Nuclear-bound quarkonium

SLAC-PUB-5102 September 1989 T/E Nuclear-Bound Quarkonium* STANLEY J. BRODSKY Stanford Linear Accelerator Stanford University, Stanford, Center California 94309 and IVAN SCHMIDT** Stanford Linear Accelerator Stanford University, Stanford, Center California 94309 and Universidad Federico Santa Marla Casilla llO- V, Valparako, Chile and GUY F. DET~RAMOND Escuela de Fkica, Universidad de Costa Rica San Jose’, Costa Rica Submitted to Physical Review Letters * Work supported by the Department of Energy, contract DE-AC03-76SF00515. ** Supported in part by Fundacibn Andes, Chile ABSTRACT We show that the QCD van der Waals interaction change provides a new kind of attractive quarkonia to nuclei. ing multi-gluon scattering. exchange with the pomeron contributions bound states. In particular, nuclei. Production gluon ex- nuclear force capable of binding The parameters of the potential The gluonic potential due to multiple are estimated heavy by identify- to elastic meson-nucleon is then used to study the properties of CCnuclear- we predict bound states of the qc with He3 and heavier modes and rates are also discussed. 2 1. INTRODUCTION One of the most interesting anomalies in hadron physics is the remarkable behavior of the spin-spin correlation 90’: as fi ANN for pp + pp elastic scattering at 8,, crosses 5 GeV the ratio of cross sections for protons scattering their incident spins parallel and normal to the scattering their spins anti-parallel plane to scattering changes rapidly from approximately = with with As shown 2:l to 4:l.l in Ref. 2, this behavior can be understood as the consequence of a strong threshold enhancement at the open-charm threshold for pp 4 A,Dp Strong final-state production, interactions since at threshold, relative velocity. in the partial are expected at fi = 5.08 GeV at the threshold for new flavor all the quarks in the final state have nearly zero The dominant enhancement in the pp + pp amplitude wave J = L = S = 1, which matches the quantum J = 1 S-wave eight-quark have opposite parity. system QQQQQQ(CC)S=~ at threshold, Even though the charm production numbers of the since the c and C rate is small, of order of 1 pLb, it can have a large effect on the elastic pp + pp amplitude the competing perturbative QCD hard-scattering transfer is also very small at fi in hadronic and nuclear collisions. where the charmonium production, amplitude at 90’ since at large momentum = 5 GeV. In this paper we discuss the possibility threshold is expected of production of hidden charm below Consider the reaction pd + (cC)He3 state is produced nearly at rest. At the threshold for charm the incident nuclei will be nearly stopped (in the center of mass frame) and will fuse into a compound nucleus (the He3 ) because of the strong attractive nuclear force. The charmonium state will be attracted to the nucleus by the QCD gluonic van der Waals force. One thus expects strong final state interactions threshold. near In fact, we shall argue that the CC system will bind to the He3 nucleus. 3 It is thus likely charmonium distinct that bound a new type of exotic to nuclear matter. pd energy, spread by the width of the charmonium a measure of the charmonium’s from a unique initial THE QCD In quantum interacts with interactions chromodynamics, potential multiple the quark Qs and nuclei; state such as the qc gluon exchange. QED van der Waals potential. interchange the effective QED, meson the will not have a short- range repulsion. is the simplest example of a nuclear force is sufficiently states such as the 7, and r]b to nuclear matter. such states will be narrow peaks in energy in the production one expects that between heavy quarkonium is and nucleons have no (or equivalently In this paper we shall show that this potential On general grounds Unlike Since there is no Pauli blocking, should be negligible. interaction This at large distances because of the Since the (Q&) states.3 The QCD van der Waals interaction bind quarkonium hadrons and test color transparency a heavy quarkonium cannot have an inverse power-law effective quarkonium-nuclear in &CD. ordinary interactions a nucleon or nucleus through in common, exchange) with VAN DER WAALS INTERACTION absence of zero mass gluonium quarks state, and it will decay state condition. the- QCD analogue of the attractive the potential at a The binding energy in the nucleus gives its decays will measure hadron-nucleus 2. state will be formed: Such a state should be observable to unique signatures such as pd + He3yy. starting nuclear bound the effective 4 The signal for cross section. non-relativistic and nucleons can be parameterized strong to potential by a Yukawa form Since the gluons have spin-one, the interaction spectrum of quarkonium-nucleus is vector-like. This implies bound states with spin-orbit a rich and spin-spin hyper- fine splitting. Thus far lattice gauge theory and other non-perturbative termined the range