ar X iv : h ep - p h / 01 06 31 2 v 1 2 7 Ju n 20 01 The Fourth SM Family Enhancement to the Golden Mode at the Upgraded

We study the observability for a Higgs boson at upgraded Tevatron via the modes gg → h → ZZ → 4l (l = e, μ). We find that the signal can be observed at an integrated luminosity of 30 fb if the fourth SM family exists. In the Standard Model (SM) one doublet of scalar fields is assumed, leading to the existence of one neutral scalar particle h. The requirements of the stability of the electroweak vacuum and the perturbative validity of the SM allow to set upper and lower bounds depending on the cutoff scale Λ up to which the SM is assumed to be valid. Experimentally, constraints on the SM Higgs boson are derived directly from the searches at LEP2 which lead to mh > 114.3 GeV [1]. The LHC should be able to cover the full range of theoretical interest up to about 1000 GeV [2]. A Feynman diagram for the Golden Mode of Higgs production and decays through heavy quark triangle loop is shown in Fig. 1. On the other hand, SM does not predict the number of families of fundamental fermions. In the democratic mass matrix (DMM) approach SM is extended to include a fourth generation of fundamental fermions with masses typically in the range from 300 GeV to 700 GeV [3], [4] (for recent situation see [5]). The fourth SM family quarks will be produced 1 copiously at the LHC [2]. At the same time a fourth generation of fermions contributes to the loop-mediated processes in Higgs production (gg → h) and decays. In this note we consider the influence of the fourth SM family on the Higgs boson search at the upgraded Tevatron. Two relevant regions of Higgs masses, namely 125 − 165 GeV and 175 − 300 GeV, require special attention. For Higgs boson mass above 135 GeV, the decay mode h → WW becomes dominant. Hadronic final state is owerwhelmed by the QCD background, therefore, one should deal with W W ⋆ → lνjj and W W ⋆ → lνlν modes [6]. However, the channel h → ZZ is also important for the final state observation in the leptonic channel. The decay width for Higgs boson in the channel h → ZZ and its branching ratio is given in Fig. 2. In the mass range 135− 180 GeV, the width of the Higgs boson grows rapidly with increasing mh. For Higgs boson masses in the range 175 < mh < 300 GeV, the h → ZZ → 4l decay mode is the most reliable channel for the discovery of a SM Higgs boson at the upgraded Tevatron if the fourth SM family exists. The discovery potential in this channel is primarily determined by the available integrated luminosity. The leading production mechanism for a SM Higgs boson at the Tevatron is the gluonfusion process via heavy quark triangle loop pp → ggX → hX (1) There are also contributions to h production from vector boson fusion processes, which remain at a low level (2− 10)% comparing to the gluon-fusion process. Furthermore, gluon fusion process yields the largest cross section, typically a factor of four above the associated production [6], [7]. The two-loop QCD corrections enhance the gluon fusion cross section by about 80%. Therefore, we simply rescale the three-level cross sections to match the NLO result for the overall rate [8]. The results are shown in Fig. 3. In calculations we have used the CTEQ4M parton distribution functions [9]. In the case of three SM families Higgs boson 2 production cross section is roughly 1.0(0.05) pb for mh = 100(300) GeV. However, this cross section is enhanced by the factor 10(6) due to the fourth family quarks. Obviously, the same enhancement takes place for the Golden Mode and this makes the signal observable over the corresponding background. In Fig. 4, we present the cross sections for the process pp → hX → 4lX depending on the Higgs mass for three and four SM family cases. The signal is reconstructed by requiring four charged leptons 4l (l = e, μ) in final state. We use the branching ratio B(Z → ll) = 3.35 × 10 for l = e, μ. In Table I we present the number of “golden” events in the four SM family case at integrated luminosity 30 fb. The most serious background is the pair production of Z bosons, pp → ZZX(Z → ll), which has σ ≈ 8 fb and should be taken into account for mh > 2mZ . This background can be suppressed by consideration of the four-lepton invariant mass distribution. Invariant mass distributions of four charged lepton final state is given in Fig. 5 for two values of Higgs boson mass. We assume the mass window of 10 GeV around the Higgs mass. In the same Figure we present the main background coming from two Z production. In the four SM family case we use m4 = 640 GeV. Taking the mass value m4 = 320 GeV leads to negligible difference in cross sections. As can be seen from the Table II, we obtain 34 signal events against 16 background events within the mass window 10 GeV if mh = 200 GeV. The statistical significance for 4l signal is 8.3 and 5.4 for mh = 200 and 250 GeV, respectively. In conclusion, the Golden Mode will be observable for 175 < mh < 300 GeV with more than 3σ significance if the fourth SM family exists. The same statement takes place also for 125 < mh < 165 GeV, however we don’t consider this region in details because it is covered by h → WW mode [6], [7].