Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2016 (2016), Article ID 3729050, 7 pages
http://dx.doi.org/10.1155/2016/3729050
Research Article

Production of in Radiative Decays

Department of Physics, Qufu Normal University, Qufu 273165, China

Received 16 March 2016; Revised 4 May 2016; Accepted 19 June 2016

Academic Editor: Alexey A. Petrov

Copyright © 2016 Qi Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

We investigate the production of in the process , where is assumed to be the counterpart of in the bottomonium sector as molecular state. We use the effective Lagrangian based on the heavy quark symmetry to explore the rescattering mechanism and calculate their production ratios. Our results have shown that the production ratios for are orders of with reasonable cutoff parameter range . The sizeable production ratios may be accessible at the future experiments like forthcoming BelleII, which will provide important clues to the inner structures of the exotic state .

1. Introduction

In the past decades, many so-called have been observed by the Belle, BaBar, CDF, D0, CMS, LHCb, and BESIII collaborations [1]. Some of them cannot fit into the conventional heavy quarkonium in the quark model [25]. Up to now, many studies on the production and decay of these states have been carried out in order to understand its nature (for a recent review, see [68]).

In 2003, the Belle collaboration discovered an exotic candidate in the process [9] which was subsequently confirmed by the BaBar collaboration [10] in the same channel. It was also discovered in proton-proton/antiproton collisions at the Tevatron [11, 12] and LHC [13, 14]. is a particularly intriguing state because on the one hand its total width  MeV [1] is tiny compared to typical hadronic widths and on the other hand the closeness of its mass to threshold ( MeV) and its prominent decays to [1] suggest that it may be an meson-meson molecular state [15, 16].

Many theoretical works have been carried out in order to understand the nature of since the first observation of . It is also natural to look for the counterpart with (denoted as hereafter) in the bottom sector. These two states are related by heavy quark symmetry which should have some universal properties. The search for may provide us with important information on the discrimination of a compact multiquark configuration and a loosely bound hadronic molecule configuration. Since the mass of may be very heavy and its is , it is less likely for a direct discovery at the current electron-positron collision facilities, though the Super KEKB may provide an opportunity in radiative decays [17]. In [18], a search for in the final states has been presented and no significant signal is observed for such a state.

The production of at the LHC and the Tevatron [19, 20] and other exotic states at hadron colliders [2126] has been extensively investigated. In the bottomonium system, the isospin is almost perfectly conserved, which may explain the escape of in the recent CMS search [27]. As a result, the radiative decays and isospin conserving decays will be of high priority in searching for [2830]. In [28], we have studied the radiative decays of (), with being a candidate for molecular state, and found that the partial widths into are about 1 keV. In [29], we studied the rescattering mechanism of the isospin conserving decays , and our results show that the partial width for is about tens of keVs.

In this work, we will further investigate production in with being molecule candidate. To investigate this process, we calculate the intermediate meson loop (IML) contributions. As well know, IML transitions have been one of the important nonperturbative transition mechanisms being noticed for a long time [3133]. Recently, this mechanism has been used to study the production and decays of ordinary and exotic states [3460] and decays [6168], and a global agreement with experimental data was obtained. Thus this approach may be suitable for the process .

The paper is organized as follows. In Section 2, we present the effective Lagrangians for our calculation. Then in Section 3, we present our numerical results. Finally we give the summary in Section 4.

2. Effective Lagrangians

Based on the heavy quark symmetry, we can write out the relevant effective Lagrangian for [68, 69]:where and correspond to the bottom meson isodoublets. is the antisymmetric Levi-Civita tensor and . Since is above the threshold of , the coupling constants between and can be determined via experimental data for [1]. The experimental branching ratios and the corresponding coupling constants are listed in Table 1. Since there is no experimental information on [1], we choose the coupling constants between and , the same values as that of .

Table 1: The coupling constants of interacting with . Here, we list the corresponding branching ratios of .