or magnitude ever, we can obtain ha&&s of the gluonic potential some constraint by identifying with the magnitude or meson-nucleus scattering pomeron exchange with the eikonalization authors sections, exchange potentialP we shall make use of the phenomenologi- must have a somewhat reflects the fact that the minimum of One can identify These developed by Donnachie and Landshoff. analogous to that of a heavy photon. gluonium quark rule for total local structure; The short-range character its couplings cross are of the pomeron mass which can be exchanged in the t-channel is of order several GeV. Interference different amplitude. note that in order to account for the additive the pomeron How- of the term linear in s of the two-gluon To obtain a specific parameterization cal model of pomeron interactions between hadrons. on the J = 1 flavor singlet interactions the potential in the meson-nucleon methods have not de- terms between amplitudes involving quarks can then be neglected. The Donnachie-Landshoff parameterization formalism of the meson-nucleon leads to an s-independent and meson-nucleus Chou-Yang cross sections at small 6. $lA Here ,0 = 1.85 GeV-1 --+ MA) [2PF~(t)12[3APFA(t)12 47r is the pomeron-quark number of the nucleus. with the helicity-zero = coupling constant, and A is the nucleon To first approximation the form factors can be identified meson and nuclear electromagnetic 5 (2) form factors. We assume that ,B is independent of the meson type and nucleus. This is reasonable even for the 77~ or J/G since the radius of the lowest charmonium very different Equation hadron-hadron and hadron-nucleus high energies. Ignoring section at s >> scattering corrections ItI with the effective slope at t = 0. Assuming due to eikonalization, + MA) coupling 0.5 fm scattering, (CC) radius is comparatively F or meson He3 scattering, RI > /6 and equation is effec- regime the qc is non-relativistic, of motion we will treat the qc as a stable particle. is applicable. The effective states from charmonium To first potential or nuclear should not be important. We compute wavefunction =< the QCD van der Waals potential is then real since higher energy intermediate &~3/dw(-rr)- by the nuclear size since the over the nuclear volume. In the threshold Schrodinger 1-1= 0.53 GeV, one finds cu N 0.3 and p N 250MeV the smearing of the local interaction In the case of vc nucleus interactions, and its - N cross section - 4 mb. 6 In the case small; thus pm2 = IdFA(t)/dtlt=o tively the only QCD interaction. (da/dt)‘i2 for the J/1c, radius, one obtains the slope is dominated excitations the cross (3) a and the range ~1 from of meson-nucleus approximation we can identify = (-2;11:2)1- elastic J/g and an effective-potential elastic cross sections from very low to very cy 1 0.46, and an integrated a = 3Ap2p2/2~. of the s-independent that due to the vector Yukawa potential $MA reflecting not than the pion radius. (2) gives a reasonable parameterization We calculate state is N 0.5 fm, the binding energy using the variational Th e condition for binding is amTed > p. This condition 6 wavefunction by the Yukawa potential $(r) = with this is not met for charmonium-proton or charmonium-deuterium increases rapidly systems. However, the binding of the qc to a heavy nucleus with A, since the potential energy < j?/2mTed strength is linear in A, and the kinetic > decreases faster than the square of the nuclear size. If the width of the CCis much smaller than its binding energy, the charmonium sufficiently long that it can be considered stable for the purposes of calculating binding to the nucleus. For qcHe3 the computed fXqEHe4 state lives the binding energy is over 100 MeV. binding energy is - 20 MeV, and The predicted large even though the QCD van der Waals potential to the one-pion-exchange Yukawa potential; blocking or a repulsive short-range potential its binding energies are is relatively weak compared this is due to the absence of Pauli for heavy quarks in the nucleus. Table I gives a list of computed binding energies for the CCand bb nuclear systems. A twoparameter variational the same results. wavefunction Our results also have implications hadrons to nuclei? However, the strong mixing makes the interpretation 3. of the form (e-@lr - e-a2T)/r SEARCHING FOR C? of strange of the 7 with non-strange quarks NUCLEAR-BOUND STATES in nuclei will be very small. cross section for charm production We estimate for bound CCto nuclei are very distinct. the inclusive process pd --+ He3X, near threshold rates in section 4. However the signals The most practical measurement where the missing mass Mx could be is constrained close mass. (See Fig. 1.) Since the decay of the bound CCis isotropic in the center-of-mass, signal-to-noise for the binding of such states more complicated. It is clear that the production to the charmonium gives essentially but backgrounds is at backward peak will be found at a distinct are peaked