Froggatt-Nielsen-like mechanism in the framework of modular symmetry for neutrino mass, mixing, and leptogenesis

We study a neutrino mass model with Froggatt-Nielsen (FN) like modular symmetry. The FN mechanism requires an additional gauge symmetry, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:msub> <a:mo stretchy="false">)</a:mo> <a:mrow> <a:mi>FN</a:mi> </a:mrow> </a:msub> </a:math> , which is spontaneously broken at high energies. But in this work, we do not need an extra symmetry as modular weights play the role of the FN charges of the additional <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mi>U</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>1</e:mn> <e:msub> <e:mrow> <e:mo stretchy="false">)</e:mo> </e:mrow> <e:mrow> <e:mi>FN</e:mi> </e:mrow> </e:msub> </e:mrow> </e:math> symmetry. We have constructed a neutrino mass model using FN-like modular symmetry in the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi>T</i:mi> <i:mo>′</i:mo> </i:msup> </i:math> group. This model can accommodate neutrino oscillation parameters and also address other phenomena beyond the Standard Model, such as neutrinoless double beta decay and the baryon asymmetry of the Universe.