Quarkonium Contribution to Meson Molecules

TL;DR

This paper investigates the quarkonium contributions to meson molecules, specifically the X(3872) and its partner, analyzing how charmonium states influence their structure and stability within a coupled-channel model.

Contribution

It introduces a model incorporating mixing between molecular states and charmonium, revealing how charmonium poles are modified and affect the nature of the X(3872) and X2(4012).

Findings

Charmonium states provide attraction or repulsion affecting binding.

X(3872) has a high molecular probability (~70-90%).

X2(4012) becomes unstable or virtual at high charmonium content.

Abstract

Starting from a molecular picture for the X(3872) resonance, this state and its J^{PC}=2++ HQSS partner [X2(4012)] are analyzed within a model which incorporates possible mixings with 2P charmonium states. Since it is reasonable to expect the bare chi_{c1}(2P) to be located above the D\bar D* threshold, but relatively close to it, the presence of the charmonium state provides an effective attraction that will contribute to bind the X(3872), but it will not appear in the 2++ sector. Indeed in this latter sector, the chi_{c2}(2P) should provide an effective small repulsion, because it is placed well below the D*\bar D* threshold. We show how the 1++ and 2++ bare charmonium poles are modified due to the D(*)\bar D(*) loop effects, and the first one is moved to the complex plane. The meson loops produce, besides some shifts in the masses of the charmonia, a finite width for the 1++ dressed charmonium state. On the other hand, the X(3872) and X2(4012) start developing some charmonium content, which is estimated by means of the compositeness Weinberg sum-rule. We also show that for X(3872) molecular probabilities of around 70-90 %, the X2 resonance destabilizes and disappears from the spectrum, becoming either a virtual state or being located deep into the complex plane, with decreasing influence in the D* \bar D* scattering line.