NLO QCD corrections to CP-even and CP-odd Higgs boson production via gluon fusion in the MSSM

Abstract

The calculation of the gluon fusion production cross section for the MSSM Higgs bosons is not quite as advanced as in the SM. Indeed, despite valiant efforts, a full computation of the two-loop quark-squark-gluino contributions, valid for arbitrary values of all the relevant particle masses, has not been made publicly available so far. Approximate analytic results, however, can be derived if the Higgs bosons are somewhat lighter than the squarks and the gluinos. In the MSSM this condition almost certainly applies to the lightest scalar h. Moreover, recent results from SUSY searches at the LHC set preliminary lower bounds on the squark and gluino masses just below the TeV (albeit for specific models of SUSY breaking), suggesting that there might be wide regions of the MSSM parameter space in which the condition also applies to the heavy scalar H and to the pseudoscalar A. In this thesis we presented an original calculation of the two-loop quark-squark-gluino contributions to the cross section for the gluon fusion processes gg → ø (where ø is a CP- even or CP-odd Higgs) in the limit of large supersymmetric particles masses. We exploited techniques previously developed for the computations of the MSSM CP-even Higgs boson production cross section, where the cases m2 « m2t and m2 » m2b were considered, in order to compute the cross section for MSSM CP-odd Higgs production to the same accuracy. We also extended the above mentioned techniques in such a way that no specific hierarchy is assumed between m2ø and m2t. This allowed us to obtain analytic formulae for CP-even and CP-odd Higgs production which are expected to give a better approximation of the full result when the Higgs mass is not too far from the top-pair production threshold. Our computation relies on an extensive use of the last generation of symbolic manipulation software like Mathematica and FORM. We generated the relevant two-loop diagrams through FeynArts, using a modified version of the MSSM model file, which implements the Background Field Method. Such a choice turns out to be important in the use of Pauli-Villars regularization (PVREG). The asymptotic expansions procedure requires the exact evaluation of two-loop disconnected diagrams, i:e: two loop integrals in which propagators involving both integration momenta are absent, while scalar products of the two integration momenta, raised to integer powers, can occur. For the reduction in Dimensional Regularization (DREG) of this class of integrals we developed a FORM code which performs an Integration By Parts (IBP) reduction by efficiently importing and enforcing the IBP identities generated with the software REDUZE. In the case of CP-odd Higgs production, we performed the computation by regularizing the loop integrals both in DREG and PVREG. While in the former inconsistencies are known to arise in connection with the de nition of the Dirac matrix ᵞ5 in d 6 ≠ 4 dimensions, the latter allows to avoid such di culties, at the price of a somehow greater computational effort. We obtained identical results in the two approaches. No such problems affect the computation of the contributions to CP-even Higgs productions, so in that case we adopted DREG only. For what concerns the top-stop-gluino contributions to CP-even Higgs production, we provided an original result based on an asymptotic expansion in the superparticle masses (which we generically denote by M), up to and including terms of O(m2 A / M2), O(m2t / M2) and O(m2 Z=M2), for which no results have been made available so far. A numerical study of the result of this asymptotic expansion based evaluation and its renormalization scheme dependence, as well as a quantitative comparison against the Taylor series based result, is underway and will be presented in a forthcoming publication. Regarding the contributions to CP-odd Higgs production cross section, we provided both the result of a Taylor expansion in the pseudoscalar mass, up to and including terms of O(m2 A=m2t) and O(m2 A=M2), and the result of an asymptotic expansion in the superparticle masses, up to and including terms of O(m2 A=M2) and O(m2t =M2). The latter can be easily adapted to the case of the bottom-sbottom-gluino contributions, which allowed us to provide a result valid up to and including terms of O(m2b=m2 A) and O(mb=M). We discussed how the tan β-enhanced terms in the bottom-sbottom-gluino contributions can be eliminated via an appropriate choice of renormalization scheme for the parameters entering the one-loop part of the calculation, and compared our results with those obtained in the effective-Lagrangian approximation. In both cases we obtained explicit and compact analytic results based on asymptotic expansions. All of our results can be easily implemented in computer codes for an efficient and accurate determination of the cross section for scalar and pseudoscalar production at hadron colliders. Finally, the results derived in this work for the production cross section can be straight- forwardly adapted to the NLO computation of the gluonic and photonic decay widths.