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Light vector-like fermions in a minimal SU(5) setup

The Standard Model fermion sector is enlarged by either one light singlet vector-like down-type quark or one light vector-like lepton doublet, which might be accommodated within a five-dimensional representation of SU(5). At low energies the inclusion of these states affects precisely measured observables in flavor physics, as well as electroweak precision measurements. These experimental results strongly constrain couplings of vector-like states to the Standard Model particles. Having these bounds, we investigate the impact of vector-like fermions on the mass matrices for down-type quarks and charged leptons in an SU(5) setting. We find that unitary transformations relating an arbitrary flavor basis to the mass eigenstate basis depend only on three free parameters. Then we discuss the parameter space constrained by low-energy data assuming vector-like quark and vector-like lepton masses to be 800 GeV and 400 GeV, respectively. We demonstrate that these two scenarios generate unique patterns for relevant proton decay widths. A further improvement of experimental bounds on proton decay modes would thus differentiate the allowed parameter space. We finally present two full-fledged SU(5) models that allow for gauge coupling unification with light vector-like fermions under consideration and discuss their viability.