Rate Induced by the Top Quark

We present the two-loop QED and QCD corrections to the f f̄H Yukawa coupling that are induced by the exchange of a virtual photon or gluon, respectively, with a heavy-fermion loop inserted. As an application, we study the corresponding O(αsM H/mt ) correction to the H → bb̄ decay rate. A Higgs boson with MH ∼< 135 GeV decays dominantly to bb̄ pairs [1]. This decay mode will be of prime importance for Higgs-boson searches at LEP 2 [2], the Tevatron [3]—or a possible 4-TeV upgrade thereof [4]—, and the next ee linear collider [5]. Techniques for the measurement of the H → bb̄ branching fraction at a √s = 500 GeV ee linear collider have been elaborated in Ref. [6]. The present knowledge of quantum corrections to the H → bb̄ decay rate has been reviewed very recently in Ref. [1]. The full one-loop electroweak corrections to this process are well established [7, 8]. At two loops, the universal [9] and non-universal [10] O(αsGFmt ) corrections have recently been calculated. The pure QCD corrections are most significant numerically. In O(αs), their full mb dependence is known [11]. In O(α2 s), the first [12] and second [13] terms of the expansion in mb/M 2 H have been found. The results of Refs. [12, 13] take into account five quark flavours. In O(α2 s), there are additional contributions involving a virtual top quark, which are not formally suppressed. These corrections may be viewed as the absorptive parts of the three-loop Higgs-boson selfenergy diagrams that involve a top-quark loop, a bottom-quark loop, and two gluon lines. These diagrams may be divided in two classes: the so-called double-triangle diagrams and the the diagrams where a gluon line with a top-quark loop insertion is attached in all possible ways to the one-loop seed diagram involving the bottom quark. The first class has been considered just recently [14]. In this letter, we shall study the second class. We shall proceed along the lines of Ref. [15], where the two-loop f f̄γ vertex correction due to a virtual massive fermion, F , was derived in QED, assuming mf ≪ |s|, where s We take this opportunity to correct two misprints in the published version of Ref. [15], which are absent in the preprint. In the second line of Eq. (5), the terms −φ2 and 53/2 should be replaced by +φ and 53/3.