The Standard Model (SM) predicts the gauge boson masses well via spontaneous symmetry breaking, while the fermion masses are parameters parametrised by the Yukawa coupling constants. In string theory, string compactifications on tori and orbifolds can lead to modular invariant theory, and the Yukawa couplings are modular forms. The string theory inputs thus can reduce the arbitrariness of the Standard Model, as the forms of the Yukawa couplings are limited and are linear combinations of the modular basis of the modular space.
To address the Standard Model’s prediction of non-zero neutrino masses, I modified the particle content by adding heavy neutrinos to the SM fields and considered the dimension-5 Weinberg operator. As a result, group theory gives the masses for the observable light neutrinos that were in the Standard Model, by the so-called see-saw formula, m = – y_D^T M_N^{-1} y_D, where y_D and M_N are the Dirac and the Majorana masses of the heavy neutrinos, respectively. Therefore, when the Majorana masses of the heavy neutrinos are large, the masses for the light neutrinos are small, explaining the unexpected light neutrino masses in particle physics.
I further investigated the necessary cancellation of the singularity in the observable light neutrino masses, and I compared the Weinberg operator obtained from integrating out heavy messenger fields and by symmetry.
Lin Feng 