X(3872) as virtual companion pole of the charm–anticharm state χc1(2P)

Abstract

We study the spectral function of the axial-vector charmonium state [Formula: see text] coupled to [Formula: see text] mesons, by employing a quantum field theoretical approach: a pronounced enhancement close to the [Formula: see text] threshold, to be identified with the [Formula: see text], emerges. In the complex plane we find two poles: a pole for the broad seed state [Formula: see text], and — in the easiest scenario — a virtual pole for the [Formula: see text]. Thus, our approach describes both the seed state and the dynamically generated [Formula: see text] simultaneously. In particular, it explains the most prominent, both molecular-like and quarkonium-like, features of the [Formula: see text]: its very small width (the decay into [Formula: see text] is predicted to be about 0.5 MeV), the enhanced radiative decay into [Formula: see text] with respect to [Formula: see text], and the isospin breaking decay into [Formula: see text] (thanks to [Formula: see text] loops mediating this decay channel). At the same time, we aim to determine the pole position and the properties of the charmonium seed state: quite interestingly, even if a pole is always present, it is possible that there is no peak corresponding to this state in the spectral function, thus potentially explaining why the corresponding resonance could not yet be seen in experiments.