Chinese Physics C REVIEWS • OPEN ACCESS Issues and Opportunities in Exotic Hadrons To cite this article: R. A. Briceño et al 2016 Chinese Phys. C 40 042001   View the article online for updates and enhancements. Related content A review of the open charm and open bottom systems Hua-Xing Chen, Wei Chen, Xiang Liu et al. - Progress towards understanding baryon resonances V Crede and W Roberts - Exotic charmonium Galina V Pakhlova, Pavel N Pakhlov and Semen I Eidel'man - Recent citations Nonmesonic weak decay of charmed hypernuclei C E Fontoura et al - The Joint Physics Analysis Center: Recent results César Fernández-Ramírez - Amplitude analysis of K N scattering César Fernández-Ramírez - This content was downloaded from IP address 186.217.236.64 on 02/07/2019 at 16:40 https://doi.org/10.1088/1674-1137/40/4/042001 http://iopscience.iop.org/article/10.1088/1361-6633/aa6420 http://iopscience.iop.org/article/10.1088/1361-6633/aa6420 http://iopscience.iop.org/article/10.1088/0034-4885/76/7/076301 http://iopscience.iop.org/article/10.1088/0034-4885/76/7/076301 http://iopscience.iop.org/article/10.3367/UFNe.0180.201003a.0225 http://iopscience.iop.org/0954-3899/45/1/015101 http://iopscience.iop.org/0954-3899/45/1/015101 http://iopscience.iop.org/1742-6596/761/1/012078 http://iopscience.iop.org/1742-6596/761/1/012078 http://iopscience.iop.org/1742-6596/730/1/012010 http://iopscience.iop.org/1742-6596/730/1/012010 http://iopscience.iop.org/1742-6596/730/1/012010 Chinese Physics C Vol. 40, No. 4 (2016) 042001 Issues and Opportunities in Exotic Hadrons * R. A. Briceño1,2 T. D. Cohen3 S. Coito4 J. J. Dudek1,2;1) E. Eichten5 C. S. Fischer6 M. Fritsch7,8 W. Gradl8 A. Jackura9 M. Kornicer10 G. Krein11 R. F. Lebed12 F. A. Machado13 R. E. Mitchell14;2) C. J. Morningstar15 M. Peardon16 M. R. Pennington1 K. Peters17 J. M. Richard18 C. P. Shen19 M. R. Shepherd14 T. Skwarnicki20 E. S. Swanson13;3) A. P. Szczepaniak21,22,9 C. Z. Yuan23 1 Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, VA 23606, USA 2 Department of Physics, Old Dominion University, Norfolk, VA 23529, USA 3 Maryland Center for Fundamental Physics, University of Maryland, College Park, MD, USA 4 Institute of Modern Physics, CAS, Lanzhou 730000, China 5 Theoretical Physics Department, Fermilab, IL 60510, USA 6 Institut für Theoretische Physik, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 16, D-35392 Gießen, Germany 7 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany 8 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany 9 Physics Department, Indiana University, Bloomington, IN 47405, USA 10 University of Hawaii, Honolulu, Hawaii 96822, USA 11 Instituto de F́ısica Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271 - Bloco II, 01140-070 São Paulo, SP, Brazil 12 Department of Physics, Arizona State University, Tempe, Arizona 85287-1504, USA 13 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA 14 Indiana University, Bloomington, Indiana 47405, USA 15 Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA 16 School of Mathematics, Trinity College, Dublin 2, Ireland 17 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany 18 Université de Lyon, Institut de Physique Nucléaire de Lyon, IN2P3-CNRS-UCBL, 4, rue Enrico Fermi, Villeurbanne, France 19 Beihang University, Beijing 100191, China 20 Syracuse University, Syracuse, NY, USA 21 Theory Center, Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, VA 23606, USA 22 Center for Exploration of Energy and Matter, Indiana University, Bloomington, IN 47403, USA 23 Institute of High Energy Physics, Beijing 100049, China Abstract: The last few years have been witness to a proliferation of new results concerning heavy exotic hadrons. Experimentally, many new signals have been discovered that could be pointing towards the existence of tetraquarks, Received 15 December 2015 ∗ Supported by U.S. Department of Energy (Cohen); the Institute of Modern Physics and Chinese Academy of Sciences under contract Y104160YQ0 and agreement No. 2015-BH-02 (Coito); the U.S. Department of Energy, for grant DE-AC05-06OR23177, under which Jefferson Science Associates, LLC, manages and operates Jefferson Laboratory and DE-SC0006765, Early Career award (Dudek); Fermilab, operated by the Fermi Research Alliance under contract number DEAC02-07CH11359 with the U.S. Department of Energy (Eichten); BMBF, under contract No. 06GI7121, and the DAAD under contract No. 56889822 and by the Helmholtz International Center for FAIR within the LOEWE program of the State of Hesse (Fischer); the German Research Foundation DFG under contract number Collaborative Research Centre CRC-1044 (Gradl); the Conselho Nacional de Desenvolvimento Cient́ıfico e Tecnológico - CNPq, Grant No. 305894/2009-9 and Fundação de Amparo à Pesquisa do Estado de São Paulo - FAPESP, Grant No. 2013/01907-0 (Krein); U.S. National Science Foundation, under grants PHY-1068286 and PHY-1403891 (Lebed); the Brazilian National Council for Scientific and Technological Development under grant CNPq/CAPES-208188/2014-2 (Machado); U.S. Department of Energy under grant DE-FG02- 05ER41374 (Mitchell); U.S. National Science Foundation under grant PHY-1306805 (Morningstar); U.S. Department of Energy, supported by Jefferson Science Associates, LLC under contract No. DE-AC05-06OR23177 (Pennington); the National Natural Science Foundation of China (NSFC) under contract No. 11575017, the Ministry of Science and Technology of China under Contract No. 2015CB856701 (Shen); U.S. Department of Energy, under grant DE-FG02-05ER41374 (Shepherd); U.S. National Science Foundation under grant PHY- 1507572 (Skwarnicki); U.S. Department of Energy, under contract DE-AC05-06OR23177 and grant DE-FG0287ER40365 (Szczepaniak); the National Natural Science Foundation of China (NSFC) under contract numbers 11235011 and 11475187 (Yuan). 1) E-mail: dudek@jlab.org 2) E-mail: remitche@indiana.edu 3) E-mail: swansone@pitt.edu Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd d 042001-1 Chinese Physics C Vol. 40, No. 4 (2016) 042001 pentaquarks, and other exotic configurations of quarks and gluons. Theoretically, advances in lattice field theory techniques place us at the cusp of understanding complex coupled-channel phenomena, modelling grows more sophis- ticated, and effective field theories are being applied to an ever greater range of situations. It is thus an opportune time to evaluate the status of the field. In the following, a series of high priority experimental and theoretical issues concerning heavy exotic hadrons is presented. Keywords: hadronic physics, exotic hadrons, tetraquark, pentaquark PACS: 12.38.Aw, 12.38.Qk, 14.40.Pq DOI: 10.1088/1674-1137/40/4/042001 1 Introduction In 2007 the Belle Collaboration claimed the discov- ery of the Z(4430). This state attracted considerable attention because it is charged and couples to charmo- nium, implying that the most economical interpretation of its quark content is cc̄ūd. The recent high statis- tics confirmation of the Z by the LHCb collaboration, and the startling demonstration of phase motion, has brought sharp focus on exotic hadronic matter. Indeed, the Z(4430) joins a long list of other putative exotic states, several of which have been reported within the past