hep-ph/0107333 Supersymmetric corrections to Higgs decays and b → sγ for large tan β

If tan β is large, supersymmetric QCD corrections can become large, putting naive perturbation theory into doubt. I show how these tan β-enhanced corrections can be controlled to all orders in αs tan β. The result is shown for the decays H + → tb and b → sγ. 1 Large corrections to all orders The Minimal Supersymmetric Standard Model (MSSM) contains two Higgs doublets H u and H d. Their neutral components acquire the vacuum expectation values v u and v d with v ≡ v 2 u + v 2 d = 174 GeV. Recently scenarios with large tan β ≡ v u /v d (corresponding to v d ≪ v u ≃ 174 GeV) have attracted increasing attention: this region of the parameter space is experimentally least constrained by the bounds from Higgs searches at LEP 1. A theoretical motivation for large tan β scenarios stems from GUT theories with bottom–top Yukawa unification, which require tan β = O(50) 2,3. At tree-level right-handed down-quark fields do not couple to H u and the bottom quark mass is related to the corresponding Yukawa coupling h b by m b = h b v d = h b v cos β. For large tan β this has two important consequences: first h b is large, of order 1. Second, radiative corrections to the couplings of Higgs bosons to b quarks proportional to h b sin β can occur. These are enhanced by a factor of tan β compared to the tree-level result and stem from the supersymmetry breaking terms. The dominant tan β-enhanced corrections are supersymmetric QCD (SQCD) contributions, i.e. loop diagrams with squarks and gluinos. Observables can be affected by these large corrections in two ways: I The leading order contribution is proportional to cot β. This suppression is lifted in the loop corrections of the next-to-leading order (NLO). II tan β-enhanced corrections enter the counterterms, which appear in higher order corrections .