Minimal SO(10) ante portas: the importance of being effective

Abstract

The minimal $SO(10)$ grand unified theory, augmented by higher-dimensional operators, is based on the following Higgs representations: adjoint $45_{\rm H}$, spinor $16_{\rm H}$ and complex vector $10_{\rm H}$. It was recently realized that, as opposed to the conventional wisdom, any intermediate mass scale has to lie close to the grand unification one. This bears profound consequences for the scalar particles mass spectrum and the proton decay lifetime. A complete analysis of the parameter space shows the following interesting correlation under the requirement of perturbativity of the theory: A color octet below approximately $5\,\rm TeV$ would imply a lower bound on neutrino mass $m_{\nu}\gtrsim 0.2\,\rm eV$, soon to be probed, a scalar weak triplet below $500\,\rm GeV$ and a scalar weak doublet, color triplet below $3\,\rm TeV$. If one were to stick to no flavor cancellations in proton decay amplitudes, one would recover a recent result of all these states being accessible at collider energies. Moreover, the proton decay lifetime would then be tantalizingly close to the present experimental bound.