year: cc̄ multiquarks X(3872), Zc(3900), Y(3940), Zc(4020), Z1(4050), Z2(4250), Y(4140) bb̄ multiquarks Zb(10610), Zb(10650) other unusual states Ds(2317), H dibaryon, Y(2175), Y(4260), Y(4660), Yb(10888), π1(1600), π(1800), f0(1500). Although hadronic exotics such as glueballs, hybrids, and multiquark states have been long expected, the un- derstanding of these states is primarily at the level of conjecture. Certainly, if the confirmation of the Z(4430) marks the beginning of the exploration of a new sector of matter, the current phenomenology concerning quark interactions will need to be radically overhauled. A com- pelling and unified understanding of the new states has not yet emerged, and the gap between theory and exper- iment remains a major deficiency in our current level of understanding of elementary particle physics. This gap has its roots in the famously difficult prob- lem of solving QCD in its many-body, strongly interact- ing, relativistic regime. Current effective field theories are inoperable in the excited spectrum, lattice field the- ory has difficulties with weakly bound diffuse coupled- channel systems, and extant phenomenological models are insufficiently well constrained to be confidently ap- plied to exotic states. Even the lack of knowledge of relatively simple dynamics, such as interactions in the Kπ system, can affect the analysis of data concerning the new states. The flood of information initiated by B factories (CLEO, BaBar, Belle), τ-charm facilities (CLEO-c, BE- SIII), and hadron machines (CDF, D0, LHCb, ATLAS, CMS) is not expected to abate soon. LHCb will continue to deliver new results in heavy quark spectroscopy for at least a decade. At the same time, BESIII at the Bei- jing Electron Positron Collider will continue its program to collect and analyze e+e− data in the energy region of the putative exotic states of charmonium. Further- more, the GlueX experiment is due to start taking data in 2015. This experiment, situated at Hall D at JLab, is designed to discover and explore the properties of light hybrid mesons. The COMPASS experiment at CERN has been, and will continue to be, very active in hadron spectroscopy. The PANDA experiment at FAIR is ex- pected to start taking data in 2019; amongst its goals is the exploration of charmonium hybrids and other exotic states. In view of this situation, a workshop was convened at the Institute of Nuclear Theory, Seattle, with the aim of assessing the status of the field and drawing up a short list of questions that have the potential to move the field forward. This document is the outcome. We stress that this is not meant as a review, for which the reader is di- rected to Refs. [1–5]. Furthermore, the topics contained herein are not meant to be comprehensive, but are of- fered in the hope that progress will be spurred in various directions. The next three sections provide specific queries in the areas of lattice field theory, experiment, and theory. The lattice method has been singled out because it has ad- vanced to the stage where modelling issues are minimal, but where results are sufficiently complex that experi- mental methods must sometimes be invoked to interpret them. Finally, the interface between theory and experi- ment is addressed in section 5. Here the emphasis is on smoothing the interaction between theorists and exper- imental collaborations with the hope of drawing on the strengths of both communities. 2 Lattice QCD calculations 2.1 Compute quantities as a function of light quark mass 042001-2 Chinese Physics C Vol. 40, No. 4 (2016) 042001 A better determination of the contribution of (vir- tual) two heavy-light meson loops in QQ̄ states below threshold is needed. Coupled channel phenomenologi- cal models suggest that for QQ̄ states near threshold these contributions are significant. After renormaliza- tion of the bare model parameters, one finds modest shifts in the leading nonrelativistic mass spectrum. Spin splittings between ground state heavy-light mesons in- duce spin-dependent effects in the spectrum and allow hadronic transitions that violate the Heavy Quark Spin Symmetry expectations. Furthermore, the mass split- tings between the Qū, Qd̄ and Qs̄ ground state heavy- light mesons allows small isospin breaking and consider- able SU(3) breaking effects. In particular, this may be evident in the large X(3872) → ρJ/ψ and ψ(2S) → ηψ transition rates. In lattice QCD calculations, as the light quark masses are varied down from infinite (quenched approximation) to the scale of the momentum in the QQ̄ system, the dominant effect of light quark loops is to modify the run- ning of the QCD coupling (αs). But as the quark masses are varied below this scale and below ΛQCD, light quark loops become spatially extended and probe the effects of coupled channels in the hadronic basis of states. Initial effort in exploring these effects are described in Refs. [6]. We suggest that detailed lattice studies of the QQ̄ mass spectrum as a function of light quark masses (mu,md,ms) for masses in a range between their phys- ical values and ≈ 2×ΛQCD will give much insight into the effects of coupling to decay channels in a model in- dependent way. Furthermore, a calculation of hadronic transition rates as a function of light quark masses would be very illuminating. 2.2 Develop and implement coupled-channel scattering formalism The recent publication [7–9] of the first determina- tions of coupled-channel scattering amplitudes from lat- tice QCD offers promise that this first-principles ap- proach to QCD might shed light on the exotic behavior being observed in charmonium. For the case of coupled two-body scattering, resonant singularities in the ampli- tudes can be explored using parameterizations of the T- matrix, where the parameters are tuned to describe the finite-volume spectra calculated in lattice QCD. From the pole positions and residues, masses, widths, and branching fractions of resonances can be determined – the distribution of poles across unphysical Riemann sheets may offer a discriminator for the internal struc- ture of the resonances. There has been no application of these coupled- channel techniques to meson systems featuring charm quarks, and only limited studies of elastic scattering, which is a situation in need of remedy. Early targets will be charmed systems near threshold like DK, Dsη and Dπ,Dη as well as exotic isospin and strangeness channels[10]. Double charmed channels like DD are also relatively simple. Hidden charm channels are challeng- ing, because while all the tools are in place to deal with the coupled DD̄,DD̄∗,D∗D̄∗,DsD̄s, · · · system, the open- ing of three-body channels like ηcππ and J/ψππ occurs at rather low energies. No complete formalism to re- late finite-volume spectra to three-body scattering am- plitudes yet exists – such a formalism will be required to study such systems in detail. Calculations of meson-baryon scattering are at a less advanced stage than those for meson-meson scattering. Current stochastic methods for dealing with quark prop- agation make the calculation of the J/ψp scattering am- plitudes straightforward with a modest increase in cost over meson-meson amplitudes, even for large volumes [11]. 