Towards the Swampland of Flavour Symmetries

In this thesis, we demonstrate the predictive power of the flavour models without explicit flavour symmetries, which we call the `swampland of flavour symmetries'. Firstly, we revisit the minimal type II seesaw model, which extends the Standard Model (SM) with a TeV-scale triplet scalar field. We find that certain flavour textures of the neutrino mass matrix can suppress the tightly constrained $\mu\to e$ transition rates and allow a $5-6$ TeV effective cut-off scale, even when the relevant flavour symmetries are all strongly broken. Next, we show two examples in which some SM flavour parameters are calculable, but the underlying symmetries remain implicit. (i) In the most minimal $SO(10)$ theory, although the quark-lepton symmetry does not manifest at low energies, we find that the $b-\tau$ mass ratio can be correctly predicted when the leptoquarks contained in the scalar sector lie at TeV scale, as motivated by the long-standing $B$ anomalies. (ii) We identify a new class of anomaly-free chiral symmetries in the SM (including three right-handed neutrinos), referred to as enhanced $B-L$, under which all neutrinos are massless. In this framework, the neutrino masses are not free parameters but arise solely through the dynamical symmetry breaking effects, known as neutrino condensate. Furthermore, we note that the swampland of flavour symmetries could also involve light new particles, in particular the flavourful axions. As a preliminary study, we calculate an overlooked two-loop contribution to the axion flavour violating interactions in a minimal axion model, and analyze its impact on explaining a recent excess at Belle II.