8–11 Sept 2015
Santiago de Compostela
Europe/Zurich timezone

Heavy Quark Spin Symmetry and the partners of the $X(3872)$

8 Sept 2015, 17:20
20m
Santiago de Compostela

Santiago de Compostela

Speaker

Prof. Francisco Fernandez (Universidad de Salamanca)

Description

The discovery of the $X(3872)$ by the Belle collaboration [1] and its confirmation by BaBar and CDF has provided the best candidate to an exotic structure in the meson sector. Because of its proximity to the $D^*D$ threshold a description of this state in terms of a $c\bar c$ state coupled to a $D^*D$ molecular structure seems to be natural. For the heavy quark sector, the spin-dependent interactions are of the order $1/m_Q$ and vanish in the heavy quark limit $m_Q\rightarrow \infty$. Then the dynamics involving heavy quarks are independent of their spin leading to heavy quark spin symmetry (HQSS). This symmetry has been often used to constrain effective hadronic models. Recently the LHCb Collaboration has determined unambiguously the $X(3872)$ quantum numbers to be $J^{PC}=1^{++}$. Based on this result HQSS suggest the existence of $X(3872)$ partners either in the $c\bar c$ sector with $J^{PC}=2^{++}$ or in the $b\bar b$ sector with $J^{PC}=1^{++}$ or $2^{++}$. An extensive experimental search has been done by LHCb for the $J^{PC}=1^{++}$ bottom partner of the $X(3872)$, the so-called $X_b$ through its decay to different channels, but no evidence of an $X_b$ signal has been observed. In this work we perform a calculation of the possible partners of the $X(3872)$ using a constituent quark model which has been successful in describing the hadronic phenomenology [2]. In this framework the $X(3872)$ resonance is understood as a mixture of a P-wave charmonium $\chi_{c1}(2P)$ and a S-wave $DD^*$ molecule. The $D-D^*$ residual interaction, driven basically by one pion exchange, is not enough attractive to form a $DD^*$ bound state but the coupling with the $c\bar c$ state, slightly above the $DD^*$ threshold produces the attraction necessary to bind the system. This is not the case of the $J^{PC}=2^{++}$ $D^*D^*$ molecule where the absence of a $c\bar c$ state nearby avoid the formation of a bound states. In the bottom sector the situation is different. In this case, as the bottom quark mass is larger than the charm quark mass, the interaction in the $BB^*$ and the $B^*B^*$ systems is enough attractive to produce loosely bound states. However in the $BB^*$ $J^{PC}=1^{++}$ case a $b\bar b$ state exists just below threshold. The coupling with this states produces repulsion and the $BB^*$ bound state disappears. In the $B^*B^*$ system any nearby $b\bar b$ state does exit and the $J^{PC}=2^{++}$ remains as a bound state with a mass of 10650 MeV.$/c^2$ Therefore, although HQSS predicts more bound states the coupled channels dynamics breaks the symmetry and only the $B^*B^*$ $J^{PC}=2^{++}$ state survives. Similar effects are analyzed in the heavy baryon sector. \vspace{12pt} [1] S. K. Choi $\it et al$ (Belle Collaboration) Phys. Rev. L $\bf 91$ 262001 (2003). [2] J. Vijande, F. Fern\'andez, and A. Valcarce, J. Phys. G {\bf 31}, 481 (2005). J. Segovia, A. M. Yasser, D. R Entem and F. Fern\'andez, Phys. Rev. D {\bf 78} 114033 (2008).

Primary author

Prof. Francisco Fernandez (Universidad de Salamanca)

Co-authors

Dr David R. Entem (Universidad de Salamanca) Dr Pablo. G. Ortega (CERN , CH-1211 Geneva, Switzerland)

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