No-scale mu -term hybrid inflation

Abstract

To solve the fine-tuning problem in mu -term hybrid inflation, we will realize the supersymmetry scenario with the TeV-scale supersymmetric particles and intermediate-scale gravitino from anomaly mediation, which can be consistent with the WMAP and Planck experiments. Moreover, we for the first time propose the mu -term hybrid inflation in no-scale supergravity. With four scenarios for the SU(3)_Ctimes SU(2)_Ltimes SU(2)_Rtimes U(1)_{B-L} model, we show that the correct scalar spectral index n_s can be obtained, while the tensor-to-scalar ratio r is predicted to be tiny, about 10^{-10}–10^{-8}. Also, the SU(2)_Rtimes U(1)_{B-L} symmetry breaking scale is around 10^{14} GeV, and all the supersymmetric particles except gravitino are around the TeV scale, while the gravitino mass is around 10^{9}–10^{10} GeV. Considering the complete potential terms linear in S, we for the first time show that the tadpole term, which is the key for such kind of inflationary models to be consistent with the observed scalar spectral index, vanishes after inflation. Thus, to obtain the mu term, we need to generate the supersymmetry breaking soft term A^{S Phi Phi '}_{kappa } kappa S Phi Phi ' due to A^{S Phi Phi '}_{kappa }=0 in no-scale supergravity, where Phi and Phi ' are vector-like Higgs fields at high energy. We show that the proper A^{S Phi Phi '}_{kappa } kappa S Phi Phi ' term can be obtained in the M-theory inspired no-scale supergravity. We also point out that A^{S Phi Phi '}_{kappa } around 700 GeV can be generated via the renormalization group equation running from string scale. We briefly comment on the supersymmetry phenomenological consequences as well.