A Precise Determination of tanβ from Heavy Charged Higgs Decay

We compute the energy spectrum of charged leptons in the decay H+ → b̄ + (t → blνl). The shape of the lepton spectrum obtained, and also the mean lepton energy, are sensitive to the handedness of the intermediate top quark. This sensitivity can be used to precisely determine tan β, a fundamental parameter of two Higgs doublet models. PACS numbers: 14.80.Gt, 12.15.Cc Address after July 1st, 1994: Institut für Theoretische Teilchenphysik, Universität Karlsruhe, D-76128 Karlsruhe, Germany Precision measurements of electroweak parameters and the strong coupling constant (αs) at LEP [1] are completely consistent with the minimal supersymmetric extension to the standard model (MSSM), with a MSSM mass scale of around 1 TeV [2]. In the MSSM the single standard model (SM) complex scalar doublet, or Higgs doublet, is replaced by two Higgs doublets (for a review see ref. [3]). After spontaneous symmetry breaking the MSSM Higgs sector consists of: two CP-even bosons h and H (mh0 < mH0); a CP-odd boson A ; and two charged scalars H. The presence of a Higgs sector that includes two doublets is a feature of most supersymmetric models. In models with only Higgs doublets (and singlets) there is no coupling of the charged Higgs to vector boson pairs (WZ or Wγ) at tree level. The most important decay channels of the H are into fermion pairs or into Wh. However, H decays into states involving charginos can, in some regions of the parameter space, be quite large [4]. For a H with mass (mH±) greater than the sum of top and bottom quarks (mt+mb) the dominant decay process isH + → tb̄. A future linear ee collider would be an ideal place to search for the decay H → tb̄. However, in practice, planned machines are limited to beam energies around 500 GeV. Recent studies [5, 6] indicate that it is feasible to also search for a H (with mH± > mt) at hadron colliders, such as the LHC, over a large region of the available parameter space. In the present letter we observe that a charged Higgs boson of the Minimal Supersymmetric Model significantly heavier than the top quark offers an opportunity to precisely measure the fundamental parameter of a two Higgs doublet model, namely the ratio of vacuum expectation values of the two doublets, tanβ ≡ v2/v1. The reason for this lies in the structure of the coupling of the charged Higgs boson to tb quarks: L = gVtb √ 2mW Ht̄ [mt cotβL+mb tanβR] b+H.c., (1) where R,L = (1 ± γ5)/2, mW is the mass of the W boson, g is the weak coupling constant, and Vtb is the relevant element of the CKM matrix. From this Lagrangian we can see that the ratio of numbers of left and right polarized top quarks produced in the decay H → tb̄ depends on the coefficients of left and right chiral projection operators L,R. At the tree level: NL NR = ( mb mt )2 tan β, (2) where NL(R) are the partial rates of production of left (right) handed top quarks. If H is significantly heavier than the top quark, so that in its decay the top is emitted with large velocity, we can determine the handedness of the top quark by analyzing the energy spectrum of the charged lepton produced in the semileptonic decay of t [7]. We see from the equation (2) that the ratio NL/NR is very sensitive to the value of tanβ. However, in practice this means that using this method one will only be able to determine the precise value of tan β over a limited range. For extreme values of tanβ the top quark will be produced exlusively in one polarization state, tR for small tanβ and tL for large. Examination of the lepton spectrum will then be useful to determine the order of magnitude of tanβ.