Kinetic Mixing, Proton Decay and Gravitational Waves in SO(10)

We present an SO (10) model in which a dimension five operator induces kinetic mixing at the GUT scale between the abelian subgroups U (1) ₁-₋ and U (1) R. We discuss in this framework gauge coupling unification and proton decay, as well as the appearance of superheavy quasistable strings with G 10^-8 - 10^-5, where denotes the dimensionless string tension parameter. We use Bayesian analysis to show that for G values 4 10^-7 - 10^-5, the gravitational wave spectrum emitted from the quasistable strings is in good agreement with the recent pulsar timing array data. Corresponding to G values 10^-8 - 2 10^-7, proton decay is expected to occur at a rate accessible in the Hyper-Kamiokande experiment. Finally, we present the gravitational wave spectrum emitted by effectively stable strings with G 10^-8 that have experienced a certain amount of inflation. This can be tested with future detectors in the Hz frequency range.