You are an expert at summarizing long articles. Proceed to summarize the following text: 
since the surprising discovery of the @xmath0 in 2003 @xcite , there has been a steadily growing list of new @xmath9 mesons discovered at the @xmath10 factories @xcite . these discoveries have revealed that the spectrum of @xmath9 mesons is richer than the charmonium states predicted by quark potential models . the candidates for some of the new @xmath9 mesons include charm meson molecules , tetraquark states , and charmonium hybrid states @xcite . an ideal experiment for studying some of the new @xmath9 mesons would be @xmath1 collisions at resonance . the effectiveness of resonant @xmath1 collisions for studying conventional charmonium states was demonstrated by the e760 and e835 experiments at fermilab @xcite . the `` @xmath9 mesons '' section of the review of particle physics @xcite was largely rewritten by these experiments . there will be future opportunities to study @xmath9 mesons through resonant @xmath1 collisions . the panda experiment at gsi is expected to begin taking data on @xmath1 collisions at energies in the charmonium region around 2014 @xcite . a recently proposed @xmath1 resonance experiment at fermilab could begin even earlier @xcite . the rate at which a resonance is produced in @xmath1 collisions is proportional to its partial width into @xmath1 . thus a resonant @xmath1 annihilation experiment would be useful for studying the new @xmath9 mesons provided their @xmath1 partial widths are sufficiently large . to estimate the @xmath1 partial widths of conventional charmonium states , one can take advantage of the measured @xmath1 partial widths of the @xmath11 , @xmath12 , @xmath13 , @xmath8 , @xmath14 , and @xmath15 . it is difficult to estimate the @xmath1 partial widths for most of the more exotic candidates for the new @xmath9 mesons . a weakly - bound s - wave charm meson molecule is an exception . its @xmath1 partial width is related in a simple way to the cross section near threshold for @xmath1 annihilation into the charm mesons that are its constituents . the energy dependence of that cross section near threshold is determined by the mass and width of the resonance . if the s - wave contribution to the cross section for @xmath1 annihilation into the charm mesons well above the threshold was known , a reasonable extrapolation to the threshold could be made in terms of the position and width of the resonance . cross sections for @xmath1 annihilation into pairs of charm mesons have not been measured . however at energies well above threshold , those cross sections can be estimated by scaling the measured cross sections for @xmath1 annihilation into the corresponding strange mesons . in this paper , we will use this strategy to estimate the partial width of the @xmath0 into @xmath1 . we will asume in this paper that the @xmath0 is a weakly - bound hadronic molecule whose constituents are a superposition of @xmath16 and @xmath17 . we first summarize the evidence for this identification . measurements of the mass of the @xmath0 by the belle , cdf , babar , and d0 collaborations @xcite , combined with a new measurement of the @xmath18 mass by the cleo collaboration @xcite , imply that the mass is extremely close to the @xmath16 threshold : @xmath19 the observation of the decay of @xmath4 into @xmath20 @xcite implies that the charge conjugation quantum number is @xmath21 . studies of the decays of @xmath4 into @xmath22 @xcite strongly favor the spin and parity @xmath23 , although @xmath24 is not excluded . the observation of decays into @xmath25 @xcite excludes @xmath26 , because the available phase space is so small . thus the quantum numbers of the @xmath0 have been determined to be @xmath27 . these quantum numbers imply that the @xmath4 has an s - wave coupling to the charm meson channel @xmath28 . the mass measurement in eq .  ( [ mx ] ) implies that it is a resonant coupling . this is sufficient to conclude that the @xmath0 is either a charm meson molecule with particle content @xmath28 or it is a virtual state of the charm mesons . the reason such an unambiguous statement can be made is that nonrelativistic systems with s - wave threshold resonances have universal properties that depend on the large scattering length of the constituents but are otherwise insensitive to their interactions at shorter distances @xcite . these universal properties have been exploited to describe the decays of @xmath4 into @xmath25 and @xmath29 @xcite , the production process @xmath30 @xcite , the line shapes of the @xmath4 @xcite , and decays of @xmath4 into @xmath12 and pions @xcite . these applications rely on factorization formulas that separate the length scale @xmath31 from all the shorter distance scales of qcd @xcite . hanhart et al . have analyzed the data from the belle and babar collaborations on the decays @xmath32 in the decay channels @xmath22 and @xmath25 and concluded that the @xmath4 must be a virtual state of charm meson @xcite . a more recent analysis that took into account consistently the effects of the @xmath33 width concluded that a charm meson molecule was preferred by the data , although a virtual state could not be excluded @xcite .    in this paper , we exploit the identification of the @xmath0 as a weakly - bound charm meson molecule to give an order - of - magnitude estimate of its partial width into @xmath1 . in section  [ sec : hi - energy ] , we estimate the cross section for @xmath34 well above the threshold by scaling measured cross sections for @xmath6 . in section  [ sec : threshold ] , we extrapolate the cross sections for @xmath34 to the threshold under the assumption that there is an s - wave threshold resonance in the @xmath7 channel . in section  [ sec : width ] , we deduce the partial width for @xmath4 into @xmath1 from the extrapolated cross section for @xmath35 . we discuss the results in section  [ sec : disc ] . given that @xmath0 is a weakly - bound s - wave hadronic molecule composed of @xmath2 or @xmath3 , its partial width into @xmath1 is proportional to the cross section for @xmath5 near the @xmath2 threshold . in this section , we estimate that cross section at energies well above the threshold by scaling the measured cross section for @xmath6 .    at the quark level , the process @xmath34 is @xmath37 . this process can proceed through the short - distance annihilation process @xmath38 followed by a long - distance process in which the remaining constituents @xmath39 and @xmath40 of the @xmath41 and @xmath42 bind to the @xmath43 and @xmath44 to form the charm mesons . the @xmath39 and @xmath40 carry only a small fraction of the momenta of the outgoing charm mesons . this process can proceed most easily via the feynman process in which the @xmath40 and @xmath39 that do not annihilate carry only a small fraction of the momenta of the colliding @xmath42 and @xmath41 . the momenta transfered to the @xmath40 and to the @xmath39 are therefore small . we assume that the cross section for this process can be factored into the rate for the short - distance annihilation process @xmath38 and a long - distance probability factor associated with the @xmath40 and @xmath39 that do not annihilate . we first consider the short - distance factor . the short - distance process involves the annihilation of @xmath45 into two virtual gluons which then create a @xmath9 pair . since it involves 6 external partons , the dimensional counting rules for this process imply that its rate scales with the center - of - mass energy @xmath46 like @xmath47 @xcite . this should be contrasted with the rate for @xmath1 annihilation at resonance into charmonium . in this case , the short - distance process is @xmath48 . the dimensional counting rules imply that its rate scales like @xmath49 , where @xmath50 is the charmonium mass @xcite . in the case of @xmath34 , the rate for the short - distance subprocess scales with two fewer powers of the center - of - mass energy , because one of the three quarks in the proton is not required to annihilate . we now consider the long - distance factor . this factor is the probability for the surviving @xmath40 and @xmath39 from the colliding @xmath42 and @xmath41 to become constituents of the outgoing charm mesons . in the initial state , the @xmath51 and the @xmath52 that annihilate act as light - like colored sources for the remaining low - momentum @xmath40 and @xmath39 . in the final state , the @xmath43 and @xmath44 act as colored sources for the low - momentum @xmath39 and @xmath40 . in the @xmath1 rest frame , these sources have equal and opposite velocities @xmath53^{1/2}$ ] . the effect of the short - distance process is to suddenly replace the light - like colored sources @xmath51 and @xmath52 by colored sources @xmath43 and @xmath44 with equal and opposite velocities @xmath54 . the long - distance factor @xmath55 is the square of the amplitude for the low - momentum @xmath40 and @xmath39 to evolve from constituents of the @xmath42 and @xmath41 into constituents of the @xmath56 and @xmath33 after the sudden change in color sources . the long - distance factor @xmath55 depends on the velocity @xmath54 of the colored sources in the final state , but it does not depend on the flavor of the particles that serve as the colored sources . the amplitude would be the same if the charm quarks @xmath43 and @xmath44 were replaced by strange quarks @xmath57 and @xmath58 with the same velocities @xmath54 . thus the rate for producing the charm mesons @xmath59 , whose quark content is @xmath60 , can be related to the rate for producing strange mesons @xmath61 , whose quark content is @xmath62 . if we take into account the masses of the mesons , a @xmath63 pair with center - of - mass energy @xmath64 has the same relative velocity @xmath65 in the center - of - mass frame as a @xmath16 pair with center - of - mass energy @xmath66 if the center - of - mass energies satisfy @xmath67 where @xmath68 . the cross section for @xmath34 can be expressed as the product of a flux factor @xmath69^{-1/2}$ ] , a phase space factor @xmath70 , and a matrix element factor . under our factorization assumption , the matrix element factor is the product of a short - distance factor that scales asymptotically like @xmath71 and a long - distance factor @xmath55 that is a function of the velocities @xmath54 of the @xmath43 and @xmath44 created by the short - distance process . if we use the asymptotic scaling behavior of the short - distance factor in the matrix element , the energy dependence of the cross section is given by @xmath72 & \sim &   \frac{1}{[s ( s - 4 m_p^2)]^{1/2 } } \ , \frac{p(\beta)}{s^2 }   \ , \frac{\lambda^{1/2}(s^{1/2 } , m_{d^ * } , m_d)}{s } . \label{sig - e}\end{aligned}\ ] ] in the limit @xmath73 , the right side of eq . ( [ sig - e ] ) approaches @xmath74 in accord with the dimensional counting rules . there is an expression analogous to eq . ( [ sig - e ] ) for the cross section for @xmath6 with the same long - distance factor @xmath55 , but with @xmath75 and @xmath76 replaced by @xmath77 and @xmath78 . using eq . ( [ sd - sk ] ) to eliminated that factor , we obtain a scaling relation between the two cross sections : @xmath79 & \approx &   \sigma [ p \bar p \to k^{*- } k^+ ; s_k ] \ , \frac { [ s_k ( s_k - 4 m_p^2)]^{1/2 } }         { [ s_d ( s_d - 4 m_p^2)]^{1/2 } } \nonumber \\ & & \hspace{1 cm } \times \left ( \frac { s_k}{s_d } \right)^3   \frac { \lambda^{1/2}(s_d^{1/2 } , m_{d^ * } , m_d ) }       { \lambda^{1/2}(s_k^{1/2 } , m_{k^ * } , m_k ) } , \label{sig - scale}\end{aligned}\ ] ] where @xmath80 is the function of @xmath81 obtained by solving eq . ( [ sd - sk ] ) .     as a function of the center - of - mass energy . the open dots are the data from refs . the two solid dots are data from the crystal barrel collaboration @xcite . the curves passing through the crystal barrel data points are extrapolations whose energy dependence is given by the analog of eq . ( [ sig - e ] ) for @xmath63 with the probability factor @xmath55 approximated by a constant . [ fig : sigmak],width=453 ]    the cross sections for @xmath6 have been measured for antiproton momenta in the lab frame ranging from 702 mev to 1642 mev @xcite . this corresponds to center - of - mass energies @xmath82 ranging from 1990 mev to 2304 mev . the only recent measurements were from the crystal barrel collaboration @xcite . the cross section was measured to be @xmath83b at @xmath84 mev and @xmath85b at 2304 mev @xcite . the relative velocities @xmath54 given by eq . ( [ sd - sk ] ) are 0.74 and 0.80 , respectively . the data points are shown in figure  [ fig : sigmak ] as a function of the center - of - mass energy . also shown in the figure are curves that pass through the crystal barrel data points and whose dependence on the energy is given by the analog of eq . ( [ sig - e ] ) for @xmath63 with the probability factor @xmath55 approximated by a constant . notice that the two curves do not differ dramatically . this suggests that at these energies , the matrix element factor in the @xmath63 cross section may already be close to its asymptotic behavior proportional to @xmath74 .    