Linear seesaw model with a modular S4 flavor symmetry

We discuss a linear seesaw model with a field content as minimum as possible,introducing a modular S4using gauged U(1)B-Lsymmetries.Owing to the rank two neutrino mass matrix,we obtain a vanishing neutrino mass eigenvalue,and only the normal mass hierarchy of neutrios is favored via the modular S4 symmetry.In our numerical Δχ~2 analysis,we especially determine a relatively sharp prediction on the sum of neutrino masses to be approximately 60 meV,in addition to other predictions.