Modular flavor symmetries and fermion mass hierarchies

A bstract We investigate fermion mass hierarchies in models with modular flavor symmetries. Several key conclusions arise from the observation that the determinants of mass matrices transform as 1-dimensional vector-valued modular forms. We demonstrate that, under some fairly general assumptions, achieving hierarchical fermion masses requires the vacuum expectation value of the modulus τ to be located near one of the critical points, i, i ∞, or ω . We also revisit the universal near-critical behavior around these points and classify the resulting mass hierarchies for the critical points i and ω . We compare the traditional Froggatt–Nielsen mechanism with its modular variant. The knowledge and boundedness of Fourier and Taylor coefficients are crucial to the predictive power of modular flavor symmetries.