Speaker
Description
The measured properties of the $X(3915)$ and $X(3930)$ make difficult their theoretical
description. These charmonium resonances, firstly detected by the
Belle and BaBar Collaborations in $\gamma\gamma$ fusion process, were measured
in different final channels: the $X(3915)$ was discovered in the $\omega
J/\psi$ [1, 2] invariant mass distribution whereas the $X(3930)$ was seen in the
$D\bar D$ one [3, 4]. Both Collaborations rapidly agreed that the $X(3930)$ has
most likely $J^{PC}=2^{++}$ quantum numbers based on the angular distribution
of the initial $\gamma\gamma$ particles. Therefore, this state was identified
as the $\chi_{c2}(2P)$ state in the Particle Data Group (PDG), despite the fact
that most quark models predict masses above the experimental one.
The assignment for the $X(3915)$ is being more controversial. Both
$J^{PC}=0^{++}$ and $2^{++}$ quantum numbers are allowed, although BaBar data
clearly prefers the $0^{++}$ assignment. Following the predictions of different
quark models [5, 6], finding good agreement with experiment on the state's mass
and width, the $X(3915)$ was assigned to the $\chi_{c0}(2P)$ in the PDG.
However, the $\chi_{c0}(2P)$ assignment was challenged by Olsen [7], who
pointed out that the decay patterns of the $X(3915)$ do not fit with those
expected for the $\chi_{c0}(2P)$ state. Moreover, new theoretical and
experimental studies reanalyzed the available data and concluded that a
$J^P=2^+$ assignment is preferred if some assumptions taken by BaBar
Collaboration in their original work were abandoned. Consequently, PDG
relabeled the state back to $X(3915)$.
Additionally, a new charmonium-like state dubbed $X(3860)$ with a mass
$3862^{+26+40}_{-32-13}$ MeV and width $201^{+154+88}_{-67-82}$ MeV has been
recently reported by the Belle Collaboration [8]. The existence of this state
agrees with the suggestion of Ref. [9], where the authors identify the broad
bump below the narrow peak of the $\chi_{c2}(2P)$ with the real
$\chi_{c0}(2P)$. Also, its mass coincides with the predictions of dynamical
coupled-channel models for the $\chi_{c0}(2P)$.
In view of the assignment puzzle of the $X(3915)$ and $X(3930)$ resonances, and
to explore the possible non-$q\bar q$ components of these resonances, in this
work we perform a coupled-channels calculation in the framework of the
constituent quark model (CQM) proposed in Ref. [10, 11], following the
formalism in Ref. [12]. Our results favors the hypothesis that the $X(3915)$
and the $X(3930)$ resonances are the same $J^{PC}=2^{++}$ state with a large
molecular component, whereas the $J^{PC}=0^{++}$ state appears with a mass
$M=3890$ MeV/$c^2$, lowered by nearby threshold effects.
[1] S. Uehara et al. (Belle Collaboration), Phys. Rev. Lett. 104, 092001
(2010).
[2] J. P. Lees et al. (BaBar Collaboration), Phys. Rev. D86, 072002
(2012).
[3] S. Uehara et al. (Belle Collaboration), Phys. Rev. Lett. 96, 082003
(2006).
[4] B. Aubert et al. (BaBar Collaboration), Phys. Rev. D81, 092003 (2010).
[5] X. Liu, Z.-G. Luo and Z.-F. Sun, Phys. Rev. Lett. 104, 122001 (2010).
[6] S. Godfrey and N. Isgur, Phys. Rev. D32, 189 (1985).
[7] S. L. Olsen, Phys. Rev. D91, 057501 (2015).
[8] K. Chilikin et al. (Belle Collaboration), arXiv:1704.01872 [hep-ex].
[9] F.-K. Guo and U.-G. Meissner, Phys. Rev. D86, 091501 (2012).
[10] J. Vijande, F. Fernandez and A. Valcarce, J. Phys. G31, 481 (2005).
[11] J. Segovia, P. G. Ortega, D. R. Entem and F. Fernandez, Phys. Rev. D93,
074027 (2016).
[12] P. G. Ortega, D. R. Entem and F. Fernandez, J. Phys. G40, 065107 (2013).