2.3 Investigate static quark interactions Recent improvements to the set of techniques avail- able for computing light quark propagation on the lattice should encourage practitioners to revisit the problem of computing potentials between static color sources and their excitation spectra [12–15]. For related work see Refs. [16–18]. These calculations have a long history and the static potential in the SU(3) Yang-Mills theory was amongst the first lattice Monte Carlo computations. Revisiting the potentials in the presence of light dynami- cal quarks [19–22] will give useful insight into the nature of the XY Z and pentaquark experimental signals. In particular, the bottom quark sector could be modelled very effectively with this data while exotic mesons in the charm sector are more sensitive to finite mass correc- tions. Phenomenological models of the exotic hadrons based on the Born-Oppenheimer picture would use these potentials as input. With a static color and anti-color source, separated along an axis at distance R, the eigenstates of the Hamil- tonian are irreducible representations of the little group of symmetries that preserve this axis. The energy of these states as a function of distance defines the poten- tial, V (R). The residual symmetry means these poten- tials are labelled by Σ = 0±,1/2,1,3/2, . . . , where there are two spin-zero potentials since a mirror symmetry is also a good symmetry for this case. The half-integer spin potentials do not appear in a theory of gluons alone but would be present in QCD. With two flavors of light quarks, QCD energy eigenstates are classified with an extra quantum number, light isospin, and this property would be inherited by states built from static sources. There would thus be a new multiplicity of spectra with isospin I = 0,1/2,1, . . . . The isospin 0 and 1 spectra would be the relevant ones for studies of hidden charm 042001-3 Chinese Physics C Vol. 40, No. 4 (2016) 042001 or bottom tetraquarks and in particular, since the Z+ states are charged, the isospin 1 spectrum is of partic- ular interest. This spectrum has not been computed in lattice QCD to date. For pentaquarks containing hidden charm cc̄ or bot- tom bb̄ the isospin 1/2 and 3/2 potentials are relevant for modelling these states. Again, there is no counter- part for this potential in the theory of strongly-coupled gluons alone. Another possible potential that might use- fully be investigated and which has no counterpart in the pure gauge theory are those associated with two color sources, Q(x)Q(y) [20, 21]. In order to neutralize this color charge, at least one light quark field must be in- cluded in the creation operator. These potentials would help model doubly-charmed or doubly-bottom baryons. 2.4 Compute form factors relevant to exotic states The determination of the elastic and inelastic form factors of the XY Z resonances directly from lattice QCD would have three major impacts. First, it would lead to the theoretical reproduction of experimentally observed production or decay rates in a model-independent way. Second, it would give access to poorly constrained quan- tities that would elucidate the nature and structure of these exotic states. Examples of such quantities in- clude the radii and electromagnetic moments of tenta- tive molecular states. Third, it would guide future ex- perimental searches of exotics. Although the studies of resonant electromagnetic processes are presently at their early stages, there have been a great deal of theoreti- cal [23–27] and numerical [28, 29] studies that demon- strate that they are in fact accessible from lattice QCD. This progress resulted in the first calculation of a radia- tive transition of a hadronic resonance [30]. This calcula- tion was performed in the light sector for πγ? → ρ→ππ. Having determined the πγ? → ρ→ππ amplitude for a range of values of the center of mass energy of the final ππ state, the authors of Ref. [30] were able to analytically continue the amplitude onto the ρ-pole and determine the π→ ρ form factor. The same technology will be applicable for future cal- culations in the heavy quark sector. 2.5 Compute decay constants for exotic states The decay constants of the vector resonances deter- mine their rate of production in e+e− and radiative tran- sitions to lighter states offer a way to produce states of other JPC . The rigorously correct way to determine these in lattice QCD is to first determine the scatter- ing amplitudes and their resonant content as described above, and to then introduce an external vector current. By extrapolating the calculated vector-current matrix el- ements to the resonance poles, off in the complex energy plane, the decay constants and radiative transition rates for resonances can be obtained. This procedure closely resembles that for the determination of form factors dis- cussed above. The techniques necessary for implement- ing this have been previously developed in Refs.[26, 31, 32]. The first calculations of this type have been of ππ- electroproduction γ? → ρ→ππ [32, 33]. A slightly less rigorous approach, which may be ac- ceptable for narrow resonances, is to ignore the hadronic decay of the states by excluding meson-meson-like oper- ators from the basis used to determine the spectrum of states – a first round of calculations of this simplified type may be justified to aid our phenomenological intuition of the vector spectrum, extending the limited calculations presented in Refs. [28, 34–38], using the excited state technology presented in Ref. [29]. 2.6 In-medium hadron properties Several model calculations predict that charmonium– nucleus exotic bound states should exist [39–42, 44– 48]. Two independent, equally important binding mech- anisms have been identified: multigluon exchanges in the form of color van der Waals forces [39–43], and D,D∗ me- son loop contributions to charmonium self-energy with medium-modified masses [45, 46]. A first, recent lat- tice calculation [49] confirms model calculation expecta- tions, finding relatively deeply bound states of J/ψ and ηc to several light nuclei. Another interesting class of charmed-hadrons nuclear bound states are D-mesic nu- clei [50, 51], which are an important source of informa- tion on chiral symmetry restoration in-medium [52]. A lattice calculation of the D-meson interaction with nucle- ons and of D-nuclei binding energies would be of great importance for constraining models, given the present lack of experimental information on the D-nucleon inter- action. 3 Experiment 3.1 Publish upper limits for negative searches Candidates for exotic hadrons have been observed in many channels. While it is clearly important to find new decay channels for these states, it is also important to limit their decays to other channels when these searches are negative. This is a reminder to experimentalists to publish upper limits on cross sections and branching frac- tions in a wide range of channels. 