Quarkonium Contribution to Meson Molecules

E. Cincioglu; J. Nieves; A. Ozpineci; A. U. Yilmazer

doi:10.1140/epjc/s10052-016-4413-1

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2016) 76: 576
https://doi.org/10.1140/epjc/s10052-016-4413-1

Regular Article - Theoretical Physics

Quarkonium Contribution to Meson Molecules

E. Cincioglu¹^*, J. Nieves², A. Ozpineci³ and A. U. Yilmazer¹

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

Abstract

Starting from a molecular picture for the X(3872) resonance, this state and its $J^{PC}=2^{++}$ heavy-quark spin symmetry partner $$[X_2(4012)]$$ are analyzed within a model which incorporates possible mixings with 2P charmonium ( $c\bar{c}$ ) 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 binding the X(3872), but it will not appear in the $2^{++}$ sector. Indeed in the 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, X(3872) and $$X_2(4012)$$ 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 $D^{(*)}\bar{D}^{(*)}$ pairs. We also show that, for reasonable values of this coupling, leading to X(3872) molecular probabilities of around 70–90 %, the $$X_2$$ 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 $D^{*}\bar{D}^{*}$ 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 $\psi (2S)\gamma$ and $J/\psi \gamma$ . Finally, we qualitatively discuss within this scheme, the hidden bottom flavor sector, paying a special attention to the implications for the $$X_b$$ and $X_{b2}$ states, heavy-quark spin–flavor partners of the X(3872).