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recent observation of resonances near the open charm threshold which decay into a specific charmonium state , @xmath1 or @xmath2 , and two or even one pion with no other observed conspicuous decay channels@xcite suggests@xcite that these resonances in fact contain the specific charmonium state ` coated ' by an excited light - hadron matter . it has been further argued@xcite that such hadro - charmonium systems are likely to arise due to binding of charmonium inside sufficiently excited light resonances through a qcd analog of the van der waals interaction .    in this paper we investigate in some detail the interaction of heavy quarkonium with excited light mesons within the simplest soft wall model of holographic qcd@xcite which provides linear behavior of regge trajectories@xcite and a reasonable behavior of a heavy - quark potential@xcite . in this approach the mesons can be considered as modes of the flavor gauge field in 5d theory ( vector mesons ) or a wilson line of this gauge field along the fifth coordinate ( @xmath3-meson ) . large - spin mesons can be considered within this approach as well . we also have to introduce heavy quarkonium in this framework . it is clear that the corresponding heavy degrees of freedom are localized near the boundary at @xmath4 at scales of order @xmath5 , where @xmath6 is the mass of the heavy quark . in the leading approximation we shall substitute the heavy meson by the point - like source . the essential local operator on the boundary can be deduced from the physical arguments and is approximated by the trace of the stress tensor . since this operator interacts with the dilaton we have a point - like dilaton source in the 5d theory . on the other hand the light exited meson with large spin is mainly localized on the ir wall scale@xcite . although it is better described by a long open string , this approximation is also reliable . thus the appropriate configuration consists of a local source at the boundary @xmath4 and extended meson at the @xmath7 interacting via dilaton exchange . it is shown that the interaction is strong enough to yield the bound state at a sufficiently large spin @xmath8 of the light meson . another feature which has to be explained is the phenomenologically apparent suppression of the decays of hadro - quarkonium into states with pairs of heavy mesons with open flavor . in the discussed picture such decays would correspond to dissociation of heavy quarkonium due to forces from light degrees of freedom . we argue that in the limit of large heavy quark mass @xmath6 such dissociation can be described by semiclassical tunneling and is suppressed by the factor @xmath9 . within the holographic approach this process is a generalization of the picture discussed in @xcite . clearly , the suppression of the dissociative decays is in qualitative agreement with the available observations . the subsequent material in the paper is organized as follows . in sec.2 a description of the interaction of heavy quarkonium with soft gluonic field is recapitulated and formulated in terms of the trace of the stress tensor in low - energy qcd . in sec.3 the interaction of the heavy quarkonium with light meson is described in terms of the soft wall holographic model and in sec.4 it is shown that this interaction necessarily results in existence of bound states for sufficiently high orbital excitation of the light meson . in sec.5 we consider the dissociation process for decays of the bound states into heavy meson pairs with open flavor and argue that such process generally carries a semiclassical suppression at large mass of the heavy quark . finally , in sec.6 we summarize our conclusions . due to the binding between heavy quark and antiquark , the states of heavy quarkonium are relatively compact in the standard hadronic scale set by @xmath10 . for this reason the interaction of quarkonium with gluonic fields inside a light meson can be considered in terms of multipole expansion@xcite . the leading nonrelativistic ( in the heavy quarks ) contribution to the van der waals type interaction then arises in the second order in the chromoelectric dipole term , and can be described by the effective hamiltonian@xcite h_eff= -1 2 ^(q |q ) e_i^a e_i^a  , [ hdiag ] where @xmath11 is the chromoelectric field and @xmath12 is the chromo - polarizability , depending on particular state of the @xmath13 system , in complete analogy