In order to calculate the process depicted in Figure 1, we also need the photonic coupling to the bottomed mesons. The magnetic coupling of the photon to heavy bottom meson is described by the Lagrangian [70, 71]withwhere is an unknown constant, is the light quark charge matrix, and is the heavy quark electric charge (in units of ). is determined in the nonrelativistic constituent quark model and has been adopted in the study of radiative decays [71]. In and systems, value is the same due to heavy quark symmetry [71]. In (2), the first term is the magnetic moment coupling of the light quarks, while the second one is the magnetic moment coupling of the heavy quark and hence is suppressed by .

Figure 1: Feynman diagrams for production in under meson loop effects.

At last, assume that is -wave molecule with given by the superposition of . and . hadronic configurations asAs a result, we can parameterize the coupling of to the bottomed mesons in terms of the following Lagrangian:where denotes the coupling constant. Since is slightly below -wave threshold, the effective coupling of this state is related to the probability of finding component in the physical wave function of the bound states and the binding energy, [36, 72, 73]:where and is the reduced mass. Here, we should also notice that the coupling constant in (6) is based on the assumption that is a shallow bound state where the potential binding the mesons is short-ranged.

Based on the relevant Lagrangians given above, the decay amplitudes in Figure 1 can be generally expressed as follows:where and are the vertex functions and the denominators of the intermediate meson propagators. For example, in Figure 1(a), are the vertex functions for the initial , final , and photon, respectively. are the denominators for the intermediate , , and propagators, respectively.

Since the intermediate exchanged bottom mesons in the triangle diagram in Figure 1 are off-shell, in order to compensate these off-shell effects arising from the intermediate exchanged particle and also the nonlocal effects of the vertex functions [7476], we adopt the following form factors:where corresponds to monopole and dipole form factor, respectively. and the QCD energy scale  MeV. This form factor is supposed and many phenomenological studies have suggested . These two form factors can help us explore the dependence of our results on the form factor.

The explicit expression of transition amplitudes can be found in Appendix  (A.) in [77], where radiative decays of charmonium are studied extensively based on effective Lagrangian approach.

3. Numerical Results

Before proceeding the numerical results, we first briefly review the predictions on mass of . The existence of is predicted in both the tetraquark model [78] and those involving a molecular interpretation [7981]. In [78], the mass of the lowest-lying tetraquark is predicated to be 10504 MeV, while the mass of molecular state is predicated to be a few tens of MeV higher [7981]. For example, in [79], the mass was predicted to be 10562 MeV, which corresponds to a binding energy to be 42 MeV, while the mass was predicted to be  MeV, which corresponds to a binding energy  MeV in [81]. As can be seen from the theoretical predictions, it might be a good approximation and might be applicable if the binding energy is less than 50 MeV. In order to cover the range of the previous molecular and tetraquark predictions on [7881], we present our results up to a binding energy of 100 MeV, and we will choose several illustrative values:  MeV.

In Table 2, we list the predicted branching ratios by choosing the monopole and dipole form factors and three values for the cutoff parameter in the form factor. As a comparison, we also list the predicted branching ratios in NREFT approach. From this table, we can see that the branching ratios for are orders of . The results are not sensitive to both the form factors and the cutoff parameter we choose.

Table 2: Predicted branching ratios for . The parameter in the form factor is chosen as , , and . The last column is the calculated branching ratios in NREFT approach.

In Figure 2(a), we plot the branching ratios for in terms of the binding energy with the monopole form factors (solid line), 2.5 (dashed line), and (dotted line), respectively. The coupling constant of in (6) and the threshold effects can simultaneously influence the binding energy dependence of the branching ratios. With the increasing of the binding energy , the coupling strength of increases, and the threshold effects decrease. Both the coupling strength of and the threshold effects vary quickly in the small region and slowly in the large region. As a result, the behavior of the branching ratios is relatively sensitive at small , while it becomes smooth at large . Results with the dipole form factors , 2.5, and 3.0 are shown in Figure 2(b) as solid, dash, and dotted curves, respectively. The behavior is similar to that of Figure 2(a).

Figure 2: (a) The dependence of the branching ratios of on using monopole form factors with (solid lines), (dashed lines), and (dotted lines), respectively. (b) The dependence of the branching ratios of on using dipole form factors with (solid lines), (dashed lines), and (dotted lines), respectively. The results with binding energy up to 100 MeV might make the molecular state assumption inaccurate.

