Precision unification and proton decay in F-theory GUTs with high scale supersymmetry

Abstract

F-theory GUTs provide a promising UV completion for models with approximate gauge coupling unification, such as the (non-supersymmetric) Standard Model. More specifically, if the superparters have masses well above the TeV scale, the resulting imperfection in unification can be accounted for by the, in principle calculable, classical F-theory correction at the high scale. In this paper we argue for the correct form of the F-theory corrections to unification, including KK mode loop effects. However, the price of compensating the imprecise unification in such High Scale SUSY models with F-theory corrections is that the GUT scale is lowered, potentially leading to a dangerously high proton decay rate from dimension-6 operators. We analyse the possibility of suppressing the decay rate by the localization of X, Y gauge bosons in higher dimensions. While this effect can be very strong for the zero modes, we find that in the simplest models of this type it is difficult to realize a significant suppression for higher modes (Landau levels). Notably, in the absence of substantial suppressions to the proton decay rate, the superpartners must be lighter than 100 TeV to satisfy proton decay constraints. We highlight that multiple correlated signals of proton decay could verify this scenario.

Pseudo-Dirac Higgsino dark matter in GUT scale supersymmetry

“…This along with the splitting between the masses of bino and other gauginos allow SUSY breaking scale to be raised all the way up to the GUT scale without causing instability in the electroweak vacuum or entering into the conflict with the observed Higgs mass. Our framework is, therefore, different from the standard split or high-scale SUSY scenarios, see for example [9,14,47], in which the supersymmetry breaking scale is restricted to appear at the intermediate scales.…”

“…(6) with matching conditions, Eqs. (9,10), at the gaugino mass scales. The decoupling of bino and wino from the spectrum also leads to threshold corrections in the quartic couplings at the respective scales.…”

“…It may be possible that both the supersymmetry and unified gauge symmetry are broken by a common mechanism leading to the SUSY breaking scale, M S , equal or close to the GUT scale. For example, this is often realized in SUSY GUT models constructed in more than four spacetime dimensions (see for example [4][5][6][7][8][9][10]) in which orbifold compactification can administer complete breaking of SUSY as well as the underlying gauge symmetry. Given the SUSY theory at M S , the properties of the observed Higgs and stability of the electroweak vacuum strongly restrict the nature of the effective theory below M S .…”

Towards the Standard Model in F-theory

“…Such relations have been studied in the perturbative Type IIA framework in [15]. The need for the moduli to obey such relations might seem ad hoc to GUT model builders; on the other hand even in GUT realisations of string theory important corrections, in the example of F-theory due to hypercharge flux or Kaluza-Klein states [8,103,[146][147][148], render unification less non-trivial than one might think.…”

High-scale supersymmetry, the Higgs boson mass, and gauge unification

“…Previous studies have indicated that in order for SUSY to be reconciled with the observed Higgs mass, there are constraints from the requirement that unification at the high scale still occur [3][4][5][6]. There are also experimental lower limits [7][8][9][10], and theoretical studies of upper limits on the scale of superpartners [4,[11][12][13][14][15][16][17][18][19][20][21]. However, for the most part, these studies have been concerned with determining approximate limits on the SUSY breaking scale in setups where the SUSY spectrum is close to degenerate.…”