Noninvertible symmetry as a solution to the strong C P problem in a GUT-inspired standard model

We propose a three-zero texture for the down-quark mass matrix within a S U ( 5 ) grand unified theory (GUT)-inspired Standard Model, enforced by a noninvertible selection rule originating from Z 2 gauging of Z N symmetries. Assuming C P invariance at the high-energy scale, our framework solves the strong C P problem while reproducing a realistic quark mass matrix. The C P symmetry is spontaneously broken down at an intermediate scale via complex vacuum expectation values of new scalar fields η i , which generate the C P phase in the Cabibbo-Kobayashi-Maskawa matrix without inducing the quantum chromodynamics (QCD) θ ¯ term. The present model incorporates three generations of matter, Higgs, and additional scalars with a common structure under the noninvertible symmetry, which may be naturally embedded into S O ( 10 ) GUTs at high energies.