Radiative decay of the X(3872)X(3872) as a mixed molecule-charmonium state in effective field theory

Assuming that $X(3872)$ is a mixture between $2P$ charmonium and $\bar{D}D^{*}$ molecular states with $J^{PC}=1^{++}$, an analysis of $X(3872)$ radiative decays into $J/\psi \gamma$ and $\psi(2S)\gamma$ is presented. The modification of the radiative branching ratio due to possible constructive or destructive interferences between the meson-loop and the short-distance contact term, which is modeled by a charm quark loop, is shown. The model predictions are shown to be compatible with the experimentally determined ratio of the mentioned branching fractions for a wide range of the $X(3872)$ charmonium content. In the case of the destructive interference, a strong restriction on the charmonium admixture is found.Comment: 10 pages, 2 figure

The effects of charmonium on the properties of the 1++1^{++} hidden charm poles in effective field theory

In this study, the properties of the $J^{PC}=1^{++}$ hidden charm poles are analyzed under the variation of the bare 2P charmonium mass within the effective field theory proposed in Ref. \cite{Cincioglu:2016fkm}. The main focus of the current work is on the pole trajectory of the $\chi_{c1}(2P)$ charmonium dressed by the $D \bar{D}^*$ meson loops. It is shown that having a bare charmonium pole above or below the two-meson threshold has radically different phenomenologies, also depending on how close the pole is to the threshold.Comment: 16 pages, 2 figure

Quarkonium Contribution to Meson Molecules

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 (c) over bar) states. Since it is reasonable to expect the bare chi(c1)(2P) to be located above the D (D) over bar* 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*(D) over bar* threshold. We show how the 1(++) and 2(++) bare charmonium poles are modified due to the D-(*)(D) over bar ((*)) 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-(*)(D) over bar ((*)) pairs. We also show that, for reasonable values of this coupling, leading to X(3872) molecular probabilities of around 70-90%, the X2 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*(D) over bar* 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 Xb(2) states, heavy-quark spin-flavor partners of the X(3872)

Quarkonium Contribution to Meson Molecules

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)