauge symmetries, where three right-handed neutrinos and one U(1)-breaking SU(2) $$_L$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow/><mml:mi>L</mml:mi></mml:msub></mml:math> singlet or doublet scalar are introduced. Because of the dependence on the lepton flavor, the structures of both Dirac and Majorana mass matrices of neutrinos are restricted. In particular, the two-zero minor and texture structures in the mass matrix for the active neutrinos are interesting. Analyzing these structures, we obtain uniquely all the neutrino parameters, namely the Dirac CP phase $$\delta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>δ</mml:mi></mml:math> , the Majorana CP phases $$\alpha _{2,3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>α</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math> and the mass eigenvalues of the light neutrinos $$m_i$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>m</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math> as functions of the neutrino mixing angles $$\theta _{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>θ</mml:mi><mml:mn>12</mml:mn></mml:msub></mml:math> , $$\theta _{23}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>θ</mml:mi><mml:mn>23</mml:mn></mml:msub></mml:math> , and $$\theta _{13}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>θ</mml:mi><mml:mn>13</mml:mn></mml:msub></mml:math> , and the squared mass differences $$\Delta m^2_{21}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi><mml:msubsup><mml:mi>m</mml:mi><mml:mn>21</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math> and $$\Delta m^2_{31}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Δ</mml:mi><mml:msubsup><mml:mi>m</mml:mi><mml:mn>31</mml:mn><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math> . In 7 minimal models which are consistent with the recent neutrino oscillation data, we also obtain the predictions for the sum of the neutrino masses $$\Sigma _i m_i$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Σ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>m</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math> and the effective Majorana neutrino mass $$\langle m_{\beta \beta }\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>⟨</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:mrow></mml:msub><mml:mo>⟩</mml:mo></mml:mrow></mml:math> and compare them with the current experimental limits. In addition, we also discuss the implication of our results for leptogenesis.