Resonant leptogenesis in inverse see-saw framework with modular S4 symmetry

Abstract We introduce a lepton mass generation and flavor mixing model, realized through a (2,3) inverse seesaw structure based on modular $$ S_4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> symmetry. The model employs modular forms to construct the lepton Yukawa couplings, significantly simplifying the framework by reducing redundant parameters. A detailed numerical analysis demonstrates consistency with current neutrino oscillation data, yielding specific outputs for the mixing angles and CP-violating phases. The Dirac CP phase is predicted to lie near $$\delta _{\textrm{CP}} \approx \pm 90^\circ $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>δ</mml:mi> <mml:mtext>CP</mml:mtext> </mml:msub> <mml:mo>≈</mml:mo> <mml:mo>±</mml:mo> <mml:msup> <mml:mn>90</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:mrow> </mml:math> , corresponding to near-maximal leptonic CP violation. The total neutrino mass lies within $$\sum m_\nu \approx 0.0587\text {--}0.0924$$ <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:mi>ν</mml:mi> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>0.0587</mml:mn> <mml:mtext>--</mml:mtext> <mml:mn>0.0924</mml:mn> </mml:mrow> </mml:math> eV, and the effective Majorana mass $$|m_{ee}| \approx (0.002\text {--}0.02)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi>ee</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>|</mml:mo> <mml:mo>≈</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>0.002</mml:mn> <mml:mtext>--</mml:mtext> <mml:mn>0.02</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:mrow> </mml:math> eV, within reach of upcoming neutrinoless double beta decay experiments such as nEXO and AMoRE-II. The model also remains consistent with current bounds on charged lepton flavor violating processes from MEG and BaBar. We further explore resonant leptogenesis enabled by quasi-degenerate heavy neutrino states and show that the observed baryon asymmetry of the universe can be successfully generated in this scenario. The combined treatment of low-energy observables and high-scale baryogenesis demonstrates the predictivity and testability of the modular $$ S_4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> -based ISS(2,3) framework.