Broken scaling neutrino mass matrix and leptogenesis based on A4 modular invariance

In this work, we have proposed a modular A(4) symmetric model of neutrino mass which, simultaneously, explains observed baryon asymmetry of the Universe (BAU). In minimal extension of the standard model (SM) with two right-handed neutrinos we work in a supersymmetric framework. At Type-I seesaw level, the model predicts scaling in the neutrino mass matrix. In order to have correct low energy phenomenology, we propose two possible scenarios of scale-breaking in the neutrino mass matrix emanating from Type-I seesaw. Scenario-1 is based on the dimension-5 Weinberg operator whereas scenario-2 implements Type-II seesaw via scalar triplet Higgs superfields (Delta, (Delta) over bar). Interestingly, the breaking patterns in both, otherwise dynamically different scenarios, are similar which can be attributed to the same charge assignments of superfields (Delta, (Delta) over bar) and the Higgs superfield H-u under modular A(4) symmetry. The breaking is found to be proportional to the Yukawa coupling of modular weight 10 (Y-1,1'(1)0). We, further, investigates the predictions of the model under scenario-2 (Type-I+II) for neutrino mass, mixings and matter-antimatter asymmetry of the Universe. The model predicts normal hierarchical neutrino masses and provide a robust range (0.05 - 0.08)eV for sum of neutrino masses (Sigma m(i)). Lepton number violating 0 nu beta beta decay amplitude (M-ee) is obtained to lie in the range (0.04 - 0.06)eV. Future 0 nu beta beta decay experiments such as NEXT and nEXO shall pose crucial test for the model. Both CP conserving and CP violating solutions are allowed in the model. Interesting correlations are obtained, specially, between Yukawa couplings of modular weight 2 and complex modulus tau. Contrary to Y-2(2) and Y-3(2), the Yukawa coupling Y-1(2) is found to be insensitive to tau and thus to CP violation because complex modulus tau is the only source of CP violation in the model. We, also, investigate the prediction of the model for BAU. The model exhibit consistent explanation of BAU for right-handed Majorana neutrino mass scale in the range ((1 - 5) x 10(13)) GeV.