3.2 Confirm marginal states A variety of signals have been observed that require confirmation. There is some urgency in achieving this because attempts to understand the data can be seri- ously misled by the acceptance of spurious signals as hadronic states. Alternatively, many signals are statisti- 042001-4 Chinese Physics C Vol. 40, No. 4 (2016) 042001 cally significant but contain unknown systematic errors due to assumptions in modelling (for example using in- terfering Breit-Wigner amplitudes to obtain asymmetric line shapes). Additional and more varied amplitude anal- ysis is required in these cases. Amongst states requiring confirmation are X(3940), Y(4008), Z1(4050), X(4160), Z2(4250), and X(4350). 3.3 Unravel the excited χcJ spectrum The masses of the charmonium 2P states are ex- pected to be around 3.8–4.0 GeV/c2 [53, 54], while χc0(2P ) and χc2(2P ) are well above the DD̄ threshold but below D∗D̄∗ threshold; they are expected to be wide. If the mass of χc1(2P ) is high enough, χc1(2P )→D∗D̄+c.c. will be its dominant decay mode. The χc2(2P ) may de- cay into D∗D̄+c.c. as well. So far the Z(3930) observed in γγ→ DD̄ [55] is re- garded as the χc2(2P ) state, and the X(3915) observed in γγ→ωJ/ψ [56] is supposed to be a χc0(2P ) candidate, although its mass is a bit too close to χc2(2P ), and it was not observed in γγ→DD̄. Further study on χcJ(2P ) decaying to DD̄ and D∗D̄+ c.c. should be performed to identify χc0(2P ) and χc1(2P ) and to confirm the χc2(2P ). With more data collected in e+e− annihilation at the ψ(4040) and ψ(4160) peaks, the E1 transitions ψ(3S) and ψ(2D)→γχcJ(2P ) should be searched for; E1 tran- sitions of χcJ(2P )→γψ(2S) are also expected to be large compared with χcJ(2P )→γJ/ψ and γψ(13DJ). Hadronic transitions χcJ(2P )→ππχcJ(1P ) should be searched for, and the reaction χcJ(2P )→ωJ/ψ may oc- cur if the mass difference between χcJ(2P ) and J/ψ is large enough. The spin-parity of the χc0(2P ) candidate, X(3915), needs to be measured and its production and decay patterns should be examined carefully to see if it is the χc0(2P ). 3.4 Measure e+e − cross sections The region at center-of-mass energies above the open charm threshold is of great interest due to the plethora of vector charmonium states: the ψ(3770), ψ(4040), ψ(4160), and ψ(4415) observed in the inclusive hadronic cross section, and the vector charmonium-like states, the Y(4008), Y(4260), Y(4360), Y(4630), and Y(4660) ob- served in exclusive hadronic modes. These states were discovered in one specific mode and are not observed in other modes. Searches for these states in all possible fi- nal states are desired. This suggests high precision mea- surements of as many as possible exclusive e+e− annihi- lation modes, including multi-body open charm modes, hadronic transitions, radiative transitions, and even ex- clusive light hadron final states. Fig. 1 shows an example of measured cross sections of two-body open charm final states and two- or three- body hadronic transition modes. Common features of the distributions are a richness of structures and a lack of precision. With more data from open charm threshold up to about 5 GeV and improved precision, better the- oretical models will likely be needed to describe the line shapes of all the final states simultaneously. In this way better knowledge on the excited ψ and the Y states can be extracted. This may result in an understanding of the nature of these states and reveal if any are charmonium hybrids. Fig. 1. (color online) The cross sections of e+e− annihilation into open charm final states (left panel, from the Belle experiment) and charmonium final states (right panel, the top is from Belle and the others from BESIII experiments.) The vertical lines are at 4.23, 4.26, and 4.36 GeV. 042001-5 Chinese Physics C Vol. 40, No. 4 (2016) 042001 With the existing data samples, BESIII can already improve precision of the open charm cross sections signif- icantly [57], and considering the BESIII experiment will continue run for another 6–8 years, better measurements at more energy points are expected. Belle-II [58] will start data taking in 2018 with a data sample expected to be fifty times larger than Belle’s. Thus the precision of all the measurements with initial state radiation will be improved. The cross sections of e+e− annihilation into open bottom and bottomonium final states should also be measured to understand the excited bottomonium and bottomonium-like states. This can only be done at the Belle-II experiment [58]. 3.5 Search for flavor analog exotic states The majority of recently discovered exotic states are placed firmly in the charmonium spectrum. Flavor- independence of gluon exchange implies that flavor ana- log states should exist. For example, the Zb(10610) and Zb(10650) are evidently hidden bottom partners to the Zc(3900) and Zc(4020) multiquark candidate states. It is possible that the Y(2175) is the hidden strange part- ner of the Y(4260). Finding flavor-analog states will yield valuable information on the dynamics underlying the new states and will probe the robustness of putative models. The case of a bottomonium analog of the X(3872) is interesting, both because of the novelty of the X and be- cause of differences that may arise. For example, if the X is a weakly bound DD̄∗ system then the Xb would be expected at mass of 10604 MeV. However, some models [59] rely on the proximity of the hidden charm ρ-J/ψ and ω-J/ψ channels to stabilize the X. This coincidence is not repeated in the case of the Xb, where the ω-Υ threshold lies 370 MeV away. This also implies that the novel isospin-breaking features of the X will not be re- peated in the Xb (isospin symmetry breaking is related to the hidden flavor mixing and to the splitting between charged and neutral DD̄ ∗ channels – neither of which is repeated in the case of the Xb). Finally the proximity of the χ′ c1 to the X(3872) is likely to be important. Again, this numerical coincidence is not repeated in the case of the Xb, where nearby χb1 states are at 10255 MeV (1P ), 10512 MeV (2P ), or 10788 MeV (3P [60]). 3.6 Search for flavor analogs of the Pc The recent evidence for the resonant P + c structures in J/ψp in the Λb → J/ψpK− decays found by the LHCb experiment has renewed the interest of the experimental and theoretical communities in pentaquark states. Fur- ther experimental work is critical for clarification of the nature of these structures. Most established and candidate exotic hadron states contain hidden heavy flavor, QQ̄. This is mainly due to experimental constraints for production and detection. However, other sectors of flavor deserve to be investi- gated. Let us give two examples. The isospin partner (c̄cudd) and the strangeness part- ners such as (c̄cuds) should be searched for, along with their b̄b analogs. One should not restrict searches to hidden heavy flavor. Pentaquark states (Q̄q4), where q4 denotes uuds, ddsu or ssdu were predicted in 1987 on the basis of a chromomagnetic mechanism very similar to the one leading to speculations about the H dibaryon. This flavored pentaquark has been searched for at Fermilab and HERA. Searches with higher statistics are desirable, especially if more hidden-flavor states such as (Q̄q′q3) are found [61, 62]. Exotic mesons with double heavy flavor, (QQ′q̄q̄), have been predicted with many methods such as po- tential models, QCD sum rules, lattice QCD and the meson-meson molecular picture. It has also been stressed that more effort should be put on double-charm and other doubly-heavy baryons. We thus suggest a search of doubly-heavy hadrons besides Bc: double- charm baryons, double-charm mesons and double-charm dibaryons, and in the future, their analogs with charm and beauty or double beauty [63, 64]. 