with the description in terms of polarizability of the interaction of atoms with long - wave electric field . the values of the chromo - polarizability for charmonium and bottomonium levels below the open flavor threshold are all real and positive@xcite . the numerical values are so far known only for the off - diagonal polarizability , describing the observed @xmath14 transitions in charmonium and bottomonium . the ` reference ' values are@xcite @xmath15gev@xmath16 in charmonium and @xmath17gev@xmath16 in bottomonium . it is fully expected@xcite that proper diagonal values of the chromo - polarizability in both systems are larger than these ` reference ' values , especially for excited states . the quoted values correspond to the normalization convention for the gluonic field strength with the qcd coupling @xmath18 included in the field strength @xmath19 .    in what follows we consider the interaction ( [ hdiag ] ) with the operator @xmath20 replaced by @xmath21 , with @xmath22 being the chromomagnetic field . in doing so we consider attraction of quarkonium into gluonic medium which is weaker by the contribution of the manifestly sign - definite term @xmath23 than the actual interaction described by the hamiltonian ( [ hdiag ] ) . this clearly leads to a conservative treatment of the problem of existence of bound states@xcite . furthermore , the operator @xmath24 is related to the trace of the stress tensor @xmath25 in qcd with ( three ) light quarks in the chiral limit by the well known anomaly relation : _ ^=(g^2 ) 4 g^4 ( f_^a)^2 - 9 32 ^2 ( f_^a)^2  , [ anom ] where we replace the qcd beta function by its first one - loop term for definiteness of subsequent numerical estimates , while our general conclusion about existence of bound states does not depend on this replacement . therefore the form of the van der waals interaction of heavy quarkonium with light hadronic matter that we consider here is h_w =- c _ ^   [ hw ] with @xmath26 $ ] . we consider the limit of large @xmath6 so that the kinetic energy of the motion of heavy quarkonium is totally neglected , and we choose the position of quarkonium ( in the three dimensional space ) at the origin @xmath27 . in a holographic model heavy quarkonium is localized at @xmath4 , so that the interaction ( [ hw ] ) corresponds to a localized at @xmath28 source of dilaton . in a holographic soft wall model@xcite an orbitally excited light meson with spin @xmath8 is described by normalizable solutions @xmath29 of the five - dimensional equation : ( _ ^- ^2 z^2 + z^2 + 2 s -2 + s^2 - 1/4 z^2 ) ( z , x ) = 0  . [ 5deq ] upon substitution of a four - dimensional plane wave @xmath30 this results in the eigenvalue problem for the masses @xmath31 of the mesons : ( - d^2 z^2 + z^2 + 2 s -2 + s^2 - 1/4 z^2 ) _ n(z ) = m_n^2 _ n(z )  , [ zeig ] where @xmath32 is the excitation number at a given @xmath8 . the spectrum of @xmath33 is then directly found from the obvious relation of this problem to a two - dimensional harmonic oscillator , and is given by@xcite m_n^2 = 4(n+s )  , [ rspec ] thus reproducing linear regge trajectories . it can be mentioned that here dimensionless units are used , corresponding to the coefficient of the  soft wall " term @xmath34 equal to one . in normal units the energy scale is set by a coefficient @xmath35 proportional to the string tension .    in the presence of a static source of the dilaton field located at @xmath36 the equation ( [ 5deq ] ) is generally no longer translationally invariant in @xmath37 , and the problem becomes a ( 3 + 1 ) dimensional eigenvalue problem for the energy @xmath38 : _ n(z , x ) = _ n^2 _ n(z , x )  , [ 5deqm ] where @xmath39 is the three - dimensional laplacian and @xmath40 is the potential resulting from the dilaton propagation from the source and interaction with the light - hadron string : v(z , x ) = g(z ) d(z , x )  , [ potgen ] with @xmath41 being the dilaton propgator from the boundary ( @xmath4 , @xmath42 ) to the bulk ( @xmath43 ) , integrated over time ( static source ) , @xmath44 is the strength of the source determined by eq.([hw ] ) , and @xmath45 is the vertex for the dilaton - string interaction . the @xmath46 dependence of the latter vertex arises due to the assumed in eq.([5deq ] ) @xmath46 dependent conformal symmetry breaking term @xmath34 . we will show that for the purpose of present discussion there is in fact no need to determine each of the factors in eq.