We also predict the branching ratios of and present the relevant numerical results in Table 3 and Figure 3 with the monopole and dipole form factors. At the same cutoff parameter , the predicted rates for are a factor of 2-3 smaller than the corresponding rates for . It indicates that the intermediate -meson loop contribution to the process is smaller than that to . This is understandable since the mass of is more far away from the thresholds of than . But their branching ratios are also about orders of with a reasonable cutoff parameter .

Table 3: Predicted branching ratios for . The parameter in the form factor is chosen as , , and . The last column is the calculated branching ratios in NREFT approach.
Figure 3: (a) The dependence of the branching ratios of on using monopole form factors with (solid lines), (dashed lines), and (dotted lines), respectively. (b) The dependence of the branching ratios of on using dipole form factors with (solid lines), (dashed lines), and (dotted lines), respectively. The results with binding energy up to 100 MeV might make the molecular state assumption inaccurate.

In [51], authors introduced a nonrelativistic effective field theory method to study the meson loop effects of . Meanwhile they proposed a power counting scheme to estimate the contribution of the loop effects, which is used to judge the impact of the coupled-channel effects. For the diagrams in Figure 1, the vertex involving the initial bottomonium is in -wave. The momentum in this vertex is contracted with the final photon momentum and thus should be counted as . The decay amplitude scales as follows:where is understood as the average velocity of the intermediate bottomed mesons.

As a cross-check, we also present the branching ratios of the decays in the framework of NREFT. The relevant transition amplitudes are similar to that given in [36] with only different masses and coupling constants. The obtained numerical results for and in terms of the binding energy are listed in the last column of Tables 2 and 3, respectively. As shown in Table 2, except for the largest binding energy MeV, the NREFT predictions of are about 1 order of magnitude smaller than the ELA results at the commonly accepted range. For shown in Table 3, the NREFT predictions are several times smaller than the ELA results in small binding energy range, while the predictions of these two methods are comparable at large binding energy. These differences may give some sense of the theoretical uncertainties for the predicted rates and indicate the viability of our model to some extent.

Here we should notice, for the isoscalar , the pion exchanges might be nonperturbative and produce sizeable effects [8183]. In [81], their calculations show that the relative errors of are about 20% for . Even if we take into account this effect, the estimated order of the magnitude for the branching ratio may also be sizeable, which may be measured in the forthcoming BelleII experiments.

4. Summary

In this work, we have investigated the production of in the radiative decays of . Based on molecular state picture, we considered its production through the mechanism with intermediate bottom meson loops. Our results have shown that the production ratios for are about orders of with a commonly accepted cutoff range . As a cross-check, we also calculated the branching ratios of the decays in the framework of NREFT. Except for the large binding energy, the NREFT predictions of are about 1 order of magnitude smaller than the ELA results. The NREFT predictions of are several times smaller than the ELA results in small binding energy range, while the predictions of these two methods are comparable at large binding energy. In [28, 29], we have studied the radiative decays and the hidden bottomonium decays of . If we consider that the branching ratios of the isospin conserving process are relatively large, a search for may be possible for the updated BelleII experiments. These studies may help us investigate deeply. The experimental observation of will provide us with further insight into the spectroscopy of exotic states and is helpful to probe the structure of the states connected by the heavy quark symmetry.

Competing Interests

The authors declare that they have no competing interests.

Acknowledgments

This work is supported in part by the National Natural Science Foundation of China (Grants nos. 11275113, 11575100, and 11505104) and the Natural Science Foundation of Shandong Province (Grant no. ZR2015JL001).

