SFB/CPP-07-46 TTP07-20

Higgs Decay to Gluons at NNLO

Marco Schreck and Matthias Steinhauser

Institut für Theoretische Teilchenphysik, Universität Karlsruhe (TH)

76128 Karlsruhe, Germany

Abstract

We present an analytical calculation of the next-to-next-to-leading order corrections to the partial decay width H → gg for a Higgs boson in the intermediate mass range. We apply an asymptotic expansion for M_{H} ≪ 2M_{t} and compute three terms in the expansion. The leading term confirms the results present in the literature. It is argued that our result is equivalent to an exact calculation up to M_{H} ≈ M_{t}. For a Higgs boson mass of 120 GeV the power-suppressed terms lead to corrections of about 9% in the next-to-next-to-leading order coefficient.

PACS numbers: 14.80.Bn 12.38.-t

1 Introduction

Up to date the Standard Model (SM) Higgs boson has evaded its direct detection. Electroweak precision data collected at the CERN Large Electron-Positron Collider (LEP), at the Stanford Linear Collider (SLC) and at the Tevatron at Fermilab predict a light SM Higgs boson below approximately 200 GeV. On the other hand, the direct search at LEP2 has excluded Higgs bosons below 114 GeV which leaves a relatively narrow window for the mass. A Higgs boson in this mass range, often also referred to as intermediatemass Higgs boson, predominantly decays into bottom quarks and W bosons depending whether the latter decay is kinematically allowed. A further decay channel which is of phenomenological interest is the one into gluons. At lowest order this process is mediated by a top quark loop [?, ?]. The next-to-leading order (NLO) corrections are quite large and amount to roughly 70% [?, ?, ?, ?, ?, ?]. About ten years ago the NNLO corrections have been computed in the limit of an infinitely heavy top quark mass [?,?]. Since the corrections amount to approximately 20% they increased the reliability of the perturbative expansion of the decay rate. This has been further substantiated by the recent evaluation of the NNNLO corrections [?], again in the infinite top quark mass limit, which provides a contribution of about 2%.

The calculations to NNLO and NNNLO are both based on an effective theory which results from the SM after integrating out the top quark. The effective Lagrangian is constructed from operators with dimension five which is sufficient to obtain the leading term in the heavy-top expansion. The inclusion of higher-dimensional operators would lead to powersuppressed terms. However, the renormalization of the corresponding effective Lagrangian is quite tedious. In this paper we follow a different approach and consider the Higgs-boson propagator in the full SM. Its imaginary part leads — with the help of the optical theorem — directly to the decay rate. The disadvantage of this method is that at NNLO fiveloop corrections to the Higgs two-point function have to be considered since the LO result already requires a three-loop diagram where the coupling of the Higgs boson to the gluons is mediated by two top quark triangles. They are connected by two gluon lines. The advantage of our method relies on the straightforward automatization using state-of-the-art techniques and program packages as we will show in Section ??.

An important feature of the Higgs boson decay into gluons is its affinity to the production mechanism in the gluon fusion channel. For the latter the NNLO corrections are again only known within the framework of the effective theory [?, ?, ?]. The calculation performed in the present paper gives a first hint about the potential size of the terms which are suppressed by the top quark mass.

Let us finally mention that the corresponding NNLO corrections to the decay of the Higgs boson into two photons have been obtained in Ref. [?]. Note that in this case a simple expansion of the Higgs-photon-photon vertex diagrams is sufficient to obtain powersuppressed terms the heavy M_{t}-limit. Thus only three- instead of five-loop diagrams have to be considered.