to estimate the cross section for @xmath34 , we insert the crystal barrel data points for the @xmath63 cross section into eq . ( [ sig - scale ] ) , where @xmath80 is the function of @xmath86 obtained by solving eq . ( [ sd - sk ] ) . the center - of - mass energies @xmath64 for the two crystal barrel data points are 2050 mev and 2304 mev . the corresponding center - of - mass energies @xmath66 for the process @xmath34 are 5714 mev and 6391 mev . if we use the higher - energy crystal barrel data point as the input , our estimate for the cross section for @xmath16 is @xmath87 \approx   \left ( \frac{m_{d^*}+m_d}{\sqrt{s } } \right)^6 \ , \frac{\lambda^{1/2}(s^{1/2 } , m_{d^ * } , m_d ) }      { [ s ( s - 4 m_p^2)]^{1/2 } }   \left ( 4800 ~ { \rm nb } \right )   . \label{sig - hi}\ ] ] if we use the lower - energy crystal barrel data point as the input , the factor of 4800 nb is replaced by 5600 nb . the relatively small difference implies that the probability factor @xmath55 in eq . ( [ sig - e ] ) does not depend dramatically on @xmath54 in the region @xmath88 . if we were to change the assumed scaling behavior of the short - distance factor in the square of the matrix element from @xmath89 to @xmath90 , the prediction in eq . ( [ sig - hi ] ) would change by a multiplicative factor of @xmath91 . given the estimate in eq . ( [ sig - hi ] ) of the cross section for @xmath34 at energies far above threshold , we would like to obtain an estimate of the cross section near threshold . we can not simply use eq . ( [ sig - hi ] ) to extrapolate to the threshold region , because this expression ignores the suppression of higher partial waves near the threshold , which can be taken into account through the probability factor @xmath55 in eq . ( [ sig - e ] ) , and because it also ignores the threshold resonance associated with the @xmath0 . we will assume that the threshold resonance is in the s - wave @xmath21 channel , and that this is the only effect that gives dramatic dependence of the s - wave phase shift on the center - of - mass energy @xmath82 . as the center - of - mass energy approaches the threshold at @xmath92 , the terms in the matrix element with nonzero orbital angular momentum quantum number @xmath93 are suppressed by a factor of @xmath94 . only the s - wave @xmath95 term survives in the limit . if the s - wave threshold resonance could be ignored , a crude extrapolation of the cross section for @xmath16 in eq . ( [ sig - hi ] ) towards the threshold could be obtained simply by multiplying it by the fraction @xmath96 of the cross section that comes from s - wave scattering . the determination of the s - wave fraction requires measurements of the angular distribution . there is some information on the angular distribution for the related process @xmath6 . in the crystal barrel experiment @xcite , it was estimated that angular momenta up to @xmath97 contribute to the cross section at center - of - mass energy 2304 mev . in ref . @xcite , the angular distribution for @xmath6 was measured at center - of - mass energy 2006 mev . the ratios @xmath98 of the coefficients of the legendre polynomials in the partial wave expansion were given for @xmath93 up to 5 . from those results , we can infer that the fraction of the cross section at 2006 mev that comes from s - wave scattering is about 9.3% . since no experimental information is available on the s - wave fraction @xmath99 for @xmath16 , we will use the s - wave fraction for @xmath63 at 2006 mev as an estimate : @xmath100 . if the threshold resonance could be ignored , we could estimate the cross section for @xmath16 near threshold obtained simply by extrapolating eq . ( [ sig - hi ] ) to the threshold and multiplying it by the fraction @xmath96 . however the existence of the @xmath0 with quantum numbers @xmath7 implies that there is a resonant enhancement of the cross section for @xmath16 near the threshold due to scattering in the s - wave @xmath21 channel . the enhancement applies only to the fraction @xmath101 of the cross section that comes from @xmath1 scattering into channels that are even under charge conjugation . experiments on @xmath1 annihilation at very low @xmath41 momentum have revealed a suppression of the production of final states that are even under charge conjugation . in ref . @xcite , the suppression of @xmath102 final states was also observed in final states containing pairs of strange mesons at the center - of - mass energy 2006 mev . the suppression factor in the case of @xmath63 can be deduced from measurements of @xmath103 , which is related by isospin symmetry . the cross section for @xmath104 followed by the decay @xmath105 , which gives a final state with @xmath102 , is only @xmath106 @xmath107b . the cross section for @xmath108 with no restriction on the decays of @xmath109 is @xmath110 @xmath107b . the ratio of these two cross sections gives an even - charge - conjugation fraction of about 13.1% . since no experimental information is available on the even - charge - conjugation fraction @xmath111 for @xmath16 , we will use the even - charge - conjugation fraction for @xmath112 at 2006 mev as an estimate : @xmath113 .    to extrapolate the cross section for @xmath34 to the threshold region , we will exploit the universal features of s - wave threshold resonances in nonrelativistic 2-body systems @xcite . these universal features can be conveniently expressed in terms of the scattering length @xmath31 in the resonant s - wave channel . if the resonance is sufficiently close to the threshold , @xmath114 will be much larger than all other length scales associated with the structure of the particles and their interactions . the scattering amplitude in the resonant channel has the universal form @xmath115 where @xmath116 is the energy relative to the 2-body threshold and @xmath50 is the reduced mass . if @xmath31 is real and positive , the amplitude in eq . ( [ f - e ] ) has a pole at @xmath117 , where @xmath118 the pole is associated with a bound state with binding energy @xmath119 . if @xmath31 is real and negative , there is no pole on the physical sheet of the complex energy @xmath116 , so there is no bound state . there is however a pole on the unphysical sheet of @xmath116 and it is conventionally referred to as a `` virtual state '' . the scattering length @xmath31 is complex if the 2-body system has inelastic scattering channels . if @xmath31 is complex , its real part can still be used to distinguish between a bound state ( @xmath120 ) and a virtual state ( @xmath121 ) . in the case @xmath120 , the bound state has a nonzero width determined by the imaginary part of @xmath31 . the existence of the @xmath0 with quantum numbers @xmath7 and mass given by eq . ( [ mx ] ) implies that there is an s - wave threshold resonance in the channel @xmath122 the scattering amplitude in this channel is given by the universal expression in eq . ( [ f - e ] ) , where @xmath123 and @xmath50 is the reduced mass @xmath124 . since @xmath0 decays , its constituents have inelastic scattering channels , so the scattering length @xmath31 must be complex . in ref . @xcite , the authors analyzed the data from the belle and babar collaborations on the @xmath0 resonance produced via @xmath32 and decaying through the channels @xmath22 and @xmath25 . they concluded that @xmath0 must be a virtual state with @xmath121 . in a subsequent analysis of the same data , the nonzero width of the constituent @xmath33 or @xmath125 of the @xmath4 was taken into account @xcite . the conclusion of that analysis was that the data preferred a bound state corresponding to @xmath120 , although a virtual state was not excluded . we will assume that the @xmath0 is indeed a bound state . we also assume for simplicity that the imaginary part of @xmath31 is small compared to its real part , so the binding energy of the @xmath4 can be approximated by the simple expression in eq . ( [ ex ] ) with @xmath50 replaced by @xmath126 . we proceed to use the universality of s - wave threshold resonances to extrapolate the estimated cross section for @xmath34 to the threshold region . matrix elements corresponding to the projection of the charm mesons onto the channel @xmath127 defined in eq . ( [ dstardbar ] ) will be enhanced at energies near the @xmath16 threshold by the resonance associated with the @xmath0 . for the process @xmath34 , the resonance enhances the matrix element near the threshold by a dimensionless factor @xmath128 where @xmath129 and @xmath130 is the momentum scale above which the effects of the nonzero range of the interaction become important . if the s - wave effective range @xmath131 for the scattering of the charm mesons was known , we could use @xmath132 as a quantitative estimate . a natural order - of - magnitude estimate for @xmath130 is @xmath133 , which is the next smallest relevant momentum scale after @xmath134 . this is a relevant momentum scale , because the low energy scattering of @xmath16 is dominated by pion exchange . our estimate of the cross section for @xmath34 near the threshold is obtained by extrapolating the estimated cross section in eq . ( [ sig - hi ] ) to the threshold region and multiplying it by the s - wave fraction @xmath100 , the even - charge - conjugation fraction @xmath113 , and the resonance factor @xmath135 : @xmath136 \approx \left ( 1.9 ~ { \rm nb } \right )   \frac{\lambda^2 k_{\rm cm}}{m_\pi ( 1/a^2 + k_{\rm cm}^2 ) }   . \label{sigd*dbar0}\ ] ] the factor of @xmath133 in the denominator in eq . ( [ sigd*dbar0 ] ) was introduced to make the last factor dimensionless . if the lower - energy crystal barrel data point was used as the input for eq . ( [ sig - hi ] ) , the prefactor in eq . ( [ sigd*dbar0 ] ) would have been 5.5 nb . to relate the cross sections for @xmath1 annihilation into @xmath16 and @xmath0 , we begin by considering the forward scattering amplitude for @xmath138 near the @xmath16 threshold . this amplitude can be expressed as the product of three factors : a short - distance factor for the transition from @xmath1 to the resonant channel @xmath127 , a long - distance resonance factor @xmath139 given by eq . ( [ f - e ] ) , and a short - distance factor for the transition from @xmath127 to @xmath1 . by the optical theorem , the total @xmath1 cross section is proportional to the imaginary part of the forward scattering amplitude . the resonant contribution to the imaginary part associated with @xmath16 or @xmath17 in the final state comes from the imaginary part of the resonance factor : @xmath140 where @xmath141 and @xmath142 is the binding energy of the @xmath4 given in eq . ( [ ex ] ) . the first term on the right side corresponds to the production of @xmath16 and @xmath17 above the threshold . the second term corresponds to the production of the @xmath0 resonance . the cross sections for producing @xmath16 near threshold , @xmath17 near threshold , and @xmath0 are    @xmath143 & = &   \mbox{$\frac12 $ } \sigma_{\rm sd }   \frac{m_\pi k_{\rm cm}}{1/a^2 + k_{\rm cm}^2 } \theta(e ) , \label{sigd*dbar - fact } \\ \sigma [ p \bar p \to d^0 \bar d^{*0};e ] & = &   \mbox{$\frac12 $ } \sigma_{\rm sd }   \frac{m_\pi k_{\rm cm}}{1/a^2 + k_{\rm cm}^2 } \theta(e ) , \label{sigddbar*-fact } \\ \sigma [ p \bar p \to x;e ] & = &   \sigma_{\rm sd }   \frac{\pi m_\pi ( 2 m_{d^ * \bar d } e_x)^{1/2}}{m_{d^ * \bar d } }   \delta(e + e_x ) , \label{sigxfact}\end{aligned}\ ] ]    where @xmath144 is a short - distance factor . in eq . ( [ sigxfact ] ) , we have used eq . ( [ ex ] ) to eliminate the scattering length @xmath31 in favor of the binding energy @xmath119 . a factor of @xmath133 has been inserted into the long distance factor to ensure that @xmath144 has the dimensions of a cross section . the delta function of the energy in eq . ( [ sigxfact ] ) arises from neglecting the width of the @xmath0 resonance . an estimate for the short - distance factor @xmath144 can be obtained by comparing the cross section in eq . ( [ sigd*dbar - fact ] ) with the estimated cross section in eq . ( [ sigd*dbar0 ] ) : @xmath145 the cross section for @xmath146 in the narrow resonance limit is related to the partial width for @xmath147 by simple kinematics . if we denote the t - matrix element for @xmath147 by @xmath148 , the partial width into @xmath1 is @xmath149 =   \frac{1}{2 m_x } \ , \frac{1}{3 } \sum_{\rm spins } | { \cal m } |^2 \ , \frac{(m_x^2 - 4 m_p^2)^{1/2}}{8 \pi m_x } . \label{gamma - t}\ ] ] the cross section for @xmath146 in the narrow resonance