3.7 Search for quantum number partners of the Y(4260) If the Y(4260) is a hybrid state it represents the first example of – what is expected to be – a large array of novel hadrons. Specifically, a spin multiplet analo- gous to those in the conventional spectrum is expected. A lattice computation of the lightest charmonium hy- brid multiplets is shown in Fig. 2. A clear structure with quantum numbers 1−− and (0,1,2)−+ is seen. This multiplet can be conveniently interpreted as arising due to an effective constituent gluon with quantum numbers (JPC)g = 1+− mixing with conventional quark-antiquark degrees of freedom[65, 66]. Fig. 2. (color online) The lightest charmonium hy- brid multiplets. Based on Ref. [67]. Given this information one can expect the spectrum shown in Table 1. The increasing luminosity expected at the colliders raises interesting possibilities for detecting these states. For example, the 0−+ and 1−+ lie below the Y(4260) and therefore should be accessible in radiative 042001-6 Chinese Physics C Vol. 40, No. 4 (2016) 042001 decays in P -wave. The hybrids can then be detected in decay modes such as ηχcJ or fJηc (see Table 2). Table 1. Expected hybrid multiplet [28]. JPC mass/MeV 2−+ ∼ 4320 1−− 4260 1−+ ∼ 4200 0−+ ∼ 4190 Table 2. Possible production and decay modes of hybrid charmonium. Y(4260) → γ1−+ →γηχc1,γ f1 ηc Y(4260) → γ0−+ →γηχc0,γ f0 ηc Y(4360) → γ2−+ →γηχc2,γ f2 ηc 3.8 Pursue properties of the X(3872) Although the properties of the X(3872) are rea- sonably well known, additional experimental effort can greatly assist in improving the understanding of this state. For example, the rate for decays to light hadrons, such as X→ηππ, can be compared to those for χc1 states in an effort to determine the expected mixing of the X with the bare χc1(2P ). Analog hidden charm states are predicted in some models and can be searched for. For example a 0++ D∗D̄∗ state is expected at 4019 MeV in pion-exchange models [1, 68]. Intriguing analog flavor-exotic states are also ex- pected in QCD. In particular, it has been argued that QQq̄q̄ states must exist in the limit where the heavy quark mass goes to infinity [64]. The phenomenology of such states is discussed by Tornqvist [68] and was anticipated long ago [63]. Specific possibilities include isoscalar KK∗, DD∗, BB∗ states with JP = 1− and K∗K∗, D∗D∗, B∗B∗, etc. Nevertheless, flavor exotic vector- vector bound states are unlikely, except possibly in the doubly charged bottom sector [68]. 3.9 Measure additional channels to investigate the Pc The interpretation of the LHCb pentaquark signal remains open. Tightly bound pentaquarks, molecular states, and rescattering effects have been proposed. More accurate determination of the quantum numbers of the pentaquark candidates would greatly help their inter- pretation. Even before more data is accumulated by the LHCb, improving parameterizations in the ampli- tude fits to the existing data may help this end. For ex- ample, models of Λ excitations, which dominate the data via decays to pK−, need to be checked for completeness since the previous experiments may have not discerned all the relevant states, especially at high masses. Non- resonant terms with slowly varying magnitude and phase can also be significant. Alternative approaches to the iso- bar model may be helpful, like, for example, the recently published coupled-channel model by Fernandez-Ramirez et al.[69]. See also Refs. [70–72]. It is important to confirm the Pc via other channels. There are already suggestions [70] such as Λb → J/ψpπ−, or Ξb → J/ψK−p, which are Cabibbo suppressed, or B → J/ψpp̄. The predictions of rescattering models for the P + c amplitudes can be tested by fitting them directly to the data. The presence (or lack thereof) of the same structures in the other channels, like Λb → J/ψpπ− or Λb → J/ψpK0π− is of great importance. Rescattering models predict the presence of struc- tures related to the P + c peaks induced by the ana- lyticity in the coupled channels, like Λb → χcJpK−, Λb → Σ(∗)+ c D̄(∗)0 and Λb → Λ(∗)+ c D̄(∗)0. Ideally, simul- taneous coupled channel analysis of the related final states should be performed. The investigation of pos- sible structures, which may include depressions rather than peaks, is a good start. Even total relative rates be- tween the different channels would be interesting. Nega- tive searches have theoretical implications and should be published. Bound-state models for the observed P + c states pre- dict other pentaquark states built by the same binding mechanisms. The same P + c states may be observable in the other decay modes too. Thus, every accessible decay mode of Λb with c and c̄ quarks among the fi- nal state hadrons should be examined, e.g. η− cpK. Other final states can be accessible from Ξb to charmonium decays. Different production mechanisms for the P + c states, or their siblings, should be investigated. Examples are prompt production at LHC or photo-production at JLab. 3.10 Test ideas for meson-nuclear interactions Presently there is a complete lack of experimental information on the low-energy interactions of charmed mesons and charmonium with nucleons and nu- clei. We look forward to several forthcoming experi- mental programs in this area: the near-threshold exper- iments by the ATHENA collaboration [73] as part of the 12 GeV program at Jefferson Lab, the proton-antiproton experiments by the PANDA collaboration at FAIR [74], and the experiments with 50 GeV high-intensity pro- ton beams at the J-PARC complex [75]. We also envis- age opportunities for finding exotic charmonium-nucleon and charmonium-nucleus bound states with the ongoing heavy-ion experiments at RHIC and LHC. In particu- lar, we suggest studies on the formation of such exotic bound states by coalescence in the late-stage evolution 042001-7 Chinese Physics C Vol. 40, No. 4 (2016) 042001 of heavy-ion collisions, as their production yields should be of comparable magnitude to those of anti-nuclei and anti-hypernuclei recently observed at RHIC [76] and LHC [77]. 3.11 Improve meson classification scheme There is a wide range in signal robustness in the spec- trum of new states. Because this can lead to confusion amongst theorists who are attempting phenomenological descriptions of these new states, we recommend that a star system for mesons be implemented by the Particle Data Group for use in the Review of Particle Proper- ties. Furthermore, the current exotic particle naming scheme is somewhat confused and is applied inconsis- tently; we therefore recommend that a consistent and flexible nomenclature be implemented. 