Composite Vectors and Scalars in Theories of Electroweak Symmetry Breaking

In the context of a strongly coupled Electroweak Symmetry Breaking, composite triplet of heavy vectors belonging to the $SU(2)_{L+R}$ adjoint representation and a composite scalar singlet under $SU(2)_{L+R}$ may arise from a new strong interaction invariant under the global $SU(2)_L\times SU(2)_R$ symmetry, which is spontaneously broken down to $SU(2)_{L+R}$. This thesis consists of two parts. The first part is devoted to the study of the heavy composite vector pair production at the LHC via Vector Boson Fusion and Drell-Yan annihilation under the assumption that the interactions among these heavy vector states and with the Standard Model gauge bosons are described by a $SU(2)_L\times SU(2)_R/SU(2)_{L+R}$ Effective Chiral Lagrangian. The expected rates of multi-lepton events from the decay of the composite vectors are also given. The second part studies the associated production at the LHC of a composite vector with a composite scalar by Vector Boson Fusion and Drell-Yan annihilation in the framework of a $SU(2)_{L}\times SU(2)_{R}/SU(2)_{L+R}$ Effective Chiral Lagrangian with massive spin one fields and one singlet light scalar. The expected rates of same sign di-lepton and tri-lepton events from the decay of the composite vector and composite scalar final state are computed. The connection of the Effective Chiral Lagrangians with suitable gauge models is elucidated.