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 $G\mu \sim 10^{-8} - 10^{-5}$, where $\mu$ denotes the dimensionless string tension parameter. We use Bayesian analysis to show that for $G\mu$ values $\sim 4 \times 10^{-7} - 10^{-5}$, the gravitational wave spectrum emitted from the quasistable strings is in good agreement with the recent pulsar timing array data. Corresponding to $G \mu$ values $\sim 10^{-8} - 2 \times 10^{-7}$, 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 $G\mu\approx 10^{-8}$ that have experienced a certain amount of inflation. This can be tested with future detectors in the $\mu$Hz frequency range.