Heavy exotic molecules with charm and bottom

Yizhuang Liu,Ismail Zahed

doi:10.1016/j.physletb.2016.09.045

Abstract

We revisit the formation of pion-mediated heavy-light exotic molecules with both charm and bottom and their chiral partners under the general strictures of both heavy-quark and chiral symmetry. The chiral exotic partners with good parity formed using the $(0^+, 1^+)$ multiplet are about twice more bound than their primary exotic partners formed using the $(0^-,1^-)$ multiplet. The chiral couplings across the multiplets $(0^\pm, 1^\pm)$ cause the chiral exotic partners to unbind, and the primary exotic molecules to be about twice more bound, for $J\leq 1$. Our multi-channel coupling results show that only the charm isosinglet exotic molecules with $J^{PC}=1^{++}$ binds, which we identify as the reported neutral $X(3872)$. Also, the bottom isotriplet exotic with $J^{PC}=1^{+-}$ binds, which we identify as a mixture of the reported charged exotics $Z^+_b(10610)$ and $Z^+_b(10650)$. The bound isosinglet with $J^{PC}=1^{++}$ is suggested as a possible neutral $X_b(10532)$ not yet reported.

Highlights

A decade ago, both the BaBar collaboration [1] and the CLEOII collaboration [2] have reported narrow peaks in the Ds+π0 (2317 MeV) and the Ds∗+π0 (2460 GeV) channels as expected from general chiral symmetry arguments [3, 4]
In QCD the light quark sector (u, d, s) is dominated by the spontaneous breaking of chiral symmetry, while the heavy quark sector (c, b, t) is characterized by heavy-quark symmetry [5]. The combination of both symmetries led to the conclusion that the heavylight doublet (0−, 1−) = (D, D∗) has a chiral partner (0+, 1+) = (D, D ∗) that is about one consituent mass heavier [3, 4]
The P-wave inter-multiplet mixing in the (0−, 1−) is enhanced by the almost degeneracy of the constituents by heavy-quark symmetry, while the S-wave cross-multiplet mixing in the (0±, 1±) is still substantial due to the closeness of the constituents by chiral symmetry

Summary

INTRODUCTION

A decade ago, both the BaBar collaboration [1] and the CLEOII collaboration [2] have reported narrow peaks in the Ds+π0 (2317 MeV) and the Ds∗+π0 (2460 GeV) channels as expected from general chiral symmetry arguments [3, 4]. Several heavy exotic molecules with quantum numbers uncommensurate with the excited states of charmonia and bottomia have been reported, such as the neutral X(3872) and the charged Zc(3900)± and Zb(10610)±. The P-wave inter-multiplet mixing in the (0−, 1−) is enhanced by the almost degeneracy of the constituents by heavy-quark symmetry, while the S-wave cross-multiplet mixing in the (0±, 1±) is still substantial due to the closeness of the constituents by chiral symmetry The latter prevents the formation of dual chiral molecules such as D ̃ Dwith charm and B ̃Bwith bottom, as we will show. The organization of the paper is as follows: In section 2 we briefly derive the essential contruct for doubly charmed exotic molecules using the strictures of chiral and heavy quark symmetries and explicit the coupled channel problem for the lowest bound states.

CHARMED EXOTICS MOLECULES

Results for bottom exotic molecules

CONCLUSIONS