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Observability of the Higgs Boson in the Presence of Extra Standard Model Families at the Tevatron

The observability of the Higgs boson via the WW^* decay channel at the Tevatron is discussed taking into account the enhancements due to the possible existence of the extra standard model (SM) families. It seems that the existence of new SM families can give the Tevatron experiments (D0 and CDF) the opportunity to observe the intermediate mass Higgs boson before the LHC


I. INTRODUCTION
It is known that the number of fermion generations is not fixed by the standard model (SM). Asymptotic freedom of the quantum chromodynamics (QCD) suggests that this number is less than eight. Concerning the leptonic sector, the large electron positron collider (LEP) data determine the number of light neutrinos to be N= 2.994 ± 0.012 [1]. On the other hand, the flavor democracy (i.e. democratic mass matrix approach [2][3][4][5]) favors the existence of the fourth SM family [6][7][8][9].
In the Standard Model, the Higgs boson is crucial for the understanding of the electroweak symmetry breaking and the mass generation for the gauge bosons and the fermions. Direct searches at the CERN e + e − collider (LEP) yielded a lower limit for the Higgs boson mass of m H > 114.4 GeV at 95% confidence level (C.L.) [1].
In this study, we present the observability of the Higgs boson at the Tevatron and find the accessible mass limits for the Higgs boson in the presence of extra SM fermion families (SM-4, SM-5 and SM-6).

II. ANTICIPATION FOR THE FOURTH SM FAMILY
According to the SM with three families, before the spontaneous symmetry breaking, quarks are grouped into the following SU(2) x U(1) multiplets: where 0 denotes the SM basis. In one family case, e.g. d-quark mass is obtained due to the Yukawa interaction which yields where m d = a d η/ √ 2 and η = 2 m W /g W = 1/ √ 2 G F ≈ 246 GeV. In the same manner, m u = a u η/ √ 2, m e = a e η/ √ 2 and m νe = a νe η/ √ 2 if ν e is a Dirac particle.
In n-family case Before the spontaneous symmetry breaking, all quarks are massless and there are no differences between d 0 , s 0 , b 0 , etc. In other words, fermions with the same quantum numbers are indistinguishable. This leads us to the first assumption [2,3]: • Yukawa couplings are equal within each type of fermion families The first assumption results in n − 1 massless particles and one massive particle with for each type of fermion F . If there is only one Higgs doublet which gives Dirac masses to all four types of fermions (u, d, ℓ, ν), it seems natural to make the second assumption [6,8]: • Yukawa couplings for different types of fermions should be nearly equal Considering the mass values of the third SM generation the second assumption leads to the statement that according to the flavor democracy, the fourth SM family should exist. In terms of the mass matrix, the above arguments mean which leads to where m denotes the mass basis. Now let us state the third assumption: • The coupling a/ √ 2 is between e = g W sin θ W and g Z = g W / cos θ W .
Therefore, the fourth family fermions are almost degenerate, in agreement with the experimental value ρ = 0.9998 ± 0.0008 [1], and their common mass lies between 320 GeV and 730 GeV. The last value is close to the upper limit on heavy quark masses which follows from the partial-wave unitarity at high energies [10]. It is interesting to note that with the preferable value of a ≈ √ 2 g W the flavor democracy predicts the mass of the fourth generation to be The masses of the first three families of fermions, as well as observable inter-family mixings, are generated due to the small deviations from the full flavor democracy [7,11,12].
The parametrization proposed in [12] gives the values for the fundamental fermion masses and at the same time predicts the values of the quark and the lepton CKM matrices. These values are in good agreement with the experimental data. In principle, flavor democracy provides the possibility to obtain the small masses for the first three neutrino species without the see-saw mechanism [13].
The fourth SM family quark pairs will be produced copiously at the LHC [16,17] and at the future lepton-hadron colliders [18]. Furthermore, the fourth SM generation can manifest itself via the pseudo-scalar quarkonium production at the hadron colliders [19]. The fourth family leptons will clearly manifest themselves at the future lepton colliders [20,21]. In addition, the existence of the extra SM generations leads to an essential increase in the Higgs boson production cross section via gluon fusion at the hadron colliders (see [22][23][24][25] and references therein). This indirect evidence may soon be observed at the Tevatron.

III. IMPLICATIONS FOR THE HIGGS PRODUCTION
The cross section for the Higgs boson production via gluon-gluon fusion at the Tevatron is given by where τ H = m 2 H /s, g(x, Q 2 ) denotes the gluon distribution function and is the partonic cross section. The amplitude I is the sum of the quark amplitudes I q which is a function of λ q ≡ (m q /m H ) 2 , defined as [26] The numerical calculations for the Higgs boson production cross sections in the three SM family case are performed using the HIGLU software [27] which includes next to leading order (NLO) QCD corrections [28]. In HIGLU, CTEQ6M [29] distribution is selected for GeV. We also include the QCD corrections [28] in the decay of the Higgs boson by using the program HDECAY [30]. Below we deal with the mass region 115 < m H < 200 GeV, therefore the formulation of ǫ with obvious modifications for five and six SM families cases can be a good approximation. Theoretical uncertainties in the prediction of the Higgs boson production cross section originate from two sources, the dependence of the cross sections on parton distributions (estimated to be around 10%) and higher order QCD corrections. The Higgs decay width Γ(H → gg) is altered by the presence of the extra SM generations, due to this effect, the H → W W ( * ) branching ratio changes as shown in Fig. 3. The decay widths and branching ratios for the Higgs decays are calculated using HDECAY program [30] after some modifications for extra SM families. Details on how the branching ratios of all Higgs decay channels change for extra SM families can be found in [25]. In this figure 4n, 5n and 6n denote the cases of one, two and three extra SM generations with neutrinos of mass ∼ = 50 GeV, respectively. We present the numerical values of the branching ratios depending on the Higgs boson mass in Table I is due to additional H → ν 4ν4 decay channel in the latter case. The upgraded Tevatron is expected to reach an integrated luminosity of 8 fb −1 before the LHC operation, which means that SM-4 (SM-5) will be verified or excluded for the Higgs mass region m H > 140 GeV (120 GeV). However, the LHC will be able to cover the whole region via the golden mode H → ZZ → ℓℓℓℓ and detect the Higgs signal during the first year of operation if the fourth SM family exists [25].
In When L int = 2 fb −1 is reached, the Tevatron data will be able to exclude or verify SM-6 * (SM-5 * ) for the mass region m H > 150 GeV (155 GeV). With 8 fb −1 integrated luminosity, this limit changes to m H > 145 GeV (150 GeV) and SM-4 * will be observed or excluded in the range 160 GeV < m H < 195 GeV.
In Table II, we present the accessible Higgs mass limits at the Tevatron with L int = 2 fb −1 and 8 fb −1 for the extra SM families.  Another possibility to observe the fourth SM family quarks at the Tevatron will be due to their anomalous production via the quark-gluon fusion process qg → q 4 , if their anomalous couplings have sufficient strength [37]. Note that the process qg → q 4 is analogous to the single excited quark production [38].
In conclusion, the existence of the fourth SM family can give the opportunity to observe