3.12 Search for pp in decays at LHC for PANDA Heavy-flavor physics will benefit from experiments with medium-energy antiproton beams. In the past, a precursor signal of the hc was seen at the CERN ISR, and many properties of the χc,J and other charmonium states were obtained from the p̄p experiment at the Fer- milab accumulator. To assist future experiments, it is desirable to get in- formation on the coupling of heavy hadronic systems to proton-antiproton pairs by detecting p̄ production at B- factories and at the LHC. This is already under way, and this should be accompanied by more theoretical studies. For instance, it remains rather mysterious that ηc(1S) decays more often to pp̄ than suggested by simple per- turbative QCD, while ηc(2S) is more weakly coupled to that channel. 4 Theory and phenomenology 4.1 Study exclusive e+e− cross sections using better coupled-channel formalism The identification of possible new resonances implied by the XY Z phenomena requires studies of analytical amplitudes that describe the relevant production and de- cay characteristics [78, 79]. For example, in the case of the Zc(3900) that is observed in the π±J/ψ spectrum in decays of the Y(4260) to π+π−J/ψ, the relevant di- rect channels involve the nearby open-charm, DD̄∗ +c.c states and need to be included in a coupled channel for- malism. The open charm resonances in the production channel, e.g., the D1(2420) can produce rapid variations of the direct channel partial waves near the Zc signal and need to be taken into account in production. The singularity structure of partial wave amplitudes is con- strained by unitarity, therefore a comprehensive analy- sis requires implementation of unitarity constraints in all relevant channels. This requires simultaneous studies of quasi two-to-two scattering amplitudes of open flavor and heavy quarkonia, e.g. DD̄∗ → J/ψπ, and eventually a study of three-to-three scattering, i.e. DD̄π → DD̄π amplitudes. 4.2 Develop tests for the dynamical diquark pic- ture In an alternate proposal for the structure of the heavy quarkonium-like exotics, both for the tetraquarks [80] and pentaquarks [81], the states are composed of com- pact diquark-antidiquark (-antitriquark) pairs rapidly separating and hence ultimately achieving large (≈ 1 fm or greater) separation before decay. This picture has features in common with the diquark models previously mentioned [82, 83], but differs in that the states are ex- tended, dynamical rather than compact, static objects, and therefore does not necessarily admit a Hamiltonian description. Nevertheless, in the limit of small separa- tion, the two pictures should coincide. The first priority in this case is therefore the development of a formal- ism in which the spectrum can reliably be predicted. A first attempt in the pentaquark sector [84], still using a Hamiltonian formalism, gives a natural explanation for a broad 3 2 − lying just below a narrow 5 2 + , consistent with the LHCb findings [85], but also predicts a large number of undiscovered states. A lattice calculation of the po- tential corresponding to a well-separated static diquark- antidiquark pair may provide valuable information on the possible spectrum. Since the exotics are so prominent in the cc̄ and bb̄ channels, some hints of the same mech- anism with ss̄ (hidden-strangeness pentaquarks) should appear in processes such as Λc → φπ0p [86] or φ pho- toproduction [87]. A primary benefit of the dynamical picture is its natural explanation of strong overlaps with spatially larger states, so a precision measurement of the ratio Z(4475) →ψ(2S)π vs. J/ψ and to other states will be illuminating. The dynamical and compact diquark models share an expected enhancement of Zc →ηcρ com- pared to the corresponding rate in molecular models [88]. The extended structure of the state may also offer inter- esting opportunities for the production of unusual final- state particle correlations. The multiparticle nature of states produced via, say, electroproduction or pp̄ annihi- lation (at JLab or PANDA, respectively) can be probed by means of constituent counting rules [89], and can help to distinguish whether compact multiquark components are produced. 4.3 Develop experimental tests for tetraquarks Compact tetraquark configurations, in which all four quarks participate in strong mutual interactions, can be distinguished from the hadron molecular picture or threshold effects through a variety of experiments. 042001-8 Chinese Physics C Vol. 40, No. 4 (2016) 042001 The most well developed tetraquark models are of the diquark-antidiquark class [82, 83], and rely on Hamil- tonians with spin-spin interactions between the quark pairs. A comparison of the expected spectra in this tetraquark model versus hadronic molecular models (and also hadrocharmonium) [90] indicates that many more states should arise if tetraquarks are the dominant ex- otic component; for example, the X(3872) should have isotriplet charged partners of the same G parity [and opposite that of the Z(3900) and Z(4020)]. Due to the proximity of thresholds, such states might exist only as very broad yet-undiscovered resonances. Large prompt production cross sections at colliders [91] argue against X(3872) being a DD̄ ∗ molecule forming through coales- cence; indeed, an extrapolation [92] of data from AL- ICE shows that production of loosely bound hadronic molecules such as d and 3He at high p⊥ will be quite suppressed, unlike current indications for X(3872), an effect that can be decisively checked in future ALICE and LHCb experiments. The molecular and diquark pic- tures also differ radically in the ratios of their branching fractions of Zc →ηcρ vs. J/ψπ or hcπ [88, 89], the former being dozens of times less frequent in molecular models. Loosely bound molecules also must obey well-known uni- versal relations (independent of the potential) between binding energy and width, and precision measurements of the resonance widths and constituent masses can help determine whether these constraints are satisfied [94]. 4.4 Develop techniques for 5q and 6q systems Potential models provide some guidance for QCD cal- culations. Two-body calculations are obvious once an explicit potential is given. Three-body and four-body computational methods now yield accurate spectra, al- though they require more delicate tools. The case of five-body and six-body systems are still debated. For instance, with similar Ansatze for the interaction, the H = (uuddss) can be found to be either stable or un- bound. We suggest to publish a set of benchmark calcu- lations to remove the ambiguities. 