Grand unification through gravitational effects

New paper! This is a followup to our earlier work 0805.0145, which characterized the size of uncertainties in coupling constant unification due to unknown short distance physics such as quantum gravity. In the new paper we show that non-supersymmetric SU(5) and SO(10) models can be made to unify for reasonable (natural) sizes of short distance effects. This raises the question of whether successful unification in supersymmetric models should be taken as strong evidence in favor of low-energy supersymmetry, as has been argued.

Grand unification through gravitational effects

Xavier Calmet, Stephen D. H. Hsu, David Reeb

We systematically study the unification of gauge couplings in the presence of (one or more) effective dimension-5 operators cHGG/4MPl, induced into the grand unified theory by gravitational interactions at the Planck scale MPl. These operators alter the usual condition for gauge coupling unification, which can, depending on the Higgs content H and vacuum expectation value, result in unification at scales MX significantly different than naively expected. We find non-supersymmetric models of SU(5) and SO(10) unification, with natural Wilson coefficients c, that easily satisfy the constraints from proton decay. Furthermore, gauge coupling unification at scales as high as the Planck scale seems feasible, possibly hinting at simultaneous unification of gauge and gravitational interactions. In an appendix we work out the group theoretical aspects of this scenario for SU(5) and SO(10) unified groups in detail; this material is also relevant in the analysis of non-universal gaugino masses obtained from supergravity.

From the introduction to the paper:

What are the boundary conditions for grand unification? One typically assumes that the gauge couplings of the broken subgroups must become numerically equal at the unification scale MX [1]. However, effects from physics above the unification scale can alter the gauge coupling unification condition. In an effective field theory approach, such effects can be caused by dimension-5 operators of the form c H Gµν Gµν /4MPl , which shift the coefficients of the gauge kinetic terms in the low-energy theory after the Higgs H acquires a vacuum expectation value in grand unified symmetry breaking [2, 3]; one obvious source of such operators is quantum gravitational effects. Indeed, it would be unnatural (or require some special explanation) to assume that the Wilson coefficients c above be zero or especially small [4]; the default assumption should be that these coefficients are of order unity in grand unified models, with consequent unification conditions.

In conventional unification models, one might expect $< H > \sim 10^16$ GeV, plausibly leading to effects from quantum gravity of order a fraction of a percent, $< H > / MPl \sim 10^{−3}$, on the gauge coupling unification condition. In [5] we showed that these dimension-5 operators can be even more relevant than previously suspected since the Planck mass MPl tends to be smaller than naively assumed due to its renormalization group evolution [6, 7] under the influence of the large number of fields in supersymmetric grand unified theories. It was noted [5] that these dimension-5 operators introduce in supersymmetric unification models an uncertainty that can be bigger than the two-loop effects which are considered to be necessary to obtain good numerical unification of the gauge couplings.

The aim of this paper is different. We study whether the dimension-5 operators discussed above can lead to perfect gauge coupling unification without supersymmetry by their modifying the gauge coupling unification condition. This unification scheme has been studied previously in the literature for models with and without supersymmetry, e.g. in [2, 3, 5, 8–13], but in less detail and generality and mostly only the effect from a single gravitational operator has been considered. ...