([potgen ] ) separately , and that the potential @xmath40 can be found using the normalization condition for the stress tensor and the fact that the propagation in the bulk of the ( conformal dimension @xmath47 ) dilaton field from a static source is described by the operator -_x - ^2 z^2 + z^2 + 2 + 15 4 z^2  . [ dilop ] the @xmath46 part of this operator corresponds to the motion of two - dimensional harmonic oscillator with angular momentum @xmath48 , and the spatial ( @xmath49 ) part corresponds to a free motion . thus one can readily find the propagator as an integral over the proper time @xmath50 of the corresponding evolution kernel@xcite and write v(z , x ) = f(z ) _ 0^ d ( 1 2 ) ^3/2 ( - x^2 2 ) e^- ^3 ( - z^2 2 )  . [ pot1 ] the function @xmath51 here includes the vertex factor @xmath45 and the source strength @xmath44 from eq.([potgen ] ) as well as normalization and @xmath46-dependent metric factors in the propagator @xmath52 . the function @xmath51 can be found by comparing the matrix elements of the hamiltonian ( [ hw ] ) and the potential ( [ pot1 ] ) over the plane - wave in @xmath53 solutions of the equation ( [ 5deq ] ) . indeed for _ any _ eigenstate in eq.([zeig ] ) the normalization of the trace of the stress tensor requires _ n(z , x ) | _ ^ | _ n(z , x ) = 2 m_n^2 _ n(z , x ) | _ n(z , x )  , [ norm ] which determines the average of the interaction ( [ hw ] ) over those states . on the other hand , the average of the potential over the same states is given by its integral over @xmath37 : _ n(z , x ) | v(z , x ) | _ n(z , x ) = _ n(z ) | v(z , x ) d^3 x | _ n(z ) = _ n(z ) | f(z ) 4 e^- z^2 / 2 z^4 | _ n(z )  , [ avpot ] where in the latter expression the result of explicit calculation of the integral over @xmath37 of the expression from eq.([pot1 ] ) is used . the latter average corresponds to the condition ( [ norm ] ) for _ any _ eigenstate equation ( [ zeig ] ) this is the virial theorem for harmonic oscillator : the average potential energy is one half of the total . ] if the averaged in the last expression in eq.([avpot ] ) function of @xmath46 is @xmath54 . taking into account also the factor @xmath55 in the hamiltonian ( [ hw ] ) one can finally write v(z , x ) = -c ( z^2+s-1 ) z^4 _ 0^ d ( 1 2 ) ^3/2 ( - x^2 2 ) e^- ^3 ( - z^2 2 e^- ) [ potf ] with @xmath56 being the dimensionless value of @xmath57 . the problem of existence of bound states between the heavy quarkonium and light mesons is thus reduced to the problem of existence of localized in @xmath37 solutions of the eigenvalue equation ( [ 5deqm ] ) . general physical arguments suggest@xcite that such solutions exist at a given @xmath58 and sufficiently large excitation in @xmath32 or / and @xmath8 . in practice a full analysis in @xmath46 and @xmath53 of states excited in @xmath32 is significantly complicated by the presence of multitude of lower energy states with lower @xmath32 and nonzero spatial momentum @xmath59 . for this reason we analyze here in some detail the excitation of the light meson in the spin @xmath8 while keeping @xmath60 . the treatment of such excitations is greatly simplified due to the fact that bound state in question is the ground state in the ` radial ' equation ( [ 5deqm ] ) at a given @xmath8 , so that the corresponding eigenfunction @xmath61 has no zeros . we thus use a straightforward variational procedure to establish existence of bound states at any nonzero @xmath58 , provided that @xmath8 is sufficiently large , and then find numerically the onset of the binding as a function of the coefficient @xmath58 at few low values of @xmath8 .    for a variational treatment of the binding problem we choose the _ ansatz _ for the eigenfunction in a factorized form _ 0(z , x)= z^s+1 2 e^- z^2/2 ( x )  , [ ansatz ] where the @xmath46 dependence is that of the ground - state wave function of the @xmath46 equation ( [ zeig ] ) at a given @xmath8 . substituting this variational function in eq.([5deqm ] ) one finds that the upper bound for the energy of the ground state of the system is then given by the eigenvalue @xmath38 found from the @xmath53 equation ( x ) = ( ^2 - 4s ) ( x )  , [ varxi ] with the effective potential @xmath62 considering large @xmath8 one can readily see that the factor @xmath63 effectively cuts off the contribution of values of @xmath50 above @xmath64 , so that the range of the potential behaves as @xmath65 . on the other hand the integral over @xmath37 of the potential is proportional to @xmath66 , which is weaker than the overal factor @xmath67 in front of and in the integral in eq.