Leptogenesis, $0\nu \beta \beta$ and lepton flavor violation in modular left-right asymmetric model with polyharmonic $Maa\beta$ forms

In the absence of supersymmetry, modular forms need not be holomorphic functions of the modulus $\tau$. Using this idea, we construct a non-supersymmetric framework using polyharmonic $Maa\beta$ forms. In this approach, the Yukawa coupling is no longer strictly holomorphic in $\tau$ but instead incorporates both holomorphic and non-holomorphic components. We realize a non-supersymmetric, left-right asymmetric model based on the ${\mathrm{\Gamma }}_3$ modular group, where the active neutrino masses are generated via an extended inverse seesaw mechanism. The model successfully predicts the sum of neutrino masses below the current experimental bound and accommodates neutrino mixing angles within the $3\sigma$ range. Given its strong predictive power in neutrino oscillation parameters, we further explore its implications for beyond Standard Model (BSM) phenomena, including neutrinoless double beta ($0\nu \beta \beta$) decay, lepton flavor violation (LFV), and baryogenesis via leptogenesis (BAU). Our findings indicate that the model predicts an effective Majorana mass and LFV branching ratios consistent with experimental constraints while also providing a viable explanation for the observed baryon asymmetry through resonant leptogenesis.