4.5 Pursue the Born-Oppenheimer method (adiabatic surface mixing) The presence of heavy charm or bottom quarks in the new putative tetraquark mesons suggests that they may be successfully studied using the Born-Oppenheimer expansion. This approach was introduced by Born and Oppenheimer in 1920 [95] to understand the binding of atoms into molecules by exploiting the large ratio be- tween the mass of an atomic nucleus and an electron, which implies that the time scale for the motion of elec- trons is orders of magnitude faster than that for the mo- tion of the nuclei. The energies of stationary states of the electrons in the presence of fixed nuclei can be calculated as functions of the separation of the nuclei. The result- ing functions are called Born-Oppenheimer potentials. In the Born-Oppenheimer approximation, these func- tions are used as potential energies in the Schrödinger equation for the nuclei, under the assumption that the electrons respond very rapidly to the motion of the nu- clei. The Born-Oppenheimer expansion involves taking the large mass ratio into account more systematically by incorporating non-adiabatic couplings between differ- ent stationary states of the electrons. This results in coupled-channel Schrödinger equations that systemati- cally improves the description of a molecule. The Born-Oppenheimer expansion was applied to mesons containing a heavy quark (Q) and antiquark (Q̄) in 1999 [96], exploiting the fact that, since the mass of the heavy quark is much larger than the typical energies of the gluons and light quarks, the time scale for the evo- lution of the gluon and light-quark fields is much faster than that for the motion of the Q and Q̄. In Ref. [96], lat- tice QCD was used to calculate the Born-Oppenheimer potentials defined by the energies of the gluons in the presence of fixed Q and Q̄ as functions of the QQ̄ sepa- ration. These energies were then used as the potential ener- gies in the Schrödinger equation for the Q and Q̄. The bound states in the Born-Oppenheimer potentials were interpreted as meson resonances. These bound-state en- ergies were compared with corresponding meson masses computed directly using lattice QCD and agreement in the level spacings to within 10% was found, strongly sup- porting the validity of the Born-Oppenheimer expansion for such systems. The approach used in Ref. [96] should be extended to apply to the XY Z mesons and to include nonadiabatic effects that can be incorporated through coupled-channel Schrödinger equations. The Born-Oppenheimer poten- tials for heavy tetraquark mesons and the nonadiabatic couplings between the potentials could be calculated us- ing lattice QCD. The heavy quark and antiquark would be treated as static, and the energies of the gluons and light quarks could then be computed as a function of the separation between the quark and the antiquark. The resulting coupled-channel Schrödinger equations could then be solved to determine the energies and widths of resonances, which can be compared with the observed XY Z mesons, and possibly to predict new tetraquark mesons. 4.6 Revisit conventional meson models While the successes of the constituent quark model are well-known in the heavy quark sector, the efficacy of the model is not expected to survive higher in the spec- trum, where gluonic and coupled channel effects become important. Of course, it should be possible to extend 042001-9 Chinese Physics C Vol. 40, No. 4 (2016) 042001 constituent models to include these additional degrees of freedom, but experimental and theoretical guidance will be required. Even the simple problem of assessing the accuracy of the constituent quark model above threshold has diffi- culties. For example, there are eight charmonium states below DD̄ threshold that are all well-described by mod- els. Alternatively, the situation above threshold is con- siderably more confused; of the approximately twenty claimed states, most of them are not understood, and even well-known states such as the ψ(3770) lie 50 MeV below the prediction of the Godfrey-Isgur model. In the bottom sector the 14 states that lie below BB̄ are well- described. In this case there are only six states above threshold, but, again, the experimental and theoretical situation is confused. Since the new experimental data lie firmly in the continuum region, it is very likely that more sophisti- cated versions of the quark model that respect unitarity must be developed. Of course, this has been known in the community for many decades, and much work has been done [97–119]. There are daunting issues to be overcome, including determining the form of the non- perturbative gluonic transition operator and evaluating the (divergent) sum over infinitely many virtual chan- nels [120]. Nevertheless it is difficult to imagine progress being made without a successful outcome to this effort. Alternative approaches exist of course: lattice gauge the- ory is rapidly making progress in working in the coupled channel regime, and one hopes that effective field theory approaches will be developed that can accommodate the extra scales present. 4.7 Develop the Dyson-Schwinger formalism The Dyson-Schwinger equations (DSEs) of QCD, to- gether with various many-body equations for bound states (Bethe-Salpeter equations for the two-body prob- lem, Faddeev and Faddeev-Yakubovsky equations for the three- and four-body problem) have the potential to re- veal the connections between the physics in different sectors of QCD. The equations encode the running of QCD Green’s functions (for example, the quark mass function) and therefore connect the perturbative cur- rent quark region with the non-perturbative constituent quark domain. Furthermore, they connect the heavy quark regime, where NRQCD or potential models are applicable, with the light quark sector, where the con- cept of a potential is not very well defined. The explanatory power of the DSE framework with respect to exotic hadrons is still in its early exploration stage. So far, light scalar mesons have been treated as tetraquarks in an approach that takes into account two- body correlations within the bound state equation for two quarks and two antiquarks [121, 122]. The resulting Bethe-Salpeter amplitude for scalar tetraquarks is dom- inated by pseudoscalar meson-meson correlations. For the lightest state, the f0(500), this explains its large de- cay width into two pions, whereas the a0 and f0 are dom- inated by their KK̄ components. In general, it turns out that all two-body correlations inside the tetraquark (i.e., (anti-)diquarks or mesons) contribute to the wave func- tion and it is a question of the internal dynamics which is the dominant cluster. For the light scalar mesons this is the ‘meson molecule’ configuration, but other results are in principle possible for other quantum numbers and different quark flavors and masses. Whether this mechanism has the potential to shed some light on the question of the internal structure of the tetraquarks among the XY Z-states, in particular their (anti-)diquark, molecular or hadrocharmonium na- ture, needs to explored. To this end, non-scalar quantum numbers need to be studied and the framework needs to be extended toward heavy-light systems. Furthermore, more quantitative precision is needed to confirm the pre- diction of an all-charm tetraquark in the 5.0–6.5 GeV mass region [121, 122]. Complementary ongoing projects within the DSE framework concern the glueball spectrum [123, 124] and the question whether states with exotic quantum numbers can be accounted for with relativistic quark- antiquark systems (in contrast to the non-relativistic quark model) [125]. 