([uofx ] ) . therefore a bound state exists at sufficiently large @xmath8 for any nonzero value of the coupling strength @xmath58 , which is necessarily positive , due to the positivity of the chromo - polarizability . the results of such variational treatment of the problem of binding are confirmed by an explicit numerical solution of the two dimensional ( in @xmath46 and @xmath68 ) schrdinger equation with the potential ( [ potf ] ) . for a fixed @xmath8 we find that a localized in @xmath53 ground state solution appears starting from a critical ( @xmath8 dependent ) value of @xmath58 . the behavior of the ` binding energy ' @xmath69 as a function of @xmath58 is shown in fig.1 for few values of @xmath8 . one can readily see that the critical value of @xmath58 decreases with @xmath8 . phenomenological applicability of our conclusions to actual charmonium or bottomonium critically depends on the values of the chromo - polarizability for specific quarkonium resonances . using the estimate for the scale factor @xmath35 as@xcite @xmath70gev@xmath71 we find for the ` reference ' value of @xmath72 : @xmath73 . according to the data presented in fig.1 such value of @xmath58 would correspond to the appearance of binding at @xmath74 . however , as already mentioned , the diagonal chromo - polarizability of the @xmath2 resonance is likely to be somewhat larger , so that bound hadro - charmonium states may exist already at @xmath75 . the notion of hadro - quarkonium necessarily assumes that the heavy quark and antiquark stay bound together as quarkonium inside the host light - matter resonance . in other words the forces from the light quarks do not split the heavy quarkonium , which would result in the decay of the whole system into final states with pairs of heavy flavored mesons , which decays are conspicuously suppressed@xcite for the discussed @xmath76 and @xmath77 resonances . the problem of dissociation of the heavy quarkonium can in fact be treated , to an extent , in the limit of large mass @xmath6 , in a semiclassical approximation . generally the problem can be formulated as that of a reconnection of strings in terms of a holographic correspondence , using , instead of the braneless soft wall model , the underlying scheme with the flavor branes localized in the radial coordinate ( for a recent review see e.g. ref.@xcite ) . the position of the flavor brane in the radial direction is fixed by the quark mass of the corresponding flavor . the mesons in this approach correspond to the open strings with ends on the flavor branes . the ends can be on the same flavor brane , in which case the meson involves quarks of one flavor , or on the different flavor branes which corresponds to a meson built from different types of quarks . any such model involves a horizon in the radial coordinate which reflects the emergent qcd scale in the holographic picture . the flavor brane corresponding to the light meson is close to the horizon while the brane corresponding to the heavy flavor is far from it . a bound state of hadro - quarkonium thus involves two strings . one string with the ends on the light - flavor brane(s ) and the other on the heavy - flavor one . the decay into states with open heavy flavor mesons corresponds to the reconnection of the strings into the configuration with two open strings both connecting the heavy - flavor brane with the light - flavor one(s ) . this process is somewhat similar to the previously considered decay of a single excited meson@xcite via a reconnection of open string ends , which has been interpreted as a schwinger type pair production and treated semiclassically . the discussed here reconnection of the strings between light and heavy flavor branes can similarly be traced to an _ induced _ production of heavy quark pair near the threshold , which approach will be presented elsewhere , and which can be useful in a more elaborate than here treatment .    