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Harry J. Lipkin

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Harry J. Lipkin oi*?- im. WlS-90/42/Nov-PH Some Comments on the Possibilities forlSearches for the Pentaquark (cjuud) Harry J. Lipkin Department of Nuclear Physics Wehmann Institute of Science Rehovot 76100, Israel and School of Physics and Astronomy Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University Tel Aviv, Israel Submitted to To Proceedings of the Rheinfels Workshop 1990 on Hadron Mass Spectrum St.Goar at the Rhine, Germany, Sept. 3-6, 1990 October 30, 1990 How can theorists help experimenters look for the H and the Pentaquark? This question was discussed extensively at Tel Aviv University thiB spring by a group of experimenters and theorists, including Yossef Dothan, whose sudden death in May 1990 was a shock to all of us. This talk is dedicated to his memory. 1. INTRODUCTION 1.1 Why it is hard to guide P experiments. Theoretical discussion about the possible existence of the exotic anticharmed strange baryon Pentaquark jejuud^ has focused mainly on its mass and binding en­ ergy [2,3,4,5] and comparison with the case of the H dibaryon [6]. So far nobody has ever seen a Pentaquark, and there are no data available to indicate its properties. At this stage the very existence of the P is open to question, whether it is bound or a res­ onance, and whether its wave function is more like a five-quark bag or a loosely bound N — D, molecule. The same uncertainties exist for the H dibaryon which ia the subject of a number of dedicated experiments. In both cases a positive result for a search would be very exciting, but a negative result gives very little information. There is still no real theory for production mechanisms and decay signatures and not very much quantitative can be said. There are no good theoretical estimate of masses, cross sections, etc. which could be used with a negative experimental result to place bounds on the existence or parameters of the H or the P. 1.2 Why experimenters should look for the Pentaquark So far no well-established multiquark states have been found, except for nuclei which have very low binding energies on the hadronic scale, a few MeV rather than 100, and are not relevant to this discussion. Simple QCD-motivated arguments suggest that multiquark systems may be bound by the color-magnetic hyperfine interaction, - 1 - which is responsible for the N - A splitting and gives rise to potential energies of the order of hundreds of MeV. Experimental information on the existence and properties of such states would be very useful in helping us understand how quarks are bound into hadrons by the interactions of QCD. The S* and 6 mesons, now called f0 and a0, have been known for many years and are outstanding candidates for four-quark states. But there still has been no convincing experiment which can show whether these are indeed exotics. It is hard to prove that they are exotic, because they do not have exotic quantum numbers. The two best candidates for bound exotics with exotic quantum numbers sug­ gested by the QCD arguments for color-magnetic binding are the Pentaquark and the H dibaryon. In contrast to the H, the P search does not require a dedicated experiment and can be undertaken as a by-product in other experiments [1,7]. The color-magnetic energy of simple model wave functions with average spacing between quarks equal to that in nucleons can be calculated in an almost model-independent manner. This po­ tential energy is found to be of the same order as the kinetic energy required to hold these particles together. Whether a change in the scale of the wave function and the introduction of correlations can produce a bound state is strongly model-dependent and difficult to calculate reliably. 1.3 The molecular model One possible approach is to assume that the H and the P are weakly bound A — A and N — D, molecules, analogous to the S* and 6 which are assumed to be K — K molecules. A simple phenomenological description for tlie molecular model uses a two- body Hamiltonian D2 V » = ST^ + —L— (1-1) 2Mff mqmqi where jTis the relative momentum of the two hadrons forming the "molecule", Mg is their reduced mass, V is a short-range hyperfine interaction and mq and mqi denote the masses of the two relevant interacting quarks in the hyperfine interaction. For a very short range interaction the value of the parameter VMnl{mqmqi) de­ termines whether the system is bound. We do not know the strength of the interaction V and can therefore not determine whether a given system will be bound. However, we can compare systems for which the ratios of V arc known to see which has the better chance of being bound. For values of MR which are too small, the system is not bound because of the high kinetic energy required to