Anomalous Single Production of the Fourth Generation Neutrino at Future ep Colliders

Possible single productions of the fourth standard model generation neutrino via anomalous interactions at the future ep colliders are studied. Signatures of such anomalous processes and backgrounds are discussed in detail. Discovery limits for neutrino mass and achievable values of anomalous coupling strength are determined.


I. INTRODUCTION
It is known that the Standard Model (SM) does not predict number of fundamental fermion generations. This number is restricted from below with LEP I data on invisible decays of Z boson as n g ≥ 3 [1]. On the other hand, n g < 9 from asymptotic freedom of QCD. According to recent precision electroweak data, existence of three or four SM generations is at the same status [2][3][4].
The flavor democracy is a natural hypothesis in the framework of SM as well as a number of models dealing with new physics (see review [5] and references therein). Concerning Standard Model, flavor democracy predicts the existence of a heavy fourth SM generation [6][7][8]. The Dirac masses of the new fermions are predicted to be almost degenerate and lie between 300 and 700 GeV, whereas, the masses of known fermions belonging to lighter three generations appear due to small deviations of the democracy [9][10][11]. The quark masses and CKM matrix are given in [9,10]. Ref. [11] gives both masses and CKM matrix (MNS matrix for leptons) for both quarks and leptons.
Obviously, TeV energy colliders are needed for discovery of the fourth SM generation fermions. The fourth generation quarks will be produced in pairs copiously at the Large Hadron Collider (LHC) [12,13]. Recently, this process is proposed as the best scenario (after Higgs) for discovery at the LHC [14][15][16]. Linear lepton colliders are the best place for pair production of the fourth generation charged lepton and neutrino [11,17,18]. However, discovery limits for pair production at lepton colliders are 2m < √ s. For example, International Linear Collider (ILC) with 500 GeV center of mass energy will cover m < 250 GeV.
The discovery capacity of lepton collider could be enlarged if the anomalous interactions of the fourth generation fermions with the first three ones exist. Such anomalous interactions seems to be quite natural due to large masses of the fourth generation fermions (see argumentation for anomalous interaction for t quark presented in ref. [19]). These anomalous interactions could provide also single production of the fourth generation fermions at future lepton-hadron colliders (see review [20] and references therein). Depending on the center of mass energy lepton-hadron colliders are named QCD Explorer with √ s = 1.4 TeV and Energy Frontier ep collider with √ s = 3.74 TeV [20][21][22][23][24][25][26][27].
Recently, anomalous production of the fourth generation charged lepton and neutrino at future ep colliders is considered in [28] and [29], respectively. Unfortunately results of the latter one are erroneous due to the wrong Lagrangian for ν 4 eW interactions. Therefore, anomalous production of the fourth generation neutrino at future ep colliders should be reconsidered. This is the aim of this study.

II. ANOMALOUS INTERACTIONS OF THE FOURTH SM GENERATION NEU-TRINO
The charged current Lagrangian for SM and the anomalous interactions of the fourth generation neutrino can be rewritten from [30,31] with minor modifications as: The main error of corresponding Lagrangian in [29] is absence of the MNS matrix element |V ν 4 l i |. Furthermore, the neutral current Lagrangian for the anomalous interactions of the fourth generation neutrino is In Eq's (1) and (2), κ ν 4 l i W and κ ν 4 ν i Z are the anomalous couplings for the charged and neutral currents with a W boson and a Z boson, respectively (in numerical calculations, we suppose . Λ is the cutoff scale for the new physics and P L is the left handed projection operator; g W and g Z are the electroweak coupling constants. In the above equations Obviously new interactions will lead to additional decay channels of the fourth family neutrino in addition to enhancement of some SM decay channels. In order to compute decay widths, we have implemented the new interaction vertices into the CompHEP [32]. Results of the calculations for different decay channels of ν 4 assuming (κ/Λ) = 1 TeV −1 are given in Table I. Experimental upper limit for |V ν 4 l i | is 0.02 [4]. Therefore, while calculating values in Table I, Table I as well as Figure 1 practically do not change).    Fig. 2 and Fig. 3, respectively. We consider ep → ν 4 X → µW X and ep → ν 4 X → eW X processes as signatures of anomalous interactions of the fourth generation neutrino. In order to extract the fourth generation neutrino signal and to suppress the background, we impose cuts on the eW invariant mass. Following [29], cuts of |m eW − m ν 4 | < 25 GeV for the mass range m ν 4 = 100 − 1000 GeV and |m eW − m ν 4 | < 50 GeV for the mass range of 1 − 2.6 TeV together with p q,l T > 10 GeV are applied. In numerical calculations CTEQ6L parton distribution functions are used [33]. The first process can be detected easily at ep colliders due to no background. Number of events for this process at TeV are presented in Table II and III, respectively. The computed signal and background cross-sections for the second process are given in Tables IV and V     Since the process ep → ν 4 X → µW X has no SM background one can use 10 events as a discovery limit. As seen from Table II, QCD Explorer will reach m ν 4 = 850 GeV (1100 GeV) with integrated luminosity of 1 fb −1 (10 fb −1 ) for (κ/Λ) = 1 TeV −1 . Corresponding limit for Energy Frontier is 1300 GeV (2100 GeV) with L int = 100 pb −1 (1 fb −1 ). Achievable For the process ep → ν 4 X → eW X we require SS > 5 as a discovery criterion. It is seen from Tables IV and V, that QCD Explorer will cover masses of the fourth generation neutrino up to 750 GeV (950 GeV) with L int = 1 fb −1 (10 fb −1 ), whereas Energy Frontier ep collider will extend the mass region up to m ν 4 = 950 GeV (1900 GeV) with L int = 100 pb −1 (1 fb −1 ). Figure 5 show that this channel is less promising than above one concerning achievable values of anomalous coupling strength.

IV. CONCLUSION
Combining results of studies on anomalous single production of the fourth SM generation charged lepton [28] and neutrino (this study) at future ep colliders we conclude that they have promising potential on the subject. For example, if m ν 4 = m l 4 = 500 GeV and (κ/Λ) = 1TeV −1 , the numbers of produced events are 740 for ep → ν 4 X → eW X and 1100 for ep → l 4 X → eZX at √ s = 1.4 TeV with L int = 10 fb −1 . Finally, QCD Explorer cover m ν 4 ,l 4 < 1 TeV, whereas Energy Frontier enlarge the region up to 2 TeV.