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Top quark effects in composite vector pair production at the LHC

In the context of a strongly coupled Electroweak Symmetry Breaking, composite light scalar singlet and composite triplet of heavy vectors may arise from an unspecified strong dynamics and the interactions among themselves and with the Standard Model gauge bosons and fermions can be described by a $SU(2)_L\times SU(2)_R/SU(2)_{L+R}$ Effective Chiral Lagrangian. In this framework, the production of the $V^{+}V^{-}$ and $V^{0}V^{0}$ final states at the LHC by gluon fusion mechanism is studied in the region of parameter space consistent with the unitarity constraints in the elastic channel of longitudinal gauge boson scattering and in the inelastic scattering of two longitudinal Standard Model gauge bosons into Standard Model fermions pairs. The expected rates of same-sign di-lepton and tri-lepton events from the decay of the $V^{0}V^{0}$ final state are computed and their corresponding backgrounds are estimated. It is of remarkable relevance that the $V^{0}V^{0}$ final state can only be produced at the LHC via gluon fusion mechanism since this state is absent in the Drell-Yan process. It is also found that the $V^{+}V^{-}$ final state production cross section via gluon fusion mechanism is comparable with the $V^{+}V^{-}$ Drell-Yan production cross section. The comparison of the $V^{0}V^{0}$ and $V^{+}V^{-}$ total cross sections will be crucial for distinguishing the different models since the vector pair production is sensitive to many couplings. This will also be useful to determine if the heavy vectors are only composite vectors or are gauge vectors of a spontaneously broken gauge symmetry.