localize a low-mass particle. For values of mqmqt which are too large, the hyperfine interaction is too small to produce binding. There is therefore an optimum value of the masses for which the chances of binding are best. For two-meson systems having the same value of V, the optimum case is the K — K system, because - 2 - -£«- > Jfe_ (1.26) mumj Tnume The P and if have been compared in this molecular model with the two-meson system with the result that they are more favorable than the K — K system[3]. Thus, if the S* and 6 mesons are indeed K — K molecules, the P and H can also be expected to be bound molecules. We now note some general properties of production mechanisms and decay modes. Th? two states of the Pentaquark isodoublet are denoted by P° and P~ for the states (csuud) and (csudd) respectively. The corresponding anti-Pentaquark states are denoted by P° and P+ for the states (csuud) and (csudd) respectively. 2. PRODUCTION MECHANISMS The P can be produced either directly or via decays of hadrons containing 6 quarks [5]. 2.1 Direct Production The production mechanisms can be divided into several classes. There are hadronic experiments and electron-positron annihilation experiments. Hadronic experiments can have proton beams, meson beams or hyperon beams, and nucleon or nuclear targets. In hadronic experiments the Pentaquark can be produced in the beam fragmentation region, the central region or the target fragmentation region. The baryon constituent of the Pentaquark can be produced from a baryon existing in the initial state or from the creation of a baryon-antibaryonpair. The first mechanism only produces the Pentaquark and not the anti-Pentaquark. The second mechanism is expected to produce both more or less equally. The anti-Pentaquark decays into final st&ies including an antibaryon. The back­ ground against which these decays are observed should be lower than for the corre­ sponding Pentaquark decays in all hadronic experiments, because of the large baryon background expected from baryons present in the initial state. In electron-positron annihilation, there should be complete symmetry between P and P. For insight into Pentaquark production from other experiments, we look for cases having some of the peculiar properties of the Pentaquark; namely that it is charmed, strange, exotic and carries baryon number. A c - c pair must be produced in all experiments producing the pentaquark, and an s — s pair as well in all experiments except those with kaon or hyperon beams. Some estimate of production cross sections are therefore obtainable from experimental data on charm production, combined charm and strangeness production and baryon-anti baryon production with charm and strangeness. Exotic states carry the quantum numbers of bound states of two or more color singlet hadrons. The only exotic states which are known to exist and to have been produced in reactions are nuclei and antinuclei, and in particular the deuteron and anti-deuteron. If the P is loosely bound, a large part of its wave function will be a bound N — Da system, similar to the two-nucleon wave function describing the deuteron, but with a higher binding energy. Some indication of the production cross section can therefore be obtained by examining nucleon and Da production in known experiments _ 3 _ and estimating the probability that the two will stick together by looking at the sticking probability for deuteron and antideuteron production in experiments at comparable energy ranges. This leads to estimates of the form, w'Jggffi1-™™* {2Aa) anc where ac(A)t &d(&) ^ ^(C) denote the cross sections for producing the hadrons A B and C respectively in a charm production experiment and in experiments where deuterons or antideuterons are produced, and F(P,d) denotes a factor expressing the ratio of the sticking probabilities of the p — D9 system in the Pentaquark and the n — p system in the deuteron. Note that the relation (2.1a) includes both the case where the nucleon in the Pen­ taquark and one of the nucleons in the deuteron are produced by pickup from the beam or target and the case where all particles are produced in the reaction and stick together as the result of some final state interaction. The relation (2.1b) neglects pickup contri­ butions since there arc no antinucleons present in the initial state of the antideuteron production experiment. The value of F(P, d) can be estimated by assuming that the sticking probability is proportional to phase space and using the binding energy as an estimate for the relative kinetic energy which determines phase space. If the P binding energy is an order of magnitude larger than that of the deuteron as suggested by the hyperfine potential energy calculations, a rough estimate F{P>d) % 30 is obtained.
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