The first construction implementing the S3 modular flavor symmetry within the Pati-Salam grand-unified framework to explain the observed masses and mixing of quarks and leptons. Matter fields are assigned as S3 doublets or singlets and Yukawa couplings are expressed as S3 modular forms of a complex modulus tau, avoiding flavon vacuum-alignment; three benchmark models fit 16 flavor observables, generate light-neutrino masses via the type-I seesaw, and predict distinctive ranges for the leptonic CP phases, the neutrino mass sum, and the neutrinoless double-beta-decay effective mass.
This particle-physics paper builds the first flavor model that combines the S3 modular symmetry with Pati-Salam grand unification to address why quarks and leptons have their observed mass hierarchie…