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)B-L 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 Gμ ~ 10⁻⁸ - 10⁻⁵, where μ denotes the dimensionless string tension parameter. We use Bayesian analysis to show that for Gμ 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 μ 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 Gμ≈ 10⁻⁸ that have experienced a certain amount of inflation. This can be tested with future detectors in the μHz frequency range.