Enhanced Three-Body Decay of the Charged Higgs Boson

If the charged Higgs boson H+ exists with mH+ < mt+mb, the conventional expectation is that it will decay dominantly into cs̄ and τντ . However, the three-body decay mode H+ → W+bb̄ is also present and we show that it becomes very important in the low tan β region for mH+ ∼ > 140 GeV. We then explore its phenomenological implications for the charged-Higgs-boson search in top-quark decay. The discovery of the top quark at the Tevatron collider [1,2] has generated a good deal of current interest in the search for new particles in the decay of the top-quark. In particular, top quark decay is known to be a promising reaction to look for the charged Higgs boson of a two-scalar doublet model and, in particular, the minimal supersymmetric standard model (MSSM) [3]. In the diagonal CKM matrix approximation the MSSM charged Higgs boson couplings to the fermions are given by L = g √ 2 mW H [cotβ mu iūidiL + tanβ md iūidiR + tan β m` iν̄i`iR] + h.c. (1) where tanβ is the ratio of the vacuum expectation values of the two scalar doublets and the index i labels the quark and lepton generation. This interaction implies a large Htb Yukawa coupling when 1 tanβ∼ < 1 and tanβ∼ >mt/mb (2) where one expects a large branching fraction for t → bH decay (given mt > mH+). Interestingly the regions tanβ ∼ 1 and ∼ >mt/mb are favored by SUSY-GUT models for a related reason – i.e. the unification of the b and τ masses which requires a large negative contribution from the top Yukawa coupling to the renormalization group equation [4]. It should be noted here that the perturbation theory limit on the Htb Yukawa coupling requires 0.2 < tanβ < 100 (3) while the GUT scale unification constraint implies stricter limits 1 ≤ tanβ ≤ mt/mb (4) which are also required if one assumes the perturbation theory limit on the Yukawa coupling to remain valid up to the GUT scale [5]. Without any GUT scale Ansatz, however, the allowed region of tan β extends down to 0.2. We shall assume only the particle content of the MSSM Higgs sector but no constraints from GUT scale physics. Our analysis will remain valid in any two-Higgs doublet model satisfying the coupling pattern of the MSSM as given by (1); i.e. the so-called class II models [6]. For mt > mH+ the dominant decay modes are usually assumed to be the two body decays H → cs̄, τν. The corresponding widths are Γcs = 3gmH+ 32πmW ( mc cot 2 β +ms tan 2 β ) (5) Γτν = gmH+ 32πmW mτ tan 2 β (6) The leading QCD correction is taken into account by substituting the quark mass parameters for eqs. (1) and (5) by the running masses at the H mass scale. Its most important effect is to reduce the charm quark mass mc from 1.5GeV to 1GeV [7]. Consequently the two rates are approximately equal when tanβ ∼ 1; the τν (cs) rate dominates when tanβ > 1 (tanβ < 1). 2 In this note we shall consider the phenomenological implications of a very important 3-body decay channel of the Higgs boson, namely