Phenomenology of on-shell Higgs production in the MSSM with complex parameters

Abstract

A computation of inclusive cross sections for the production of neutral Higgs bosons through gluon fusion and bottom-quark annihilation is presented in the MSSM with complex parameters. The predictions for the gluon-fusion process are based on an explicit calculation of the leading-order cross section for the general case of arbitrary complex parameters which is supplemented by higher-order corrections. Massive top- and bottom-quark contributions are included at NLO QCD. In the effective theory of a heavy top-quark the top-quark contribution is taken into account up to N$^3$LO QCD in an expansion around the threshold of Higgs production for the $\mathcal{CP}$-even component of the light Higgs boson. For the $\mathcal{CP}$-odd component of the light Higgs boson and the heavy Higgs bosons the contributions in the effective field theory are incorporated up to NNLO QCD. Two-loop electroweak effects mediated through light quarks are also incorporated, and SUSY QCD corrections at NLO are interpolated from the MSSM with real parameters. Finite wave function normalisation factors for the external Higgs bosons ensuring the correct on-shell properties are incorporated from the code FeynHiggs. In the numerical analysis for the typical case of a strong admixture of the two heavy Higgs bosons it is demonstrated that squark effects are strongly dependent on the phases of the complex parameters, and the relevance of the resummation of squark effects in the bottom-quark Yukawa coupling is emphasised. The remaining theoretical uncertainties in the cross section predictions are discussed. The results have been implemented into an extension of the numerical code SusHi called SusHiMi