Grand unification and the Planck scale: An $\mathit{SO}(10)$ example of radiative symmetry breaking

Abstract

Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise the Standard Model at low energies, the unified symmetry group has to be partially broken by a suitable scalar potential in just the right way. The scalar potential contains several couplings, whose values dictate the residual symmetry at a global minimum. Some (and possibly many) of the corresponding symmetry-breaking patterns are incompatible with the Standard Model and therefore non-admissible.Here, we initiate a systematic study of radiative symmetry breaking to thereby constrain viable initial conditions for the scalar couplings, for instance, at the Planck scale. We combine these new constraints on an admissible scalar potential with well-known constraints in the gauge-Yukawa sector into a general blueprint that carves out the viable effective-field-theory parameter space of any underlying theory of quantum gravity.We exemplify the constraining power of our blueprint within a non-supersymmetric SO(10) GUT containing a 16 H -and a 45 H -dimensional scalar representation. We explicitly demonstrate that the requirement of successful radiative symmetry breaking to the correct subgroups significantly constraints the underlying microscopic dynamics. The presence of non-admissible radiative minima can even entirely exclude specific breaking chains: In the SO(10) example, Pati-Salam breaking chains cannot be realised since the respective minima are never the deepest ones.

Dynamically vanishing Dirac neutrino mass from quantum scale symmetry

“…We ask whether a quantum scaleinvariant regime due to an asymptotically safe fixed point can provide such a fundamental explanation of some of the free parameters, including the neutrino Yukawa coupling. We consider asymptotic safety of gravity and matter [37,38] as a promising candidate to achieve such an explanation, because it has been found to reduce the number of free parameters in the SM [39][40][41][42][43] and beyond [44][45][46][47][48][49][50][51][52][53], to dynamically generate small scales [54] and to generate mass-splittings, e.g., between top-and bottom-quark mass [43].…”