µ-Term Hybrid Inflation and Split Supersymmetry

Abstract

We consider μ-term hybrid inflation which, in its minimal format with gravity mediated supersymmetry breaking, leads to split supersymmetry. The MSSM μ-term in this framework is larger than the gravitino mass mG, and successful inflation requires mG (and hence also |μ|) & 5×107 GeV, such that the gravitino decays before the LSP neutralino freezes out. Assuming universal scalar masses of the same order as mG, this leads to split supersymmetry. The LSP wino with mass ≃ 2 TeV is a plausible dark matter candidate, the gluino may be accessible at the LHC, and the MSSM parameter tan β ≃ 1.7 in order to be compatible with the measured Higgs boson mass. The tensor-to-scalar ratio r, a canonical measure of gravity waves, can be as high as 0.001. 1 E-mail:okadan@ua.edu 2 E-mail:shafi@bartol.udel.edu Minimal supersymmetric F-term hybrid inflation employs a renormalizable superpotential W and a canonical Kahler potential K [1, 2]. The form of W is determined by a U(1) Rsymmetry, which contains the MSSM ‘matter’ parity as a Z2 subgroup. In the supersymmetric limit an underlying gauge symmetry G is spontaneously broken to a subgroup H . With minimal W and K, G breaks to H at the end of inflation. The first calculations exploited quantum corrections induced by supersymmetry breaking to drive inflation, and the scalar spectral index in this case was estimated to be ns = 1 − 1/N ≃ 0.98 [1], where N = 60 denotes the number of e-foldings necessary to resolve the horizon and flatness problems of Big Bang Cosmology. Subsequently, it was realized [3, 4] that a class of linear soft supersymmetry breaking terms also should be included in the inflationary potential, and this allows improved agreement with scalar spectral index values of ns = 0.96 − 0.97 determined by the WMAP [5] and Planck satellite experiments [6]. The importance of this linear soft supersymmetry breaking term had previously been emphasized by Dvali, Lazarides and Shafi (DLS) [7] in the context of inflation and the MSSM μ problem. The U(1) R-symmetry, following [7], prevents the appearance of the direct MSSM μ term. The latter is generated after the inflaton field acquires a non-zero VEV as a consequence of supersymmetry breaking. Assuming minimal K, the magnitude of μ is typically larger than the gravitino mass mG [7]. In this paper we explore the phenomenological implications that follow from implementing the DLS mechanism in the framework of minimal supersymmetric hybrid inflation. We will find that a consistent inflationary scenario, taking into account reheating and the cosmological gravitino constraint, yields rather concrete predictions regarding supersymmetric dark matter and Large Hadron Collider (LHC) phenomenology. In particular, the gravitino must be sufficiently heavy (mG & 5 × 10 GeV), so that it decays before the freeze out of the lightest superpartner (LSP) neutralino dark matter. A particularly compelling dark matter candidate turns out to be the wino with mass ≃ 2 TeV. The soft scalar mass parameter m0 is expected to be of the same order as mG or larger, which can reproduce a SM-like Higgs boson mass ≃ 125 GeV for suitable tan β values, where tan β is the ratio of the VEVs of the two MSSM Higgs doublets. Depending on the underlying gauge symmetry G associated with the inflationary scenario, the observed baryon asymmetry in the universe can be explained via leptogenesis [8, 9]. Compelling examples of G in which the DLS mechanism can be successfully merged with inflation include U(1)B−L and SU(2)L×SU(2)R×U(1)B−L. Other examples of G are SU(5) and SU(4)c×SU(2)L×SU(2)R [10]. The latter, however, require extra care because of the presence of monopoles and we leave this for discussion elsewhere. In the minimal supersymmetric model under discussion, inflation is associated with the