forward, He3 cm angles. If the qc is bound to the He3, a value of incident pd energy: fi 7 the most favorable = MVc + MH,~ - 6, spread by the intrinsic predicted of the Q. Here c is the qC-nucleus binding width from the SchrGdinger equation. The momentum distribution frame is given by dN/d3p of the outgoing is given by the wavefunction TlG kinematics certainty for several different principle to the uncertainty The width parameter distribution gives a of the momentum y, which is tabulated dis- in Table I. reactions are given in Table II. From the un- we expect that the final state momentum in the CC position energy and recoil momentum wavefunction, nucleus in the center-of-mass = l$(p312. Thus th e momentum direct measure of the cc-nuclear wavefunction. tribution energy when it decays. distribution j’is By measuring in p’, one determines which then can be easily inverted related inversely the binding the Schrodinger to give the quarkonium-nuclear potential. Energy conservation Here A!lL = (l/Mx missing invariant in the center of mass implies + l/M~)-l is the reduced mass of the final state system. mass is always less than the mass of the free 7, : Mx=M~~-~-~. thus the invariant be understood The mass varies with (5) aA&; ’ the recoil momentum. The mass deficit can as the result of the fact that the Q decays off its energy shell when bound to the nucleus. More information is obtained by studying completely exclusive channels such as pd -+ yy He 3. Observation 8 specified final states- of the two-photon decay of the Q would be a decisive signal for nuclear-bound bound CC at the instant of its decay is distributed to the eigen-wavefunction $(q. the study of the propagation of hadrons through the nucleus starting and spin quantum the nucleons transit the nuclear medium, nuclear final state interactions. tum spectrum hadronic numbers. condition. their outgoing The differential More interesting In each case, the initial wavefunction with wave will be modified by between the energy and momen- should be a sensitive measure of the is the fact that the nucleons are initially formed from the CC + gg decay amplitude. of the order of the charm Compton from a wave- Consider, then, the decay qc + pi. As of the proton and anti-proton amplitudes. of the decays of the CC system allows for the decay is specified by the Schrodinger specific orbital The position in the nuclear volume according Thus the hadronic packet centered on the nucleus, a novel initial state condition quarkonia. The size of the production length ! - l/m,. region is The proton and anti-proton thus interact in the nucleus as a small color singlet state before they are asymp- totic states. hadron formation 4. The distortion POSSIBILITY OF J/+-NUCLEUS matter interactions effect, illustrated in Fig. than the qc interaction to MeV. in nuclear because of the possibility of which allow the CC system to couple to the qc. This 2, adds inelasticity to the effective CC nuclear potential. In effect the bound J/+ - H e3 can decay to qc d p and its width tens of KeV thus tests BOUND STATES of the J/lc, and other excited states of charmonium are more complicated spin-exchange hadron momenta and color transparency8 zone physics6 The interactions of the outgoing However if the J/$- nucleus binding then the Q plus nuclear continuum will change from is sufficiently states may not be allowed kinematically, 9 strong, and the bound J/+ could then retain its narrow width, N 70 KeV. As seen in Table I this appears to be the case for the J/1c, - H e4 system. An important the bound vector charmonium state will be the exclusive @e- signature for plus nucleus final state. The narrowness of the charmonium states implies that the charmonium-nucleus bound state is formed at a sharp distinct and the much smaller probability duality the product constant. cm energy, spread by the total width that it will decay back to the initial of the cross section peak times its width The formation corresponding orbital predict a hyperfine a or higher angular system. momentum bound In the case of J/lc, bound energy resolution. In principle there could state excitations to spin-half separation of the L = 0 ground state corresponding of the nuclei, we to states of Th is separation will measure the gluonic magnetic moment of the nucleus and that of the J/$. could in principle of by a series of narrow spikes of the various CC states. total spin J = 3/2 and J = l/2. 