Structure of leptonic Yukawa couplings in the Zee model

TL;DR

This paper derives a novel identity linking leptonic Yukawa couplings and neutrino mass matrices in the Zee model, enabling potential determination of Yukawa entries from neutrino data and exploring implications for muon g-2.

Contribution

It introduces a unique identity connecting Yukawa couplings and neutrino mass matrices in the Zee model, independent of certain parameters, and applies it to specific textures.

Findings

Five Yukawa entries can be determined from neutrino data and the identity.

Remaining Yukawa entries can be chosen based on phenomenology.

Application to the B2 texture enhances muon g-2 explanation.

Abstract

The radiative neutrino mass matrix $m^\nu$ in the Zee model depends on leptonic Yukawa couplings $F$ to a singlet scalar and $Y^\ell$ to a new Higgs doublet. Leveraging the skew-symmetric structure of $F$, we derive a unique identity linking $F$ and $m^\nu$ that is explicitly independent of $Y^\ell$. This relation implies that five entries of $Y^\ell$ can, in principle, be determined directly from $m^\nu$ and $F$, while the remaining four can be selected based on phenomenological assumptions. As an illustration, we apply this framework to the two-zero texture $B2$, highlighting its enhancement of the muon $g-2$.