Phase motion in the Z ? ( 4430 ) amplitude in B 0 → ψ ′ π ? K + decay

摘要

In view of the proliferation in the number of new charmonium states, it is really important to have an experimental way to prove that an observed bump is, indeed, a real resonance. To do that, in this paper we present an alternative method to demonstrate the resonant behavior of a state. With this method, the phase variation of a generic complex amplitude can be directly revealed through interference in the Dalitz-plot region where it crosses a well established resonant state, used as a probe. We have tested the method for the Z ? ( 4430 ) state by generating Monte Carlo samples for the B 0 → ψ ( 2 S ) π ? K + decay channel. We have shown that the proposed method gives a clear oscillation behavior, related to the phase variation associated with a real resonant state, in the case where the Z ? ( 4430 ) is considered as a regular resonance with a strong phase variation.