Tevatron constraints on the Higgs boson mass in the fourth-generation fermion models revisited

Recent Tevatron exclusion interval of the masses of Higgs boson considerably reduces in case of the light quasistable fourth generation neutral lepton.

If the fourth sequential quark-lepton generation does exist then the cross section of Higgs boson production at hadron colliders is considerably enhanced in comparison with that in Standard Model (SM) [1]. This result was used in a recent Tevatron paper according to which a standard-modellike Higgs boson in the mass interval 131 GeV < m H < 204 GeV (1) is excluded at the 95% Confidence Level in the model with the fourth generation [2]. The statement about exclusion follows from Fig. 4c of [2], where an experimental upper bound on the product σ(gg → H) × Br(H → W + W − ) is compared with the theoretical prediction for this product. The result obtained in [2] strongly depends on the lower mass bounds on the fourth generation fermions. The point is that the new decay channel H → ff opens if a mass of any of these new particles is less than m H /2. Then Br(H → W + W − ) diminishes and the exclusion interval of m H reduces. Concerning the fourth generation quarks we know from Tevatron that their masses are larger than 300 GeV [3]. The mass of the charged lepton m E is bounded to be above 100 GeV by LEP II, so the decay H → E + E − practically does not occur for m H from the excluded domain. For the fourth generation neutrino a lower bound on its mass m N > 80 GeV obtained at LEP II [4] is used in [2]. In [2] two scenarios are considered: m N = 80 GeV (low mass scenario) and m N ≫ 80 GeV (high mass scenario). The above mentioned exclusion interval of m H refers to low mass scenario; for high mass scenario an exclusion interval of m H stretches till m H = 208 GeV.
The aim of the present note is to stress that a lower bound m N > 80 GeV [4] is applicable only to the case when the mixing angle of the fourth generation neutral lepton with at least one neutral lepton from three light generations is larger than 3 · 10 −6 . In this case N decays to charged leptons from the first three generations inside L3 detector. For smaller mixing angles (quasistable N) the mass of N is bounded only from the analysis of Z boson decays, m N > 46.7 GeV [5]. 1 If the decay of Higgs boson to a pair of heavy neutral leptons is kinematically allowed, then it dominates [6]. In [7] we study how Standard Model Higgs boson branching ratios is changing in the presence of light N.
In Fig. 1 we compare the branching ratios of Higgs to WW calculated with modified HDECAY code [8] for m N = 80 GeV, m E = 100 GeV, m U = 450 GeV, m D = 400 GeV (black curve) with the branchings used in [2] (red curve). The agreement between two calculations is very good. In Fig. 2 the same branching ratios for m N = 46.7 GeV are shown.
In the Table we present the branching ratios of H → W + W − decays for m N = 80 GeV and for m N = 46.7 GeV for m H from 110 to 300 GeV.  Figures 4(c-d) and Tables I-II of [2] we obtain the following model independent exclusion interval: 155 GeV < m H < 204 GeV excluded at 95% C.L. .
Our second comment refers to the case of m N > 80 GeV. Fourth generation change considerably the constrains on m H from electroweak precision data. In particular, one can choose the values of the fourth generation masses so, that heavy Higgs is allowed. Only an upper bound m H < ∼ 1 TeV from perturbative unitarity [9] remains. In [10] we study the value of m H (where minimum of χ 2 of the electroweak data fit occurs) as a function of the mass of the neutral lepton N. According to Fig. 5 from [10] for the case of one extra generation and the fourth lepton heavier than 80 GeV, Higgs boson mass less than 240 GeV corresponds to the χ 2 minimum. It would mean that a considerable part of the allowed interval of m H is depreciated by the bound (1) valid for m N > 80 GeV. However, in the analysis of paper [10] we neglect a possible CKM type mixing of the fourth generation quarks with the quarks of three "light" generations. This mixing was taken into account in the recent paper [11] with the following result: for m N = 101 GeV and sine of quark mixing angle s 34 ∼ 0.1 ÷ 0.2 the value of m H up to 600 GeV is allowed. At the absence of mixing in accordance with our results [10] Tevatron bound (1) almost excludes the existence of the fourth generation with heavy N. However the conclusion of [11] that zero CKM mixing s 34 is excluded is not valid for the interval of heavy neutrino masses m N = 46.7 − 70.0 GeV.
In a very interesting recent paper [12] the fourth generation with extremely small mixing with lighter three generations is considered. The main issue of [12] is the preservation of baryon and lepton asymmetries against sphaleron erasure in this model. The fact that the exclusion interval of the higgs boson masses (1) diminishes to (2) in case of the quasistable N enlarge the allowed parameter space which could be used in [12]. The bounds from the EW precision data are discussed for the case of light N in the ST U formalism in [12]. In [10] we specially address an issue of inaplicability of ST U formalism in the case of light N. The use of the proper parameters (V i or S ′ , T ′ , U ′ ) would change the allowed domain in the m U − m D plot (Fig 1) of [12].
In summary, we demonstrated that model independent exclusion interval of the values of Higgs boson masses from Tevatron direct searches in case of fourth generation is reduced to 155 GeV < m H < 204 GeV, by allowing small heavy neutrino masses m N = 45.7 − 80.0 GeV.
M.V. is partially supported by the grant N-Sh 4172.2010.2 and the contract 02.740.11.5158 of the Ministry of Education and Science of the RF.