limit averaged over the spins of the proton and antiproton is @xmath150 =   \frac{1}{2 m_x ( m_x^2 - 4 m_p^2)^{1/2 } }   \ ,   \frac{1}{4 } \sum_{\rm spins } | { \cal m } |^2 \ , \frac{\pi}{m_x } \delta(e + e_x ) . \label{sigma - t}\ ] ] eliminating the t - matrix element from eqs . ( [ gamma - t ] ) and ( [ sigma - t ] ) , we obtain @xmath150 =   \frac{6 \pi^2 \gamma[x \to p \bar p]}{m_x^2 - 4 m_p^2 }   \delta(e + e_x ) . \label{sigma - gamma}\ ] ] comparing with eq . ( [ sigxfact ] ) and using the estimate of the short - distance factor @xmath144 in eq . ( [ sigma - sd ] ) , we obtain an estimate of the partial width of @xmath4 into @xmath1 : @xmath149 = \frac{(m_x^2 - 4 m_p^2 ) \lambda^2 ( 2 m_{d^ * \bar d } e_x)^{1/2 } }      { 3 \pi m_\pi m_{d^ { * } \bar d } } \left ( 1.9 \ { \rm nb } \right ) . \label{gamxppbar}\ ] ] the partial width is proportional to the square root of the binding energy @xmath119 . the current measurement of the binding energy is given by eq . ( [ mx ] ) : @xmath151 mev . the expression in eq . ( [ gamxppbar ] ) can be reduced to @xmath149 = \left ( \frac{\lambda}{m_\pi } \right)^2 \left ( \frac{e_x}{0.6 \ { \rm mev } } \right)^{1/2 } \left ( 28   \ { \rm ev } \right )   . \label{gamxppbar : est}\ ] ] the total width of the @xmath4 must be greater than the width of its constituent @xmath33 , which is about 70 kev . thus the estimate in eq . ( [ gamxppbar : est ] ) implies that the branching fraction for @xmath147 is less than about @xmath152 . we have estimated the partial width of @xmath0 into @xmath1 . the estimate was obtained by a sequence of well - motivated steps . the first step was estimating the cross section for @xmath34 well above the threshold by scaling measured cross sections for @xmath6 . the second step was estimating the contribution from the s - wave @xmath7 channel using suppression factors @xmath99 and @xmath111 for the @xmath63 process . the third step was extrapolating the cross section for @xmath34 to the @xmath16 threshold under the assumption that there is an s - wave threshold resonance in the @xmath7 channel . the cross section for @xmath146 was obtained from the cross section for @xmath34 near threshold by using the universal properties of an s - wave threshold resonance . the partial width for @xmath147 is related to the cross section for @xmath146 by simple kinematic factors . our estimate for the partial width is given in eq . ( [ gamxppbar : est ] ) . it is widely believed that the production of a loosely - bound molecular state in a process involving energies much greater than the binding energy should be strongly suppressed . there is some suppression , but it is not as strong as one might expect . in the estimate in eq . ( [ gamxppbar : est ] ) , the suppression is taken into account by the factor proportional to @xmath153 . this factor goes to @xmath154 as @xmath155 , suggesting that there would be complete suppression in this limit . however the suppression factor has this simple form proportional to @xmath153 only if @xmath119 is greater than @xmath156 , where @xmath157 is the total width of the @xmath4 . there is no further suppression once @xmath119 becomes comparable to @xmath156 . a lower bound on @xmath157 is provided by the width of the constituent @xmath33 or @xmath125 : @xmath158 = 66 \pm 15 $ ] kev . thus even if the binding energy is much smaller than 0.6 mev , the associated suppression factor can not decrease the estimate in eq . ( [ gamxppbar : est ] ) by more than about a factor of 0.2 . the estimate for the partial width for @xmath159 in eq . ( [ gamxppbar : est ] ) is proportional to @xmath160 , where @xmath130 is the momentum scale above which the effects of the nonzero range of the interaction between the charm mesons becomes important . thus the rate is very sensitive to @xmath130 . the scale @xmath130 can be identified with @xmath161 , where @xmath131 is the effective range for the scattering of the charm mesons , which is not known . we have suggested that a natural scale for @xmath130 is @xmath133 , since low - energy scattering of charm mesons is dominated by pion exchange . the estimates of the rate for @xmath162 in refs . @xcite were also proportional to @xmath160 . in this case , the choice @xmath163 may underestimate the rate by about an order of magnitude . thus setting @xmath163 in eq . ( [ gamxppbar : est ] ) may also underestimate the partial width of @xmath147 by an order of magnitude .    