Light vectorlike fermions in a minimalSU(5)setup

Abstract

The Standard Model fermion sector is enlarged by either one light singlet vectorlike down-type quark or one light vectorlike 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 vectorlike states to the Standard Model particles. Having these bounds, we investigate the impact of vectorlike 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 vectorlike quark and vectorlike 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 vectorlike fermions under consideration and discuss their viability.