5. should be roughly with good incident cross section is thus characterized to the binding quarkonium-nuclear hadronic By Thus the narrowness of the resonant energy leads to a large multiple the peak cross section, favoring experiments be higher state. I M easurements of the binding energies be done with excellent precision, thus determining fundamental measures with high accuracy. STOPPING FACTOR The production cross section for creating the quarkonium-nucleus is suppressed by a dynamical “stopping” factor representing the nucleons and nuclei in the final state convert their kinetic quark pair and are all brought to approximately 10 bound state the probability that energy to the heavy zero relative velocity. For example, - in the reaction momentum pd + (cE)H e3 the initial from pcm to zero momentum proton and deuteron must each change in the center of mass. The probability a nucleon or nucleus to change momentum and stay intact of its form factor Fj( qi), + p&,)l/’ where 4; = [( Mi is given by the square - bf~)~ - p&J. We can use as a reference cross section the pp -+ c~pp cross section above threshold, estimated which was in ref. 2 to be of order N 1 pb. Then For the pd -+ &Ye3 pp channel of Fj(4.6 channel, we thus obtain a suppression factor relative to the GeV2)Fi(3.2 GeV2)/F$(2.8 GeV2) section which may be as large as 1O-35 cm2. Considering signal and the extra enhancement viable experimental 6. for N lop5 giving a cross the uniqueness of the at the resonance energy, this appears to be a cross section. CONCLUSIONS In QCD, the nuclear forces are identified with the residual strong color interexchange. ‘r actions due to quark interchange and multiple-gluon identity of nucleons, a short-range of the quark constituents is also present (Pauli-blocking). nium interactions From this perspective, in nuclear matter flavors of the quarks involved is particularly Because of the repulsive component the study of heavy quarko- interesting: in the quarkonium-nucleon due to the distinct interaction there is no quark exchange to first order in elastic processes, and thus no one-meson-exchange potential from which to build a standard there is no Pauli-blocking nuclear potential. and consequently 11 no short-range For the same reason, nuclear repulsion. The nuclear interaction in this case is purely gluonic and thus of a different nature from the usual nuclear forces. We have discussed the signals for recognizing quarkonium production of nuclear-bound nuclei with exotic components the charmonium c&standing quarkonium correlation ing.2 In this case, the interaction but it can provide characteristic would be the first realization bound by a purely gluonic potential. -nucleon interaction the spin-spin bound in nuclei. The would provide Furthermore, basis for un- anomaly in high energy p - p elastic scatter- is not strong enough to produce a bound state, a strong enough enhancement of an almost-bound the dynamical of hadronic system. at the heavy-quark threshold 12 Acknowledgements We wish to thank GFdeT S. Drell and M. Peskin for helpful also thank E. Henley and W. Haxton of Washington Summer Institute. 12 discussions. for the hospitality SJB and of the University A ( Ri >‘I2 p a rnred 1 3.9 0.529 0.458 0.715 >o 0.85 2 10.7 0.229 0.172 1.15 >o 1.563 0.18 -0.0012 9.5 0.26 0.327 1.45 2.16 0.65 -0.050 9.9 0.25 0.301 0.60 -0.040 8.2 0.299 0.585 1.52 -0.303 8.4 0.292 0.557 0.87 -0.127 1.45 -0.271 8.7 0.282 0.519 0.81 -0.107 1.35 -0.232 6 11.2 0.22 0.470 1.95 0.89 -0.128 3.50 1.63 -0.293 9 11.2 0.22 0.705 2.20 1.53 -0.407 4.42 3.11 -0.951 12 12.0 0.204 0.819 2.36 1.92 -0.637 5.09 4.16 -1.546 16 13.4 0.183 0.876 2.49 2.17 5.74 5.0 -2.046 -3 - 4 1.66 (;) (H) 0.40 -0.019 0.37 -0.015 0.92 -0.143 -0.805 m,,,(~) 2.66 (H) >o Table I Binding energies E = 1 < H > 1 of the qC and 776to various nuclei, in GeV. Here y (in GeV) is the range parameter of the variational and Q are the parameters of the Yukawa potential. GeV-‘) wavefunction, The data for < R; are from ref. 9. We have assumed Mqb = 9.34 GeV.l’ 13 and p (in GeV) >lj2 (in Process yHe3 -+ (He3qc) Ml M2 MA 6 fi Pcm Ppb 0 2.808 2.808 0.020 5.77 2.20 4.52 0.938 1.876 2.808 0.020 5.77 2.48 7.64 j?He4 -+ (H3qc) 0.938 3.728 2.808 0.020 5.77 1.48 2.30 yHe4 t 0 3.728 3.728 0.120 6.59 2.24 3.96 0.938 2.808 3.728 0.120 6.59 2.60 6.09 1.876 1.876 3.728 0.120 6.59 2.71 9.51 pd + (He3qc> (He4yc) nHe3 -+ (He4p) --- -dd + (He4qc) Table 11 Kinematics for the production of vC-nucleus bound states. All quantities in GeV. 14 are given REFERENCES 1. G. R. Court D. Krisch, et al., Phys. Rev. Lett. 57, 507 (1986); for a review, see A. University of Michigan Report No. UM-HE-86-39, 1987 (unpub- lished). 2. S. J. Brodsky -a.-See, and G. F. de Teramond, Phys. Rev. Lett. 60, 1924 (1988). for example, T. Appelquist and W. Fischler, Phys. Lett. m, 405 (1978). 4. 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The signal for the production Science +7, 231 (1957). The He3 and et al., Phys. Rev. m, Nuovo Cimento a, 1396 (1977). 483 (1978). et al., Phys. Rev. Lett. 49, 771 (1982). of almost-bound nucleon (or nuclear) charmo- nium systems near threshold such as in yp + (cc)~ is the isotropic of the recoil nucleon (or nucleus) at large invariant mass Mx production N Mq,, MJ,,, Figure Captions Fig. 1. Formation of the (CC) - He3 bound state in the process pd --+ He3X. Fig. 2. Decay of the J/+ - He3 bound state into qcpd. 16 9-89 6469Al Fig. 1 9-89 6469A2 Fig. 2 .-, View publication stats