Interplay and Correlations Between Quark and Lepton Observables in Modular Symmetry Models

In a predictive modular invariant theory of flavour there should exist correlations between the quark and lepton observables. So far these observables have been analyzed separately, making it impossible to investigate their interconnections. We perform for the first time a joint analysis of quark and lepton observables (22 altogether) in a modular flavour model. The model is based on $2O$ flavour symmetry and, within its class, it is characterized by the minimal number of free parameters (14 real constants). The joint analysis shows that the model is in good agreement with the experimental data for normal neutrino mass ordering, while predicting the leptonic Dirac CP-violating (CPV) phase ($\delta_{CP}$), the two Majorana CPV phases ($\eta_1$, $\eta_2$), the lightest neutrino mass ($m_1$) and the effective neutrino masses probed by beta and neutrinoless double beta decay ($m_\beta$ and $m_{\beta\beta}$). A detailed comparison of the separate (lepton-only and quark-only) and combined (lepton and quark) fit results shows differences in best-fit values and jointly allowed regions, that reflect a nontrivial interplay between quark and lepton observables in the model. Most importantly, our analysis highlights the existence of significant correlations between various pairs of such observables. For instance, the ratio of the strange and bottom quark masses, $r_{sb}$, is strongly negatively correlated with each of the three lepton mixing angles and with $\delta_{CP}$, $m_1$, $m_\beta$ and $m_{\beta\beta}$, while being positively correlated with $\eta_1$ and $\eta_2$. These findings, that are missed in separate analyses of quark and lepton flavour sectors, fall within ranges that can be tested by current and future experiments.