Print version ISSN 0103-9733
Braz. J. Phys. vol.38 no.3b São Paulo Sept. 2008
Neutral bilepton boson production in pp collisions from 3-3-1 model
E. Ramirez BarretoI; Y. A. CoutinhoI; J. Sá BorgesII
IUniversidade Federal do Rio de Janeiro 21941-972 - Rio de Janeiro, RJ, Brazil
IIUniversidade do Estado do Rio de Janeiro 20550-013 - Rio de Janeiro, RJ, Brazil
Our aim is to establish some signatures of the extra neutral gauge boson X0, predicted in a version of the SU(3)c x SU(3)L x U(1)x model with right-handed neutrinos, by considering the process p+p → X0 + X0* + X. In this work, we show some results concerning the LHC energy regime (√s = 14 TeV) and projected luminosity. Some distributions are shown and the X0 width is calculated. We conclude that hadron colliders can show a clear signature for the existence of X0 by comparing its production with Z pair production.
Keywords: Beyond the Standard Model; New Gauge Bosons
A peculiar feature of the Standard Model (SM) is that none of the gauge bosons carry baryon or lepton number. Many extensions of the SM predicted the existence of exotic particles carrying global quantum numbers, like leptoquarks and bileptons. The bileptons are defined as bosons carrying two units of lepton number and are present in SU(15) grand unification theory and 3 3 1 models, for example.
In the 3 3 1 minimal version [1, 2], there are charged and doubly-charged bileptons and, on the other hand, the version with right-handed neutrinos  contains neutral and single-charged bileptons. In addition to these new gauge bosons, there are new quarks that carry two units of lepton number, they are called bileptoquarks. The production of charged bileptons at linear and hadron colliders was extensively studied and presents a unique signature, because they come from processes were total lepton number is conserved but the individual flavor lepton number is violated [4, 5].
A deep analysis of the extra neutral gauge boson X0 pair production was not yet done. We intend to study the production of neutral gauge bileptons in hadron colliders. In this paper we show the total cross section and some distributions for the process p+p → X0 + X* + X calculated from at tree level. In the next section, we gives a brief review of the 3 3 1 model with right-handed neutrinos. Section 3 is devoted to our results and discussion. In section 4 we presents the conclusions.
II. THE MODEL
The right-handed neutrino version (3 3 1 RHN), has in each leptonic triplet representation both the right- and left-handed neutrino.
where a = 1, 2, 3 is the generation index.
Two quark generations (m = 1,2) belong to anti-triplet and the other to triplet representation
The new heavy quarks and carry and T' carries units of positron charge.
The 3 3 1 model includes five new gauge bosons: a new neutral (Z') two charged bileptons (V±) and two bileptons (X0) and (X0*) with no electric charge.
One of the main features of the model comes from the relation between Z' and V± and X0 masses:
From this relation we obtain and so Z' is forbidden to decay into a bilepton pair (V+V- or X0*X0).
Three SU(3)L triplet η, ρ and χ are necessary to generate masses for the particles and break the simmetry. These triplet develope vev's ν, u and w respectively satisfying the relation ν2 + u2 = . We have considered in our calculations that 
The interaction between the quark fields and the neutral bilepton X0 is given by:
As the exotic quark are very heavy, we discard their possible mixing with the ordinary physical quark fields and use the physical states identical to the symmetry states.
Keeping in mind this last observation, there is no flavor changing neutral currents (FCNC) coupled to Z and Z', moreover we do not consider Z - Z' mixing. The neutral current Lagrangian is:
where are auark fields and the vector and the axial couplings, and are given in the Table I, where we have considered the approximation between the vev's expressed in Eq. (5).
The trilinear couplings between Z and Z' with X0 and X0* are respectively
The total width of the X0 calculated from and νν channel contributions, where represents the three bileptoquark and ν includes the three neutrino flavors. For = 800,1000 and 1200 GeV are 1.54,6.70 and 14.70 GeV. We use the Com-pHep package  in our calculations and assume = 600 GeV.
The main contributions for X0 pair production in pp collision depend on the initial quark q charge. When q = u, only Z and Z' via s-channel contribute and, on the other hand, when q = d we have an additional t-channel heavy quark exchange contribution. We display, in Fig. 1 and in Fig. 2 respectively, the X0 angular distribution relative to the initial beam direction for the elementary processes and adopting the following cuts on the final bileptons angle, rapidity and transverse momentum:
The angular distribution shapes are different for u and d initial quarks. We observe the correct behavior of the total cross section for the elementary processes as shown the Fig. 3.
The total cross section and the distributions for the pp process are obtained by the convolution of the elementary cross sections with the CTEQ661  structure functions. The angular, invariant mass and rapidity distributions are displayed in Figs. 4, 5 and 6, respectively.
We conclude that the final X0 angular distribution is almost flat. There is no preferential direction. We note that the total cross section for = 600 GeV decreases when the MZ' increases.
In this work we present preliminary results for the production of neutral bileptons, predicted for the 3 3 1 RHN, from pp collision. In a simple framework, without Z - Z' mixing and considering the absence of flavor changing neutral currents (FCNC), we have shown the bileptons distributions for the elementary processes and the results for pp collisions.
For an annual luminosity at the LHC ( = 100 fb-1) we find around one thousand X0 pairs produced per year. The study of the production of charged bileptons in pp collisions from the minimal version of the 3 3 1 model is being developed and the preliminar results indicate a large number of events as well. The next step in our analysis is to consider the X0 decay into two leptons in order to compare it with Z decay. This comparison can possibly reveal a signature of the neutral bilepton production.
We acknowledge the financial support from CAPES (E.R.B.) and FAPERJ (Y.A.C.).
 F. Pisano and V. Pleitez, Phys. Rev. D 46, 410 (1992). [ Links ]
 P. H. Frampton, Phys. Rev. Lett. 69, 2889 (1992). [ Links ]
 J. C. Montero, F. Pisano, and V. Pleitez, Phys. Rev. D 47, 2918 (1993); [ Links ] R. Foot, H. N. Long, and T. A. Tran, Phys. Rev. D 50, R 34 (1994); [ Links ] Hoang Ngoc Long, Phys. Rev. D 53, 437 (1996); ibid 54, 4691 (1996); [ Links ] V. Pleitez, Phys. Rev. D 53, 514 (1996). [ Links ]
 B. Dion, T. Gregoire , D. London, L. Marleau, and H. Nadeau, Phys. Rev. D 59, 075006 (1999). [ Links ]
 E. Ramirez Barreto, Y. A. Coutinho, and J. Sá Borges, Phys. Lett. B 632, 675 (2006). [ Links ]
 Alex G. Dias, Thesis "O Problema da Violação CP Forte e o Limite Perturbativo em extensões SU(3)c x SU(3)l x U(1)x do Modelo Padrão", 2005. [ Links ]
 A. Pukhov et al., INP MSU 98-41/512, hep-ph/9908288. [ Links ]
 J. Pumplin et al., JHEP 207, 12 (2002). [ Links ]
(Received on 1 April, 2008)