BLED WORKSHOPS
IN PHYSICS
VOL. 13, NO. 1
p. 17
Proceedings of the Mini-Workshop
Hadronic Resonances
Bled, Slovenia, July 1 - 8, 2012
Exotic molecules of heavy quark hadrons
Atsushi Hosaka
Research Center for Nuclear Physics (RCNP)
Osaka University, Ibaraki, 567-0047, Japan
Abstract. We discuss hadronic molecules containing both heavy and light quarks. The
interactions are provided by meson exchanges between light quarks in the constituent
hadrons. The tensor force in the one-pion exchange potential mixes states of different spins
and angular momenta. This provides attraction and generates rich structure in exotic chan-
nels in the heavy quark sectors. The method has been applied to exotic baryons with a c̄
or b̄ quark, and exotic mesons containing bb̄ including the recently found Z ′bs.
Recent interest in hadron physics has been largely motivated by the observations
of candidates for exotic multi-quark states which are not (easily) explained by the
conventional quark model [1–4]. Many of them appear near the threshold region
of their possible decay channels. The finding of the twin Zb’s is perhaps the most
striking in that they appear very close to the BB∗ and B∗B∗ thresholds [4–6].
Strictly, multiquarks does not make much sense for light flavors especially
for u and d quarks when the quark number is not a conserved quantity. In fact,
they interact strongly at the energy scale of ΛQCD, creating qq̄ pairs and gener-
ating massive constituent quarks. It is known that it is a consequence of sponta-
neous breaking of chiral symmetry. In the low energy region we expect that such
constituent quarks become active degrees of freedom as almost on-shell parti-
cles, forming exotic multi-quark states. Contrary to the light flavor sector heavy
quarks such as c and bwith massM≫ ΛQCD conserve their quark number. Thus
we can treat them as almost on shell particles with non-relativistic kinematics at
low energies of typical hadron resonances.
Starting from the conventional quarkmodel picture for orbitally excited states,
multiquark configurations can mix with them because the typical excitation en-
ergy of about 0.5-1 GeV is sufficient to create a (constituent) qq̄ pair. A color
singlet multiquark system of more than the minimal number (q̄q or qqq) may
form color singlet sub-systems (clusters) of hadrons. Clustering phenomena of
multiparticle systems have been extensively studied in nuclear physics for many
years [7]. Alpha particles saturate the dominant component of spin and isospin
dependent nuclear force. The spin-isospin neutral alpha particles interact rather
weakly and can form loosely bound states near the threshold regions of alpha
decay.
In QCD, the state corresponding to alpha particle is a hadron which satu-
rates the strong color dependent force. If these hadrons have sufficient amount of
attraction (but weak as compared to the color force), they may form a bound or
18 Atsushi Hosaka
resonant state, which is the hadronic molecule. it must be a rather loosely bound
state having an extending spatial structure to retain the identity of hadronic con-
stituents. We expect that the relevant energy scale of binding and resonant states
should be sufficiently small as compared to ΛQCD of some hundreds MeV.
To establish exotic states is interesting not only for its own sake, but also
because it is expected to reveal important aspects of non-perturbative dynam-
ics of QCD. In this respect, as experimental observations imply, hadrons of light
and heavy quarks are interesting, where more candidates of exotic states are ob-
served. There, heavy quark symmetry and chiral symmetry play simultaneously.
The former suppresses the spin dependent interactions, leading to degeneracy
of different spin states. On the other hand, the latter is responsible for the pion
coupling to the light quarks, which provides the source of the strong one pion
exchange potential between heavy flavor hadrons. When these two conditions
are satisfied, we expect the formation of exotic hadronic molecules. The spin and
isospin dependent nature of the pion exchange potential as well as its orientation
dependence of the tensor structure are the cause of the rich structure of hadron
spectrum.
Based on these ideas, we have studied hadronic molecular states for exotic
heavy baryons in Refs. [8–10], and for exotic heavy mesons in Ref. [11–13]. They
are exotic not only due to hadronicmolecular structure but also due to their exotic
quantum numbers which are not accessible by the minimal number of quarks. In
forming the hadronic molecular state, the following three points are important;
(1) heavy mass which suppresses kinetic energy of constituent hadrons, (2) one
pion exchange force of tensor nature which mixes the 0− and 1− states (DD∗ and
BB∗), and (3) degeneracy of 0− and 1− states which makes the wider space of
coupled channels more effective to gain more attraction.
