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

TL;DR

This paper proposes an $SO(10)$ grand unified model with kinetic mixing that predicts observable proton decay and gravitational wave signals from superheavy strings, consistent with recent pulsar timing data and testable in future experiments.

Contribution

It introduces a novel $SO(10)$ model with kinetic mixing at the GUT scale, linking proton decay, gravitational waves, and string phenomenology in a unified framework.

Findings

Gravitational wave spectrum matches pulsar timing array data for certain string tensions.

Proton decay rates are within reach of Hyper-Kamiokande.

Future detectors can test gravitational waves from stable strings with inflationary history.

Abstract

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.