A combination of the neutrino trimaximal mixings and $$\mu $$-$$\tau $$ reflection symmetry in the type-I seesaw model
Zhen-hua Zhao
Abstract
Abstract In this paper, we make an attempt to combine the neutrino trimaximal (TM1 and TM2) mixings and $$\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math> - $$\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> </mml:math> reflection symmetry in the type-I seesaw model. Such a scenario is highly restrictive and predictive: in addition to three right-handed neutrino masses, there are only five real parameters; all the lepton flavor mixing parameters except for $$\theta ^{}_{13}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>θ</mml:mi> <mml:mn>13</mml:mn> <mml:mrow/> </mml:msubsup> </mml:math> will be predicted. The relations between the model parameters and the measurable neutrino parameters will be derived. The implications of this scenario for leptogenesis will be explored in detail. A further reduction of this scenario to the more restrictive and predictive minimal seesaw model with only two right-handed neutrinos will also be considered. In addition, we will also discuss a possible approach to get the desired mass matrices and study the compatibility of the trimaximal $$\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math> - $$\tau $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>τ</mml:mi> </mml:math> reflection symmetry with texture zeros.