https://doi.org/10.1140/epjc/s10052-016-4413-1
Regular Article - Theoretical Physics
Quarkonium Contribution to Meson Molecules
1
Department of Physics Engineering, Ankara University, Ankara, Turkey
2
Instituto de Física Corpuscular (IFIC) Centro Mixto CSIC-Universidad de Valencia, Institutos de Investigación de Paterna, 46071, Valencia, Spain
3
Department of Physics, Middle East Technical University, Ankara, Turkey
* e-mail: elif.cincioglu@gmail.com
Received:
13
June
2016
Accepted:
30
September
2016
Published online:
25
October
2016
Starting from a molecular picture for the X(3872) resonance, this state and its 
heavy-quark spin symmetry partner 
are analyzed within a model which incorporates possible mixings with 2P charmonium (
) states. Since it is reasonable to expect the bare 
to be located above the 
threshold, but relatively close to it, the presence of the charmonium state provides an effective attraction that will contribute to binding the X(3872), but it will not appear in the 
sector. Indeed in the latter sector, the 
should provide an effective small repulsion, because it is placed well below the 
threshold. We show how the 
and bare charmonium poles are modified due to the 
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 dressed charmonium state. On the other hand, X(3872) and 
start developing some charmonium content, which is estimated by means of the compositeness Weinberg sum rule. It turns out that in the heavy-quark limit, there is only one coupling between the 2P charmonia and the pairs. We also show that, for reasonable values of this coupling, leading to X(3872) molecular probabilities of around 70–90 %, the 
resonance destabilizes and disappears from the spectrum, becoming either a virtual state or one being located deep into the complex plane, with decreasing influence in the 
scattering line. Moreover, we also discuss how around 10–30 % charmonium probability in the X(3872) might explain the ratio of radiative decays of this resonance into 
and 
. Finally, we qualitatively discuss within this scheme, the hidden bottom flavor sector, paying a special attention to the implications for the 
and 
states, heavy-quark spin–flavor partners of the X(3872).
© The Author(s), 2016
