Vector leptoquark pair production in e+e− annihilation

We study the full unitary matrix models, introducing a new term llogU, where l plays the role of the discrete time. On the other hand, the full unitary matrix model contains a topological term. In the continuous limit it gives rise to a phase transition at θ = π. The ground state is characterized by the discrete time l. The discrete time l acts as the instanton number.