Type III seesaw under $$A_4$$ modular symmetry with leptogenesis
Priya Mishra, Mitesh Kumar Behera, Papia Panda, Rukmani Mohanta
Abstract
Abstract We make an attempt to study neutrino phenomenology in the framework of type-III seesaw by considering $$A_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> modular symmetry in the super-symmetric context. In addition, we have included a local $$U(1)_{B-L}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>-</mml:mo> <mml:mi>L</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> symmetry which eventually helps us to avoid certain unwanted terms in the superpotential. Hitherto, the seesaw being type-III, it involves three fermion triplet superfields $$\Sigma _R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:math> , along with which, we have included a singlet weighton field $$(\rho )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ρ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . In here, modular symmetry plays a crucial role by avoiding the usage of excess flavon (weighton) fields. Also, the Yukawa couplings acquire modular forms which are expressed in terms of Dedekind eta function $$\eta (\tau )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>η</mml:mi> <mml:mo>(</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . However, for numerical analysis we use q expansion expressions of these couplings. Therefore, the model discussed here is triumphant enough to accommodate the observed neutrino oscillation data and also successfully explains observed baryon asymmetry of the universe through leptogenesis.