Testing realistic SO(10) SUSY GUTs with proton decay and gravitational waves

Abstract

We present a comprehensive analysis of a supersymmetric SO(10) grand unified theory, which is broken to the Standard Model via the breaking of two intermediate symmetries. The spontaneous breaking of the first intermediate symmetry, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>B</a:mi><a:mo>−</a:mo><a:mi>L</a:mi></a:mrow></a:math>, leads to the generation of cosmic strings and right-handed neutrino masses and further to an observable cosmological background of gravitational waves and generation of light neutrino masses via type-I seesaw mechanism. Supersymmetry breaking manifests as sparticle masses below the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>B</c:mi><c:mo>−</c:mo><c:mi>L</c:mi></c:math> breaking but far above the electroweak scale due to proton decay limits. This naturally pushes the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>B</e:mi><e:mo>−</e:mo><e:mi>L</e:mi></e:math> breaking scale close to the grand unified theory scale, leading to the formation of metastable cosmic strings, which can provide a gravitational wave spectrum consistent with the recent pulsar timing arrays observation. We perform a detailed analysis of this model using two-loop renormalization group equations, including threshold corrections, to determine the symmetry-breaking scale consistent with the recent pulsar timing arrays signals such as NANOGrav 15-year data and testable by the next-generation limits on proton decay from Hyper-K and JUNO. Simultaneously, we find the regions of the model parameter space that can predict the measured quark and lepton masses and mixing, baryon asymmetry of our Universe, a viable dark matter candidate and can be tested by a combination of neutrinoless double beta decay searches and limits on the sum of neutrinos masses. Published by the American Physical Society 2024

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