References

  1. K. A. Olive, K. Agashe, C. Amsler et al., “Review of particle physics,” Chinese Physics C, vol. 38, no. 9, Article ID 090001, 2014. View at Publisher · View at Google Scholar
  2. N. Brambilla, S. Eidelman, B. K. Heltsley et al., “Heavy quarkonium: progress, puzzles, and opportunities,” The European Physical Journal C, vol. 71, article 1534, 2011. View at Publisher · View at Google Scholar
  3. S. Godfrey and S. L. Olsen, “The exotic XYZ charmonium-like mesons,” Annual Review of Nuclear and Particle Science, vol. 58, pp. 51–73, 2008. View at Publisher · View at Google Scholar
  4. N. Drenska, R. Faccini, F. Piccinini, A. Polosa, F. Renga, and C. Sabelli, “New hadronic spectroscopy,” Rivista del Nuovo Cimento, vol. 33, no. 11, pp. 633–712, 2010. View at Publisher · View at Google Scholar · View at Scopus
  5. G. T. Bodwin, E. Braaten, E. Eichten, S. L. Olsen, T. K. Pedlar, and J. Russ, “Quarkonium at the frontiers of high energy physics: a snowmass white paper,” http://arxiv.org/abs/1307.7425.
  6. W. Chen, W.-Z. Deng, J. He et al., “XYZ states,” http://arxiv.org/abs/1311.3763.
  7. X. Liu, “An overview of XYZ new particles,” Chinese Science Bulletin, vol. 59, no. 29, pp. 3815–3830, 2014. View at Publisher · View at Google Scholar
  8. H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, “The hidden-charm pentaquark and tetraquark states,” Physics Reports, vol. 639, pp. 1–121, 2016. View at Publisher · View at Google Scholar
  9. S.-K. Choi, S. L. Olsen, K. Abe et al., “Observation of a narrow charmoniumlike state in exclusive B±K±π+π-J/ψ decays,” Physical Review Letters, vol. 91, no. 26, Article ID 262001, 6 pages, 2003. View at Publisher · View at Google Scholar
  10. B. Aubert, M. Bona, Y. Karyotakis et al., “Study of the B-J/ψK-π+π- decay and measurement of the B-X3872K branching fraction,” Physical Review D, vol. 71, no. 7, Article ID 071103, 2005. View at Publisher · View at Google Scholar
  11. V. M. Abazov, B. Abbott, M. Abolins et al., “Observation and Properties of the X(3872) decaying to J/ψπ+π- in pp- Collisions at s=1.93 TeV,” Physical Review Letters, vol. 93, no. 16, Article ID 162002, 6 pages, 2002. View at Publisher · View at Google Scholar
  12. T. Aaltonen, J. Adelman, T. Akimoto et al., “Precision measurement of the X(3872) Mass in J/ψπ+π- decays,” Physical Review Letters, vol. 103, Article ID 152001, 2009. View at Publisher · View at Google Scholar
  13. S. Chatrchyan, V. Khachatryan, A. M. Sirunyan et al., “Measurement of the X(3872) production cross section via decays to J/ψπ+π- in pp collisions at s=7 Tev,” Journal of High Energy Physics, vol. 2013, article 154, 2013. View at Publisher · View at Google Scholar
  14. R. Aaij, C. Abellan Beteta, B. Adeva et al., “Determination of the X(3872) Meson quantum numbers,” Physical Review Letters, vol. 110, no. 22, Article ID 222001, 8 pages, 2013. View at Publisher · View at Google Scholar
  15. N. A. Tornqvist, “Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson,” Physics Letters B, vol. 590, no. 3-4, pp. 209–215, 2004. View at Publisher · View at Google Scholar
  16. C. Hanhart, S. Kalashnikova, A. E. Kudryavtsev, and A. V. Nefediev, “Reconciling the X(3872) with the near-threshold enhancement in the D0D-0 final state,” Physical Review D, vol. 76, no. 3, Article ID 034007, 9 pages, 2007. View at Publisher · View at Google Scholar
  17. T. Aushev, W. Bartel, A. Bondar et al., “Physics at super B factory,” https://arxiv.org/abs/1002.5012.
