Possible impact of the fourth generation quarks on production of a charged Higgs boson at the LHC

We investigate the impact of the fourth generation quarks on production and decays of the charged Higgs boson at CERN Large Hadron Collider (LHC) with triple $b$-tagging. The signal is the process $gg\to \bar{u_4}u_4$, followed by $\bar{u_4}\to W^{-} \bar{b}$ and $u_4\to h^{+} b$ decays with subsequent $h^{+}\to t \bar{b}$ and corresponding hermitic conjugates. It is shown that, if $m_{u_{4}}= 400$ GeV, considered process will provide unique opportunity to discover charged Higgs boson with mass range of 200 to 350 GeV at the first years of the LHC run.


Introduction
It is known that two-Higgs doublet model 2HDM , in general, and minimal supersymmetric extension of the standard model MSSM , in particular, predict the existence of a charged scalar particle as well as two neutral scalar particles in addition to the standard model SM Higgs boson 1 . Experimental observations of these particles could be indirect indication of SUSY. Experiments at LEPII limit the mass of a charged Higgs boson from below as 79.2 GeV 2 . The Tevatron CDF excludes masses of a charged Higgs boson below 105 and 130 GeV for tan β 1 and tan β 40, respectively, by searching t → h ± b decays 3 . Obviously, higher energy reach of the Large Hadron Collider LHC will give opportunity to search charged 2 ISRN High Energy Physics Higgs boson in wider mass region. The production of the charged Higgs boson at the LHC for three SM generation case is considered in a number of papers 4-9 .
On the other hand, flavor democracy, which is quite natural in the SM framework, predicts the existence of the fourth-generation see review 10 and references therein . The masses of the fourth-generation quarks and charged leptons are expected to be almost degenerate with preferable range of m 4 300-500 GeV. Obviously, the fourth-generation quarks in this mass region will be observed at the first few years of the LHC data taking 11-16 . Meanwhile, data collected at Tevatron experiments set limits on m u 4 and m d 4 as 358 GeV and 372 GeV, respectively 17 . Naturally, as the Tevatron searches h ± in t-quark decays, the LHC may do the same in u 4 -quark decays.
In this paper, we investigate the impact of the fourth-generation quarks on production and decays of the charged Higgs boson of 2HDM at the LHC with 14 TeV center of mass energy. In Section 2, the lagrangian describing decays of the charged Higgs is presented and the branching ratios of decays of the fourth SM generation up quark and charged Higgs boson are evaluated. The production of the charged Higgs boson at the LHC via gluon-gluon fusion process gg → u 4 u 4 , followed by u 4 → W − b and u 4 → h b decays with subsequent h → tb, as well as the SM background, is studied in Section 3. The statistical significance of the charged Higgs boson signal at the LHC is estimated assuming three b-quark jets to be tagged. Finally, concluding remarks are made in Section 4.

Charged Higgs Boson Decays
Interactions involved charged Higgs boson can be described as below 6 : where i 1, 2, 3, 4 denotes the generation index and tan β is defined as ratio of the two Higgs doublets vacuum expectation values. Applying the flavor democracy to three-generation MSSM results in tan β m t /m b ≈ 40 10 , whereas tan β m u 4 /m d 4 ≈ 1 is preferable in fourgeneration case. The Cabibbo-Kobayashi-Maskawa CKM matrix elements are not shown in 2.1 . In numerical calculations, we use CKM mixings given in 18 .
In order to compute decay widths of the charged Higgs boson, above lagrangian has been implemented into the CompHEP 19 . The decay branching ratios of the fourthgeneration up quark with mass of 400 GeV used at the rest of the paper , which is the midpoint of preferable range of u 4 mass mentioned at the Section 1, are plotted in Figure 1

Charged Higgs Boson Production at the LHC
We study the gg → u 4 u 4 → W − bbh → W − bbtb → W − bbbbW and its hermitic conjugate production process at the LHC, followed by leptonic decay of one W and hadronic decay of the other. The calculated production cross-sections with m u 4 400 GeV are plotted in Figure 3 for charged Higgs boson mass values of 200 and 300 GeV. CTEQ6L1 parton distribution functions 20 are used in numerical calculations. The SM background 6 jet 1 lepton missing energy cross-sections are computed using MadGraph package 21 . This background is potentially much larger than the signal. However, in order to extract the charged Higgs boson signal and to suppress the SM background, we impose some kinematic cuts. In addition, we assume that three b-quark jets are tagged. We choose the following set of selection cuts: P T > 80 GeV cut for at least one of b-jets and P T > 20 GeV for the rest of the jets and the lepton |η| < 2.5, where η denotes pseudorapidity, a minimum separation of ΔR Δφ 2 Δη 2 1/2 > 0.4 φ is the azimuthal angle between the lepton and the jets as well as each pair of jets. The signal and background cross-sections are given in Figure 4    The number of events-in a window of 40 GeV around selected m h ± values-for signal S , and SM background B , along with the statistical significance S/ √ B for 100 fb −1 and 10 fb −1 of integrated luminosity is presented in Tables 1 and 2  of 10 fb −1 . To compare with three SM generation case, for example, we obtain the signal significance 9.6σ with 10 fb −1 for the four-family case at tan β 40 and m h ± 300 GeV, whereas S/ √ B is 6.2 with 100 fb −1 in three SM generation case as given in 7 . The signal significance discussed here assumes perfect detector. More realistic detector future such as the effect of the realistic jet-mass resolutions as well as the method of how to choose the best combination is discussed in 9 .

Conclusion
Our study shows that the existence of the fourth SM generation provides new channel for charged Higgs boson search at the LHC. If the fourth-generation quarks and charged Higgs boson have appropriate masses, then this channel will be a discovery mode. More detailed study including higher m u 4 mass values, as well as further optimizations of cuts, detector features, and so forth, is ongoing.