Resonant Production of Color Octet Electron at the LHec

In composite models with colored preons leptogluons (l_(8)) has a same status with leptoquarks, excited leptons and quarks etc. We analyze resonant production of color octet electron (e_(8)) at QCD Explorer stage of the Large Hadron electron Collider (LHeC). It is shown that the e_(8) discovery at the LHeC will simultaneously determine the compositeness scale.


I. INTRODUCTION
A large number of "fundamental" particles, as well as observable free parameters (put by hand), in Standard Model (SM) indicate that it is not "the end of story". Physics has met similar situation two times in the past: one is the Periodic Table of the Elements which was clarified by Rutherford's experiment later, the other is hadron inflation which has resulted in quark model. This analogy implies the preonic structure of the SM fermions (see [1] and references therein). The preonic models predict a zoo of new particles such as excited leptons and quarks, leptoquarks, leptogluons etc. Excited fermions and leptoquarks are widely discussed in literature and their searches are inseparable parts of future collider's physics programs. Unfortunately, leptogluons did not attract necessary attention, while they are predicted in all models with colored preons (see, for example, [2], [3], [4], [5], [6], [7]).
Lower bound on leptogluon masses, 86 GeV, given in PDG [8] reflects twenty years old Tevatron results [9]. As mentions in [10] D0 clearly exclude 200 GeV leptogluons and could naively place the constraint M LG 325 GeV. Fifteen years old H1 results on color octet electron, e 8 , search [11] has excluded the compositeness scale Λ 3TeV for M e8 ⋍ 100 GeV and Λ 240 GeV for M e8 ⋍ 250 GeV. The advantage of lepton-hadron colliders is the resonant production of leptogluons, whereas at hadron and lepton colliders they are produced in pairs.
The sole realistic way to TeV scale in lepton-hadron collisions are presented by linac-ring type electron-proton colliders (see reviews [12], [13], [14] and references therein). Recently CERN, ECFA and NuPECC initiated the study on the LHC based ep colliders [15]. Two options are considered for the Large Hadron electron Collider (LHeC): the construction of new e-ring in the LHC tunnel [16] or the construction of e-linac tangentially to the LHC [17], [18], [19]. It should be noted that energy of electrons in first option is limited by synchrotron radiation, whereas in second option energy of electrons can be increased by lengthening the linac. Tentative parameters for linac-ring options of the LHeC are presented in the Table   1. QCD Explorer stage(s) is mandatory: it will provide necessary information on PDF's for adequate interpretation of future LHC results and it will clarify QCD basics, as well. In this paper we investigate potential of QCDE stages of the LHeC in search for color octet electron via resonant production. In section 2, Lagrangian for e 8 interactions is presented and it's decay widths and production cross sections at different stages of LHeC are evaluated.
Section 3 is devoted to detailed analysis of leptogluon signatures at QCD-E stages of the LHeC. Finally, concluding remarks are given in section 4.

CROSS SECTION
For the interaction of leptogluons with corresponding lepton and gluon we use the following Lagrangian [8], [20]: where G α µν is field strength tensor for gluon, index α = 1, 2, ..., 8 denotes the color, g s is gauge coupling, η L and η R are the chirality factors, l L and l R denote left and right spinor components of lepton, σ µν is the anti-symmetric tensor and Λ is the compositeness scale. The leptonic chiral invariance implies η L η R = 0. For numerical calculations we add leptogluons into the CalcHEP program [21].
Decay width of the color octet electron is given by In Fig. 1 decay widths of leptogluons are presented for two scenarios, Λ = M e8 and Λ = 10 TeV.  The resonant e 8 production cross sections for there stages at the LHeC from     Concerning η j , most of signal lies above η = 0, whereas 99 % of background is concentrated in −2 < η j < 0 region. For this reasons below we use p T > 150, |η e | < 4 and 0 < η j < 4.
With these cuts we present in Fig. 8 invariant mass distributions for signal and background.   Advantage of resonant production will provide an opportunity to probe compositeness scale will above the center of mass energy of the collider. For statistical significance we use following formula: where S and B denote number of signal and background events, respectively.
Numbers of signal and background events for different M e8 values are presented in Table   2 for L int = 1f b −1 . In calculating these values, in addition to cuts given above, we have    used mass windows as M e8 − 2Γ e8 < M ej < M e8 + 2Γ e8 for Γ e8 > 10 GeV and M e8 −20 GeV < M ej < M e8 + 20 GeV for Γ e8 < 10 GeV. It is seen that resonant production of color octet electron will provide very clean signature for masses up to M e8 ≃ 1TeV.
In Table 3 we present reachable compositeness scale values for L int = 1 and L int = 10f b −1 .
It is seen that multi-hundred TeV scale can be searched for M e8 = 500 GeV. Then, increase of the luminosity by one order results in two times higher values for Λ.

B. LHeC/QCDE-2 stage
In order to determine corresponding cuts we present p T , η j and η e distributions for signal and background processes in Figs 9, 10 and 11, respectively. The figures indicate that significant change takes place only for η j . In this subsections we will use p T > 150, |η e | < 4 and −0.5 < η j < 4. The invariant mass distributions obtained with this cuts are given in     Table   3 show that twofold increasing of the electron energy results in: 1.5 times higher values of Λ for M e8 = 500 GeV, 2 times -for M e8 = 750 GeV and 4 times -for M e8 = 1000 GeV.
Moreover, multi-ten TeV scales can be achieved for M e8 = 1250 and 1500 GeV, which are not available at LHeC/QCDE-1.

IV. CONCLUSION
It seems that QCD Explorer stage(s) of the LHeC, together with providing necessary information on PDF's and QCD basics, could play essential role on the BSM physics, also.
The discovery of e 8 at this machine, simultaneously will determine compositeness scale.