  18. X. H. He, C. P. Shen, C. Z. Yuan et al., “Observation of e+e-π+π-π0xbJ and Search for Xbωγ1S at s=10.867,” Physical Review Letters, vol. 113, no. 14, Article ID 142001, 2014. View at Publisher · View at Google Scholar
  19. F. K. Guo, U. G. Meißner, W. Wang, and Z. Yang, “Production of the bottom analogs and the spin partner of the X(3872) at hadron colliders,” The European Physical Journal C, vol. 74, article 3063, 2014. View at Publisher · View at Google Scholar
  20. F.-K. Guo, U.-G. Meißner, and W. Wang, “Production of charged heavy quarkonium-like states at the LHC and Tevatron,” Communications in Theoretical Physics, vol. 61, no. 3, pp. 354–358, 2014. View at Publisher · View at Google Scholar
  21. C. Bignamini, B. Grinstein, F. Piccinini, A. D. Polosa, and C. Sabelli, “Is the X(3872) production cross section at s=1.96 Tev compatible with a hadron molecule interpretation?” Physical Review Letters, vol. 103, no. 6, Article ID 162001, 4 pages, 2009. View at Publisher · View at Google Scholar
  22. A. Esposito, F. Piccinini, A. Pilloni, and A. D. Polosa, “A mechanism for hadron molecule production in pp-(p) collisions,” Journal of Modern Physics, vol. 4, pp. 1569–1573, 2013. View at Publisher · View at Google Scholar
  23. P. Artoisenet and E. Braaten, “Production of the X(3872) at the Tevatron and the LHC,” Physical Review D, vol. 81, Article ID 114018, 2010. View at Publisher · View at Google Scholar
  24. P. Artoisenet and E. Braaten, “Estimating the production rate of loosely bound hadronic molecules using event generators,” Physical Review D, vol. 83, no. 1, Article ID 014019, 10 pages, 2011. View at Publisher · View at Google Scholar
  25. A. Ali and W. Wang, “Production of the exotic 1-- Hadrons ϕ(2170), X(4260), and Yb(10890) at the LHC and Tevatron via the Drell-Yan mechanism,” Physical Review Letters, vol. 106, no. 19, Article ID 192001, 2011. View at Publisher · View at Google Scholar
  26. A. Ali, C. Hambrock, and W. Wang, “Hadroproduction of γnS above the BB- thresholds and implications for Yb(10890),” Physical Review D, vol. 88, no. 5, Article ID 054026, 2013. View at Publisher · View at Google Scholar
  27. S. Chatrchyan, V. Khachatryan, A. M. Sirunyan et al., “Search for a new bottomonium state decaying to ϒ(1S)π+π- in pp collisions at s=8 TeV,” Physics Letters B, vol. 727, no. 1–3, pp. 57–76, 2013. View at Publisher · View at Google Scholar
  28. G. Li and W. Wang, “Hunting for the Xb via radiative decays,” Physics Letters B, vol. 733, pp. 100–104, 2014. View at Publisher · View at Google Scholar
  29. G. Li and Z. Zhou, “Hunting for the Xb via hidden bottomonium decays,” Physical Review D, vol. 91, no. 3, Article ID 034020, 2015. View at Publisher · View at Google Scholar
  30. M. Karliner, “Doubly heavy tetraquarks and baryons,” EPJ Web of Conferences, vol. 71, Article ID 00065, 2014. View at Publisher · View at Google Scholar
  31. H. J. Lipkin, “Cancellations in two-step OZI-violating transitions,” Nuclear Physics B, vol. 291, pp. 720–730, 1987. View at Publisher · View at Google Scholar
  32. H. J. Lipkin and S. F. Tuan, “OZI-violating dipion decays of heavy quarkonia via an intermediate heavy meson pair state,” Physics Letters B, vol. 206, no. 2, pp. 349–353, 1988. View at Publisher · View at Google Scholar · View at Scopus
  33. P. Moxhay, “Coupled-channel effects in the decay Υ(3S)Υ(1S)π+π-,” Physical Review D, vol. 39, no. 11, pp. 3497–3499, 1989. View at Publisher · View at Google Scholar
  34. Q. Wang, C. Hanhart, and Q. Zhao, “Decoding the Riddle of Y(4260) and Zc(3900),” Physical Review Letters, vol. 111, no. 13, Article ID 132003, 2013. View at Publisher · View at Google Scholar