Hadronicmolecules have been also studied forDN systems of ordinary quan-
tumnumbers [14,15]. These channels allow evenmore attraction leading to deeply
bound states of a binding energy of order a few hundred MeV with much spa-
tially compact configuration. Here qq̄ annihilation is also possible, the treatment
of which is more difficult than in the case of exotic channel without qq̄ annihila-
tion.
Turning to the exotic channels, employing an interactions between heavy
flavor hadrons in a boson exchangemodel including one pion exchange potential,
we find several bound and resonant states near the threshold regions. Many of
them with small binding energy of order ten MeV or less have a rather extended
size compatible to hadronic molecules. For baryons, we have found bound states
of JP = 1/2− states of exotic quark content c̄q-qqq and b̄q-qqq just below the
threshold of D̄N and BN, respectively. Other resonant sates are also found for
JP = 3/2−, 1/2+, 3/2+, 5/2+ with similar structure of mass spectrum for c and b
quark sectors [9, 10].
For mesons, in the hidden bottom sector, we have found ten BB̄, BB̄∗, B∗B̄∗
molecules for low lying spin J ≤ 2. In particular, the hidden bottom exotic mesons
Zb’s are well predicted [11]. Further exotic states of double heavy flavor (charm
and bottom) mesons are also found [12]. In Ref. [13], we have estimated the decay
and production rates of various states in the limit of heavy quarks which are
Exotic molecules of heavy quark hadrons 19
characteristic to the hadronic molecular structure. These theoretical predictions
for rich structure of hadronic molecules can be studied in the facilities such as
Belle, JPARC and LHC.
Acknowledgements:
The author thanks, S. Yasui, S. Ohkoda, Y. Yamaguchi, K. Sudoh for discussions.
This work is partly supported by the Grant-in-Aid for Scientific Research on Pri-
ority Areas titled “Elucidation of New Hadrons with a Variety of Flavors” (E01:
21105006).
References
1. T. Nakano et al. [LEPS Collaboration], Phys. Rev. Lett. 91, 012002 (2003) [arXiv:hep-
ex/0301020].
2. B. Aubert et al. [BABAR Collaboration], Phys. Rev. Lett. 90, 242001 (2003) [arXiv:hep-
ex/0304021].
3. S.K. Choi et al. (Belle Collaboration), Phys. Rev. Lett. 91, 262001 (2003).
4. I. Adachi [Belle Collaboration], arXiv:1105.4583 [hep-ex].
5. A. Bondar et al. [Belle Collaboration], Phys. Rev. Lett. 108, 122001 (2012)
[arXiv:1110.2251 [hep-ex]].
6. J. Beringer et al. (Particle Data Group), Phys. Rev. D86, 010001 (2012).
7. K, Ikeda, H. Horiuchi and S. Saito, Prog. Theor. Phys. Supple. 68, 1 (1980).
8. S. Yasui and K. Sudoh, Phys. Rev. D 80, 034008 (2009) [arXiv:0906.1452 [hep-ph]].
9. Y. Yamaguchi, S. Ohkoda, S. Yasui and A. Hosaka, Phys. Rev. D 84, 014032 (2011)
[arXiv:1105.0734 [hep-ph]].
10. Y. Yamaguchi, S. Ohkoda, S. Yasui and A. Hosaka, Phys. Rev. D 85, 054003 (2012)
[arXiv:1111.2691 [hep-ph]].
11. S. Ohkoda, Y. Yamaguchi, S. Yasui, K. Sudoh and A. Hosaka, Phys. Rev. D 86, 014004
(2012) [arXiv:1111.2921 [hep-ph]].
12. S. Ohkoda, Y. Yamaguchi, S. Yasui, K. Sudoh and A. Hosaka, Phys. Rev. D 86, 034019
(2012) [arXiv:1202.0760 [hep-ph]].
13. S. Ohkoda, Y. Yamaguchi, S. Yasui and A. Hosaka, arXiv:1210.3170 [hep-ph].
14. J. Hofmann and M. F. M. Lutz, Nucl. Phys. A 763, 90 (2005) [hep-ph/0507071].
15. T. Mizutani and A. Ramos, Phys. Rev. C 74, 065201 (2006) [hep-ph/0607257].