On a possible effective four-boson interaction and its implications at the upgraded LHC

We consider a possibility of a spontaneous generation of fourfold effective interactions of electroweak gauge bosons $W^a$ and $B$. The conditions for the spontaneous generation are shown to lead to a set of compensation equations for parameters of the interaction. In case of a realization of a non-trivial solution of the set, important electro-weak parameter $\sin^2\theta_W$ is defined. The existence of two non-trivial solutions is demonstrated, which provide a satisfactory value for the electromagnetic fine structure constant $\alpha$ at scale $M_Z$: $\alpha(M_Z) = 0.007756$. There is a solution with the high effective cut-off being close to the Planck mass by the order of magnitude. The most interesting solution corresponds to effective cut-off $\simeq 10^2\,TeV$. This solution gives quite definite prediction for non-perturbative effects in processes $p+p\to\bar t t (W^\pm, Z)$, which could be observed at the upgraded LHC.