  35. X.-H. Liu and G. Li, “Exploring the threshold behavior and implications on the nature of Y(4260) and Zc(3900),” Physical Review D, vol. 88, no. 1, Article ID 014013, 9 pages, 2013. View at Publisher · View at Google Scholar
  36. F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, and Q. Zhao, “Production of the X(3872) in charmonia radiative decays,” Physics Letters B, vol. 725, no. 1–3, pp. 127–133, 2013. View at Publisher · View at Google Scholar
  37. Q. Wang, C. Hanhart, and Q. Zhao, “Systematic study of the singularity mechanism in heavy quarkonium decays,” Physics Letters B, vol. 725, no. 1–3, pp. 106–110, 2013. View at Publisher · View at Google Scholar
  38. M. Cleven, Q. Wang, F.-K. Guo, C. Hanhart, U.-G. Meißner, and Q. Zhao, “Confirming the molecular nature of the Zb(10610) and the Zb(10650),” Physical Review D, vol. 87, no. 7, Article ID 074006, 12 pages, 2013. View at Publisher · View at Google Scholar
  39. D.-Y. Chen and X. Liu, “Zb (10610) and Zb (10650) structures produced by the initial single pion emission in the Y(5S) decays,” Phys. Rev. D, vol. 84, Article ID 094003, 2011. View at Publisher · View at Google Scholar
  40. G. Li, F. I. Shao, C. W. Zhao, and Q. Zhao, “Zb/ZbΥπ and hbπ decays in intermediate meson loops model,” Physical Review D, vol. 87, Article ID 034020, 2013. View at Publisher · View at Google Scholar
  41. G. Li and X.-H. Liu, “Investigating possible decay modes of Y(4260) under D12420D-+c.c. molecular state ansatz,” Physical Review D, vol. 88, no. 9, Article ID 094008, 8 pages, 2013. View at Publisher · View at Google Scholar
  42. G. Li, C. S. An, P. Y. Li, D. Liu, X. Zhang, and Z. Zhou, “Investigations on the charmless decays of Y(4260),” Chinese Physics C, vol. 39, no. 6, Article ID 063102, 2015. View at Publisher · View at Google Scholar
  43. G. Li, X. H. Liu, and Z. Zhou, “More hidden heavy quarkonium molecules and their discovery decay modes,” Physical Review D, vol. 90, no. 5, Article ID 054006, 7 pages, 2014. View at Publisher · View at Google Scholar
  44. G. Li, X.-H. Liu, and Q. Zhao, “Evasion of HSR in S-wave charmonium decaying to P-wave light hadrons,” The European Physical Journal C, vol. 73, article 2576, 2013. View at Publisher · View at Google Scholar
  45. G. Li, “Hidden-charmonium decays of Zc (3900) and Zc (4025) in intermediate meson loops model,” The European Physical Journal C, vol. 73, article 2621, 2013. View at Publisher · View at Google Scholar
  46. G. Li, X.-H. Liu, Q. Wang, and Q. Zhao, “Further understanding of the non-DD- decays of ψ(3770),” Physical Review D, vol. 88, Article ID 014010, 8 pages, 2013. View at Publisher · View at Google Scholar
  47. G. Li and Q. Zhao, “Revisit the radiative decays of J/ψ and ψγηc(γηc),” Physical Review D, vol. 84, no. 7, Article ID 074005, 7 pages, 2011. View at Publisher · View at Google Scholar
  48. M. B. Voloshin, “Enhanced mixing of partial waves near threshold for heavy meson pairs and properties of Zb(10610) and Zb(10650) resonances,” Physical Review D, vol. 87, no. 7, Article ID 074011, 4 pages, 2013. View at Publisher · View at Google Scholar
  49. M. B. Voloshin, “Radiative transitions from Υ5S,” Physical Review D, vol. 84, no. 3, Article ID 031502, 2011. View at Publisher · View at Google Scholar
  50. A. E. Bondar, A. Garmash, A. I. Milstein, R. Mizuk, and M. B. Voloshin, “Heavy quark spin structure in Zb resonances,” Physical Review D, vol. 84, Article ID 054010, 2011. View at Publisher · View at Google Scholar