since the p - wave charmonium state @xmath8 has the same quantum numbers @xmath7 as the @xmath0 , it is useful to compare the @xmath1 partial widths of the @xmath0 with that of @xmath8 , which is @xmath164  ev . if we set @xmath163 and @xmath165 mev in eq . ( [ gamxppbar : est ] ) , our estimate of the @xmath1 partial width of @xmath0 is within a factor of 2 of that of @xmath8 . the e760 experiment on charmonium production at resonance in @xmath1 collisions measured the total width of the @xmath8 with an uncertainty of 0.14 mev @xcite . our estimate for the partial width of @xmath0 suggests that a new resonant @xmath1 experiment at gsi @xcite or at fermilab @xcite should be able to measure the properties of the @xmath0 with comparable or higher accuracy than those of the @xmath8 . it is also useful to compare the production rates of @xmath0 and @xmath8 in other processes . the production rate of @xmath4 by the exclusive decay @xmath166 has been measured by the belle and babar collaborations @xcite . dividing the measured product of the branching fractions for @xmath166 and @xmath167 by the branching fraction for @xmath168 @xcite , we obtain @xmath169 } { \gamma [ b^+ \to k^+ + \chi_{c1 } ] } = \frac { 0.023 \pm 0.005}{br[x \to j/\psi \ , \pi^+ \pi^- ] } . \label{rbk}\ ] ] some information on the branching fraction for @xmath4 into @xmath22 is provided by a measurement of the relative production rates for @xmath170 and @xmath25 in the @xmath0 resonance region by the belle collaboration @xcite : @xmath171}{br[x \to j/\psi \ , \pi^+ \pi^- ] }   = 8.8^{+3.1}_{-3.6 } . \label{rbrx}\ ] ] this measurement suggests that the branching fraction for @xmath4 into @xmath170 is less than about 1/8.8 , which implies that the production ratio in eq . ( [ rbk ] ) is greater than about 0.2 . the production rates of @xmath0 and @xmath8 are subject to various suppression factors . in the case of @xmath0 , they include the factor @xmath153 associated with the large mean separation of its constituents . in the case of @xmath8 , they include a factor of @xmath172 associated with the small relative momentum @xmath173 of the @xmath43 and @xmath44 . these suppression factors apply equally well to all production processes . however there is one suppression factor in resonant @xmath1 production that does not apply to exclusive @xmath10 meson decay . this is the suppression factor associated with the annihilation of all three quarks in the proton in the case of @xmath8 and the annihilation of only two of the quarks in the case of @xmath0 . because of this suppression factor , the production ratio for @xmath0 and @xmath8 in resonant @xmath1 collisions should be larger than the production ratio in eq .  ( [ rbk ] ) . this is consistent with the estimated production ratio in resonant @xmath1 collisions obtained by dividing eq . ( [ gamxppbar : est ] ) by the measured partial width for @xmath174 .    in summary , our estimate of the partial width for @xmath0 into @xmath1 in eq . ( [ gamxppbar : est ] ) indicates that it should be comparable to and perhaps even larger than that of the @xmath8 . this implies that a future experiment on @xmath1 collisions at the @xmath0 resonance will allow the properties of this remarkable meson to be studied in great detail .
we present an estimate of the partial width of @xmath0 into @xmath1 under the assumption that it is a weakly - bound hadronic molecule whose constituents are a superposition of the charm mesons @xmath2 and @xmath3 . the @xmath1 partial width of @xmath4 is therefore related to the cross section for @xmath5 near the threshold . that cross section at an energy well above the threshold is estimated by scaling the measured cross section for @xmath6 . 
 it is extrapolated to the @xmath2 threshold by taking into account the threshold resonance in the @xmath7 channel . 
 the resulting prediction for the @xmath1 partial width of @xmath0 is proportional to the square root of its binding energy . for the current central value of the binding energy , 
 the estimated partial width into @xmath1 is comparable to that of the p - wave charmonium state @xmath8 .