the leading at large @xmath6 behavior of the probability of heavy quarkonium dissociation can be evaluated by a simple nonrelativistic quantum - mechanical consideration , using a potential model for quarkonium combined with a stringy picture at larger separation between quarks . indeed a potential @xmath78 between heavy quark and antiquark in quarkonium generically is assumed to be of the form@xcite : v_q(r ) = v_c(r ) + r  , [ potmod ] where the linear term is associated with the stringy behavior at long distances , while the term @xmath79 is the short - distance ` perturbative ' part , e.g. in the one - gluon exchange picture this is a coulomb - like potential @xmath80 . in the hadro - quarkonium configuration the total energy of the string is @xmath81 , where @xmath82 is the distance between the heavy quark and the antiquark , and @xmath83 is the length of the light - meson string . when the string reconnects between heavy and light quarks , there is no string at all between the heavy quark and antiquark , so that the minimal energy of the reconnected configuration is @xmath84 . therefore the dependence of the minimal ( over the relative orientations ) energy on @xmath82 becomes in fact given by v_hq(r ) = v_c(r ) - r  , [ vhq ] and this effective potential presents a barrier , tunneling through which results in dissociation of the heavy quarkonium . the tunneling rate then can be estimated as ( -2    critically depends on the presently unknown position of the energy of the quarkonium below the top of the barrier . in a generic case of this energy gap being of order @xmath10 this coefficient is parametrically of order one , and the rate is strongly suppressed for heavy quarks . to summarize . we have considered the van der waals type interaction between a heavy quarkonium and an excited light meson within a soft wall holographic model of qcd . in this model the heavy quarkonium acts as a source of the dilaton field localized at the boundary . the interaction of the light matter with the dilaton field is then described by a 5d equation with the potential derived from the dilaton propagation from the boundary to the bulk . we have shown by a variational estimate that such interaction necessarily results in bound hadro - quarkonium states localized near the source at sufficiently high spin excitation of the light meson . we have also found by a numerical calculation that bound states arise at low values of the spin already for moderate values of the strength of the source , which values are close to those expected for charmonium phenomenology . furthermore , it is argued that the hadro - quarkonium resonances are metastable with respect to dissociation into final states with open - flavor heavy mesons in the limit of large heavy quark mass . the behavior of the hadro - quarkonium states argued in the present paper agrees well with the observed properties of some of the y and z resonances near the open charm threshold . the work of s.d . and m.b.v . is supported in part by the doe grant de - fg02 - 94er40823 . the work of a.g . is supported in part by the grants rfbr-06 - 02 - 17382 , intas-1000008 - 7865 , pics-07 - 0292165 . a.g . acknowledges the warm hospitality at the william i. fine theoretical physics institute where this work was done .            c.  z.  yuan _ et al . _ [ belle collaboration ] , phys . lett . * 99 * , 182004 ( 2007 ) ; g.  pakhlova _ et al . _ [ belle collaboration ] , phys . d * 77 * , 011103 ( 2008 ) ; b.  aubert _ et al . _ [ babar collaboration ] , arxiv:0710.1371 [ hep - 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we consider the recently suggested model for some resonances near the open charm threshold as bound states of charmonium inside excited light mesons . it is argued in the soft - wall holographic model of qcd that such states of heavy quarkonium necessarily exist at sufficiently large spin of the light meson . 
 the bound state is provided by the dilaton exchange through the 5d bulk . 
 we also argue that the decay of such bound systems into mesons with open heavy flavors due to splitting of the heavy quarkonium can be treated as semiclassical tunneling and is suppressed . 
 this behavior is in agreement with the known relative suppression of the decay of the discussed charmonium - like resonances into channels with @xmath0 mesons . 
 * william i. fine theoretical physics institute + university of minnesota + *    itep - th-18/08 + ftpi - minn-08/12 + umn - th-2643/08 + april 2008 +    * holographic hadro - quarkonium + * school of physics and astronomy , university of minnesota , + minneapolis , mn 55455 , usa , + * a. gorsky + * institute of theoretical and experimental physics , moscow , 117218 , russia + and + * m.b . 
 voloshin + * william i. fine theoretical physics institute , university of minnesota , + minneapolis , mn 55455 , usa + and + institute of theoretical and experimental physics , moscow , 117218 , russia +