  51. F.-K. Guo, C. Hanhart, and U.-G. Meißner, “Extraction of the light quark mass ratio from the decays ψJ/ψπ0η,” Physical Review Letters, vol. 103, no. 8, Article ID 082003, 2009, Erratum: Physical Review Letters, vol. 104, no. 8, 109901, 2010. View at Publisher · View at Google Scholar
  52. F.-K. Guo, C. Hanhart, G. Li et al., “Novel analysis of the decays ψhcπ0 and ηcχc0π0,” Physical Review D, vol. 82, Article ID 034025, 2010. View at Publisher · View at Google Scholar
  53. F.-K. Guo, C. Hanhart, G. Li, U.-G. Meißner, and Q. Zhao, “Effect of charmed meson loops on charmonium transitions,” Physical Review D, vol. 83, no. 3, Article ID 034013, 2011. View at Publisher · View at Google Scholar
  54. D.-Y. Chen, X. Liu, and T. Matsuki, “Charged bottomoniumlike structures in the hidden-bottom dipion decays of Υ(11020),” Physical Review D, vol. 84, no. 7, Article ID 074032, 5 pages, 2011. View at Publisher · View at Google Scholar
  55. D.-Y. Chen, X. Liu, and T. Matsuki, “Interpretation of Zb(10610) and Zb(10650) in the ISPE mechanism and the Charmonium Counterpart,” Chinese Physics C, vol. 38, no. 5, Article ID 053102, 2014. View at Publisher · View at Google Scholar
  56. D.-Y. Chen, X. Liu, and T. Matsuki, “Reproducing the Zc (3900) structure through the initial-single-pion-emission mechanism,” Physical Review D, vol. 88, no. 3, Article ID 036008, 2013. View at Publisher · View at Google Scholar
  57. D.-Y. Chen, X. Liu, and T. Matsuki, “Novel charged charmoniumlike structures in the hidden-charm dipion decays of Y(4360),” Physical Review D, vol. 88, no. 1, Article ID 014034, 5 pages, 2013. View at Publisher · View at Google Scholar
  58. Q. Wang, G. Li, and Q. Zhao, “Open charm effects in the explanation of the long-standing ‘ρπ puzzle’,” Physical Review D, vol. 85, no. 7, Article ID 074015, 2012. View at Publisher · View at Google Scholar
  59. Y. J. Zhang, G. Li, and Q. Zhao, “Manifestation of intermediate meson loop effects in charmonium decays,” Chinese Physics C, vol. 34, no. 9, pp. 1181–1184, 2010. View at Publisher · View at Google Scholar
  60. G. Li, Y. J. Zhang, Q. Zhao, and B. S. Zou, “Isospin violating mechanisms in quarkonium hadronic decays,” Chinese Physics C, vol. 34, no. 6, pp. 842–847, 2010. View at Publisher · View at Google Scholar
  61. D.-S. Du, X.-Q. Li, Z.-T. Wei, and B.-S. Zou, “Inelastic final-state interactions in BVVπ K processes,” The European Physical Journal A, vol. 4, no. 1, pp. 91–96, 1999. View at Publisher · View at Google Scholar
  62. C.-H. Chen and H.-N. Li, “Final-state interaction and BKK decays in perturbative QCD,” Physical Review D, vol. 63, no. 1, Article ID 014003, 12 pages, 2000. View at Publisher · View at Google Scholar
  63. X. Liu and X.-Q. Li, “Effects of hadronic loops on the direct CP violation of Bc,” Physical Review D, vol. 77, no. 9, Article ID 096010, 2008. View at Publisher · View at Google Scholar
  64. P. Colangelo, F. De Fazio, and T. N. Pham, “B-K-Xc0 decay from charmed meson rescattering,” Physics Letters B, vol. 542, no. 1-2, pp. 71–79, 2002. View at Publisher · View at Google Scholar
  65. H.-Y. Cheng, C.-K. Chua, and A. Soni, “Final state interactions in hadronic B decays,” Physical Review D, vol. 71, no. 1, Article ID 014030, 38 pages, 2005. View at Publisher · View at Google Scholar
  66. C.-D. Lu, Y.-L. Shen, and W. Wang, “Final state interaction in BKK decays,” Physical Review D, vol. 73, Article ID 034005, 2006. View at Publisher · View at Google Scholar
  67. X. Liu, Z.-T. Wei, and X.-Q. Li, “Contribution of final-state interaction to the branching ratio of BJ/ψD,” The European Physical Journal C, vol. 59, no. 3, pp. 683–689, 2009. View at Publisher · View at Google Scholar
