Gravity-assisted exact unification in minimal supersymmetric SU(5) and its gaugino mass spectrum

Minimal supersymmetric SU(5) with exact unification is naively inconsistent with proton decay constraints. However, it can be made viable by a gravity-induced nonrenormalizable operator connecting the adjoint Higgs boson and adjoint vector boson representations. We compute the allowed coupling space for this theory and find natural compatibility with proton decay constraints even for relatively light superpartner masses. The modifications away from the naive SU(5) theory have an impact on the gaugino mass spectrum, which we calculate. A combination of precision Linear Collider and Large Hadron Collider measurements of superpartner masses would enable interesting tests of the high-scale form of minimal supersymmetric SU(5). hep-ph/0312159 December 2003 The three gauge couplings of the minimal supersymmetric standard model (MSSM) unify to within 1% of each other at a high scale ∼ 2× 10GeV. Simple Grand Unified Theories (GUTs) predict such an outcome, where the low-scale gauge couplings must flow to within a small neighborhood of each other (less than few percent mismatch) at the high scale. Exact unification occurs only when all threshold corrections at the high scale are properly taken into account. The simplest supersymmetric GUT model is minimal SU(5), with matter representations {10i, 5i, 1i}, the gauge boson representation 24, and Higgs representations {24H , 5H , 5H}. Precise gauge coupling unification at the high-scale must take into account threshold corrections from heavy GUT remnants of the 24, 24H , and 5H + 5H representations. The colored Higgsino triplets Hc from the 5H + 5H representations also contribute to dangerous dimension five operators mediating proton decay [1]. A careful analysis of both gauge coupling unification and proton decay in minimal supersymmetric SU(5) concludes MHc > ∼ 10 GeV (from proton decay constraints) (1) MHc ≃ few × 10 GeV (from gauge coupling unification constraints) (2) if superpartner masses are in the TeV region. This has led to the conclusion that minimal SU(5) is dead [2, 3, 4] or perhaps at least highly constrained with superpartner masses in the 10TeV range [5] which strains its ability to naturally explain the electroweak symmetry breaking scale. 1 In this letter we wish to point out two conclusions we have come to recently, apropos to the discussion above. First, similar to the effects found in Refs. [7]-[13] we have found that expected non-renormalizable gauge-kinetic operators in the GUT theory can redeem minimal SU(5) without requiring unnaturally large coefficients. Second, we have computed the imprint of this effect on the gaugino masses, and found the resulting magnitudes of their relative shifts at the GUT scale to be within the sensitivities of future and planned colliders. Minimal SU(5) as a purely renormalizable supersymmetric theory was never viable because unification of down-quark Yukawa couplings with lepton Yukawa couplings does not work for the first two generations. It has been understood for a very long time now that non-trivial non-renormalizable operators (NROs) are needed. This is no extraordinary burden on the theory, however, as the Planck scale is not far from the GUT scale and There exist other SU(5) models that are consistent with both gauge coupling unification and proton decay. For example, see Ref. [6].