Exotic Quark Production in ep Collisions

We investigate the single production and decay of charge -1/3, weak isosinglet vectorlike exotic $D$ quarks in string inspired $E_6$ theories at future ep colliders; THERA with $\sqrt s$=1 TeV, L=40 $pb^{-1}$ and CERN Large Hadron Electron Collider (LHeC) with $\sqrt s$=1.4 TeV, $L=10^4$ $pb^{-1}$. We found that an analysis of the decay modes of $D$ should probe the mass ranges of 100-450 GeV and 100-1200 GeV at the center of mass energies, 1 and 1.4 TeV, respectively.


I. INTRODUCTION
String inspired E 6 theories predict existence of exotic particles. In E 6 , each generation of fermions is assigned to the 27-dimensional representation [1,2]. The presence of additional fermions causes Flavor Changing Neutral Current (FCNC) interactions and possible deviations from weak universality in Charged Current (CC) [3]. In this study we consider exotic down quark (D), a charge -1/3, quark which is a weak isosinglet particle.
Production of exotic quarks have been studied at HERA [4,5] and LEP [6] energies as CC and FCNC reactions. We analyze the possible production of these quarks and some of their indirect signatures including the contributions of boson-gluon fusions [7] at two future high energy ep collider options; THERA with √ s=1 TeV and L = 40 pb −1 [8] and CERN Large Hadron Electron Collider (LHeC) with √ s=1.4 TeV and L = 10 4 pb −1 at which 7 TeV LHC protons collide with 70 GeV ring electron or positron beam [9]. These colliders complement the hadron collider programmes and provide new discovery potential to them.
A relatively high integrated luminosity of 10 f b −1 at the LHeC makes an essential facility to resolve possible puzzles of the LHC data.

II. PRODUCTION AND DECAYS OF D
The single production of exotic down quarks occur via the following t-channel subprocesses in ep collisions as shown in Fig. 1; i) Charged Current reaction; eu → ν e D ii) FCNC reaction; ed → eD iii) Boson-Gluon Fusions; W g →ūD, Zg →dD and γg →dD.
The CC and FCNC interactions for the exotic D quarks mixed with standard fermions and standard bosons W , Z are given by where θ are the mixing angels between the ordinary quarks and the exotic down quarks, g denotes the gauge coupling relative to SU(2) symmetries.
As we consider the strong interactions, D quarks couple to gluons in exactly the same here M W , M Z and Γ W , Γ Z are masses and decay widths of a W and Z bosons. a e (a d ) and v e (v d ) stand for axial and vector coupling constants of electron (down quark) and m refers to D masses.
The total production cross section is obtained by folding the partonic cross section over the parton distributions in the proton. In numerical calculations of the total cross sections we have used the MRST parametrization [10] for the partons and the Weizsäcker-Williams distribution [11,12] Tables I and II, we present the total production cross sections of the five reactions for various masses at THERA and LHeC, respectively. As can be seen, for 100-300 GeV D quarks Z-gluon and γ-gluon fusions are dominant reactions but for higher mass range contributions of these fusions decrease very fast.
Since these exotic quarks must be at a scale well above 100 GeV [13], the main decays of them would be D → dZ and D → uW and partial decay widths can be written as where q is up or down quark, V denotes W − and Z bosons, α is the fine structure constant, Eq. (4) gives rise to branching ratios of BR(D → dZ)=30 % and BR(D → uW )= 70 % which do not change significantly depending on D masses, as seen from Table III. Therefore, D → ul −ν l is taken as the relevant background process since the D → uW is dominant one. In Tables IV and V we present the cross sections resulting the background processes ( considering only the first generation of leptons) for √ s=1 and 1.4 TeV, respectively. Results reported in these tables were obtained by using the high energy package CompHEP [14] along with CTEQ6L [15] which has been used in the background calculations and an optimal cut of P T > 10 GeV has taken for electron, jet and missing momenta.
In In obtaining these numerical values, we have taken an appropriate mixing angle value of sin 2 θ=0.05 which is at the order of the angle in the CKM matrix.