  68. P. Colangelo, F. De Fazio, and T. N. Pham, “Nonfactorizable contributions in B decays to charmonium: the case of B-K-hc,” Physical Review D, vol. 69, Article ID 054023, 2004. View at Publisher · View at Google Scholar
  69. R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio, and G. Nardulli, “Phenomenology of heavy meson chiral lagrangians,” Physics Report, vol. 281, no. 3, pp. 145–238, 1997. View at Publisher · View at Google Scholar · View at Scopus
  70. J. Hu and T. Mehen, “Chiral Lagrangian with heavy quark-diquark symmetry,” Physical Review D, vol. 73, no. 5, Article ID 054003, 11 pages, 2006. View at Publisher · View at Google Scholar
  71. J. F. Amundson, C. G. Boyd, E. E. Jenkins et al., “Radiative D decay using heavy quark and chiral symmetry,” Physics Letters B, vol. 296, no. 3-4, pp. 415–419, 1992. View at Publisher · View at Google Scholar · View at Scopus
  72. S. Weinberg, “Evidence that the deuteron is not an elementary particle,” Physical Review, vol. 137, pp. B672–B678, 1965. View at Google Scholar · View at MathSciNet
  73. V. Baru, J. Haidenbauer, C. Hanhart, Y. Kalashnikova, and A. E. Kudryavtsev, “Evidence that the a0(980) and f0(980) are not elementary particles,” Physics Letters B, vol. 586, no. 1-2, pp. 53–61, 2004. View at Publisher · View at Google Scholar
  74. X.-Q. Li, D. V. Bugg, and B.-S. Zou, “Possible explanation of the ‘ρπ puzzle’ in J/ψ, ψ decays,” Physical Review D, vol. 55, no. 3, pp. 1421–1424, 1997. View at Publisher · View at Google Scholar
  75. M. P. Locher, Y. Lu, and B. S. Zou, “Rates for the reactions p-pπϕ and γϕ,” Zeitschrift für Physik A Hadrons and Nuclei, vol. 347, no. 4, pp. 281–284, 1994. View at Publisher · View at Google Scholar
  76. X.-Q. Li and B.-S. Zou, “Significance of single pion exchange inelastic final state interaction for DVP processes,” Physics Letters B, vol. 399, no. 3-4, pp. 297–302, 1997. View at Publisher · View at Google Scholar
  77. C.-W. Zhao, G. Li, X.-H. Liu, and F.-L. Shao, “Effects of heavy meson loops on heavy quarkonium radiative transitions,” The European Physical Journal C, vol. 73, no. 7, article 2482, 2013. View at Publisher · View at Google Scholar
  78. A. Ali, C. Hambrock, I. Ahmed, and M. J. Aslam, “A case for hidden bb- tetraquarks based on e+e-bb- cross section between s=10.54 and 11.20 GeV,” Physics Letters B, vol. 684, no. 1, pp. 28–39, 2010. View at Publisher · View at Google Scholar
  79. N. A. Törnqvist, “From the deuteron to deusons, an analysis of deuteronlike meson-meson bound states,” Zeitschrift für Physik C Particles and Fields, vol. 61, no. 3, pp. 525–537, 1994. View at Publisher · View at Google Scholar
  80. M. Karliner and S. Nussinov, “The doubly heavies: Q-Qq-q and QQq-q- tetraquarks and QQq baryons,” JHEP, vol. 1307, article 153, 2013. View at Publisher · View at Google Scholar
  81. F.-K. Guo, C. Hidalgo-Duque, J. Nieves, and M. P. Valderrama, “Consequences of heavy-quark symmetries for hadronic molecules,” Physical Review D, vol. 88, no. 5, Article ID 054007, 5 pages, 2013. View at Publisher · View at Google Scholar
  82. T. Mehen and J. W. Powell, “Heavy quark symmetry predictions for weakly bound B-meson molecules,” Physical Review D, vol. 84, Article ID 114013, 2011. View at Publisher · View at Google Scholar
  83. M. P. Valderrama, “Power counting and perturbative one pion exchange in heavy meson molecules,” Physical Review D, vol. 85, no. 11, Article ID 114037, 21 pages, 2012. View at Publisher · View at Google Scholar