Digital Object Identifier (DOI) 10.1140/epjc/s2004-01725-5 Eur. Phys. J. C 34, 285–289 (2004) T HE EUROPEAN P HYSICAL JOURNAL C Bilepton production in e - γ collisions Dang Van Soa 1,∗ , Takeo Inami 1 , Hoang Ngoc Long 2,∗∗ 1 Department of Physics, Chuo University, Kasuga 1-13-27, Bunkyo, Tokyo 112, Japan 2 The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy Received: 5 August 2003 / Published online: 23 March 2004 – c  Springer-Verlag / Societ` a Italiana di Fisica 2004 Abstract. We study the production of bileptons, new gauge bosons of lepton number two, in the minimal 3-3-1 model in high energy e - γ collisions. If the bilepton masses are in the range of 300 GeV the reaction will give observable cross-sections in future colliders. 1 Introduction All models of physics beyond the standard model (SM) predict the existence of new particles. One of the more exotic of these is the bilepton, a particle of lepton number 2. Bileptons occur in a few of the models of new physics. One of them is the gauge model based on the SU(3) C ⊗ SU(3) L ⊗ U(1) N (3-3-1) gauge group [1–5]. These models contain a number of intriguing features: First, the models predict three families of quarks and leptons if the anomaly free condition on SU(3) L ⊗ U(1) N and QCD asymptotic freedom are imposed. Second, the Peccei–Quinn symmetry naturally occurs in these models [6]. The third interesting point is that one generation of quarks is treated differently from two others [7]. This could lead to a natural explanation for the unbalancingly heavy top quark. It has recently been argued that the 3-3-1 model arises naturally from gauge theories in spacetime with extra di- mensions [8], where the scalar fields are the components in the extra space dimensions of a higher dimensional gauge field [9]. A few different versions of the 3-3-1 model have been proposed [10]. The production of doubly charged vector bileptons in high energy collisions has been widely discussed both in the generic model [11] and in the minimal model [12]. Recent investigations have indicated that signals of new gauge bosons in these models may be observed at the CERN LHC [13] or Next Linear Conllider (NLC) [14]. The pro- duction of scalar leptoquarks [15] and constraints on the extra gauge bosons [16] in eγ collisions were studied. The potentiality of the projects of TESLA and CLIC based eγ colliders were discussed in [17]. In [18] the trilinear gauge boson couplings were pre- sented and production of bileptons in e + e - collisions was ∗ On leave of absence from Department of Physics, Hanoi Uni- versity of Education, Hanoi, Vietnam ∗∗ On leave of absence from Institute of Physics, NCST, P.O.Box 429, Bo Ho, Hanoi 10000, Vietnam calculated. In this paper we turn our attention to a future perspective experiment, namely the e - γ collision. This pa- per is organized as follows. In Sect. 2 we summarize the basic elements of the minimal 3-3-1 model. Section 3 is devoted to single bilepton production in γe - collisions. Finally, the conclusions are presented in Sect. 4. 2 A review of the minimal 3-3-1 model To frame the context, it is appropriate to recall briefly some relevant features of the minimal 3-3-1 model [1, 2]. The model treats the leptons as SU(3) L antitriplets [2, 5] f aL =   e aL -ν aL (e c ) aL   ∼ (1, ¯ 3, 0), (1) where a =1, 2, 3 is the family index. Two of the three quark generations transform as triplets of the SU(3) L and the third is treated differently. It belongs to an antitriplet. We have Q iL =   u iL d iL D iL   ∼  3, 3, - 1 3  , (2) u iR ∼ (3, 1, 2/3), d iR ∼ (3, 1, -1/3), D iR ∼ (3, 1, -1/3), i =1, 2, Q 3L =   d 3L -u 3L T L   ∼ (3, ¯ 3, 2/3), (3) u 3R ∼ (3, 1, 2/3), d 3R ∼ (3, 1, -1/3), T R ∼ (3, 1, 2/3). The nine gauge bosons W a (a =1, 2,..., 8) and B of SU(3) L and U(1) N are split into four light gauge bosons