4.8 The status of large Nc considerations One striking thing about modern exotics— the XY Z states—is that they all involve the physics of heavy quarks. This raises an interesting issue: are heavy quarks necessary for the formation of exotics, or do exotics ex- ist for light quark systems? The experimental data on this is murky. The large Nc limit may provide a bit of insight. The subtle point is that the large Nc and heavy quark limits may not commute so that generic large Nc arguments based on scaling arguments really apply for light quark systems. The standard version of the large Nc limit with quarks in the fundamental rep- resentation of SU(Nc) can be shown not to have nar- row tetraquarks at large Nc [126], apparently supporting the proposition that the heavy quarks are necessary for the existence of tetraquark states. However, there is a variant of the large Nc limit where quarks are in the two-index anti-symmetric representation of SU(Nc) in which it can be shown that states with exotic tetraquark quantum numbers must exist as narrow resonances (i.e. states whose widths go to zero as Nc goes to infinity) re- gardless of the mass of the quarks [127]. Minimally this shows that QCD-like gauge theories are not excluded from having tetraquark states even if the quarks are light. 042001-10 Chinese Physics C Vol. 40, No. 4 (2016) 042001 5 Theory-experiment collaboration The following are a few suggestions that could help facilitate collaboration between theory and experiment. 5.1 Improve parameterizations of the data One of the challenges in many of the experimental studies of the XY Z states is to develop correct param- eterizations of the data. For example, amplitude anal- yses often find a need to introduce non-resonant terms. At present, very little theoretical guidance is provided except for the amplitude formulations based on the K- matrix approach. However, the latter is not always prac- tical. To improve this situation, we have two recommenda- tions. First, we encourage that, when appropriate and ben- eficial, experimentalists and theorists directly work to- gether on the analysis of data. This could be accom- modated by theorists becoming co-authors on specific experimental papers they substantially contributed to, or joint submission of experimental and theoretical pa- pers cross-referencing each other. The experiments are encouraged to formalize procedures making such collabo- ration possible, and theorists are encouraged to approach the experiments when they think they might directly aid specific data analysis topics. Further progress could be made by more persistent forms of collaboration, includ- ing direct involvement of theorists in the data analysis process within the established procedures of the experi- mental collaborations. Second, we encourage theorists, when possible, to publish complete functional forms (amplitudes, etc.) that could be used in the fitting of data. One example of this is in the parameterization of rescattering ampli- tudes. The current theoretical calculations are depen- dent only on the center of mass energy [72, 78, 128], whereas amplitudes used in fitting require a flexible pa- rameterization involving the angular information of the decay. If theorists develop more complete rescattering amplitudes, experimentalists could use them in analy- ses. This would most likely involve some collaborative effort in understanding both how the experimental anal- ysis is performed and what the theoretical requirements are for such amplitudes. Another example is in resonance parameterizations: it would be useful for experimental- ists if a number of alternate resonance parameterizations were available that could be used in systematic studies. 5.2 Make experimental results more accessible for subsequent interpretation The analysis of data from many modern experiments often necessitates complying with internal rules designed to provide collaborative controls over the quality of sta- tistical methods used and the proper evaluation of sys- tematic uncertainties. Therefore it is unrealistic to ex- pect that all data will be made available for analyses outside of this collaborative setting. A correct analysis of data would benefit from the types of closer interaction between experiment and theory discussed in the previous point. A different issue is how published data (for exam- ple, Dalitz plots) should be subsequently interpreted. It often occurs that experimental results are made public in a manner that does not easily allow for subsequent interpretation. One example is the discovery of the Zc(3900) decay- ing to π±J/ψ in the process e+e− →π+π−J/ψ [129, 130]. The data presented in the discovery papers include sev- eral effects that are difficult to take into account when performing theoretical fits. First, the BESIII data [129] was taken at √ s = 4.26 GeV, while the Belle data [130] includes a range of energies around the Y(4260) peak. This makes the Belle data, in particular, hard to subse- quently fit, since any changes (beyond the size of avail- able phase space) in the π±J/ψmass spectrum as a func- tion of π+π−J/ψ mass are unknown. Second, the two experiments have different experimental efficiencies over 0 10 20 30 40 50 60 70 data fit background PHSP MC data total fit background fit PHSP MC sideband 0 20 40 60 80 100 3.73.7 3.83.8 3.93.9 4.04.0 4.1 4.2 Mmax(π ±J/ψ)/(GeV/c2) Mmax(πJ/ψ)/(GeV/c2) ev en ts /0 .0 2 G eV /c 2 ev en ts /0 .0 1 G eV /c 2 Fig. 3. (color online) The observation of the Zc(3900) from BESIII [129] (left) and from Belle [130] (right). The different shapes at low M(π±J/ψ) mass are due to differences in experimental detection efficiencies. 042001-11 Chinese Physics C Vol. 40, No. 4 (2016) 042001 the Dalitz plot due to differing detectors and kinemat- ics. These effects are not quantified in the publications. The importance of these two effects can be seen when comparing the M(π±J/ψ) plots from BESIII and Belle, which differ substantially, especially in the low-mass re- gion (Fig.3). It is therefore not clear how one could cor- rectly analyze the published data with various new pa- rameterizations to test, for example, differences between cusp and resonant models of the Zc(3900). When deemed appropriate, experiments are therefore encouraged to make efficiency-corrected data available for external analyses. Or, when possible or desired, ex- periments could make published plots publicly available along with efficiency curves and instructions for how to use the plots for subsequent analysis. This could be provided as supplemental information to a publication. This may be easy for simple three-body final states (like ππJ/ψ, where the Dalitz plot could be provided), but impractical for more complicated final states. Another suggestion, especially when amplitude anal- yses have been performed, is to publish a complete pa- rameterization of the data, including both the formulas and the numerical values for each fit parameter. Making data public in these ways could help facilitate ongoing efforts to test and build models. It could also permit combined fits of data from different experiments or different channels, thus helping a more global picture to emerge. 5.3 Preview upcoming analysis results It may be useful, in some circumstances, for experi- mental collaborations to provide a list of upcoming ex- perimental results. This might be a fruitful way to elicit new theoretical predictions or ideas. For example, if the community knows a certain measurement is being per- formed, there is then a chance to make predictions prior to the publication of experimental results. It also per- mits setting priorities in theoretical computations and enhances the possibility of arranging collaborative effort. 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