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. As a general guide to suitable reactions, P production can be expected to be en­ hanced over other processes if there already is strangeness or charm in the initial state. Naked strangeness is present in reactions produced by kaon or hyperon beams. There are no beams with naked charm. However, one might consider reactions using charnv anticharm pairs present in hadron wave functions; e.g. knocking a charmed quark out of the sea in a proton, thereby leaving a c in the proton in a cuud configuration which needs only to pick up a strange quark to make the P. Some reactions with these features are A- + p -» D*° + D~ + p -» D*° + P (2.2a)

A + p->P + Ac (2.26)

A + p-* (Ac) + {cp) ->XC + P (2.2c) where A denotes any beam particLe and Xc a multiparticle charmed state. 2.2 Production from B Decays Searches for the P in B decays have also been suggested[5). Although the branching ratios for B decays into final states containing the P are expected to be small, they

- A - may still be comparable to the branching ratios for other rare B decays which are already under investigation in search experiments; e.g. charmless decays into final states containing only two charged particles and no neutrals. Significant numbers of P's may be found in experiments producing large numbers of B's. There should be a reasonable branching ratio for B decays into baryon-antibaryon final states. These will nearly always contain a charmed quark, since the dominant decay mode for the 6 quark is b-+c-\-u + d »2.3)

The most favored case for P production is the Ba, since the strange quark is already present in the initial state. The creation of two additional nonstrange quark-anti quark pairs by two or more gluons after the weak transition (2.3) produces the constituents of the N — ND8 final state which should have a reasonable probability of "sticking" to make a P and a nucleon. This gives the favored weak decay,

B8(bs) -*c+3 + u + d-+c + s-i-u + d + (uu) + {dd) -»

-*P° + n (2.4a)

B3{hs) -*c + s + u + d->c + s + u + d + {uu) + (dd) -+ -* P° + n (2.46)

± The Bd and B can also decay to final states containing the P via the favored weak transition (2.3) and creating two additional quark-antiquark pairs by two or more gluons. except that one of these pairs must be strange and there must therefore be a strange antibaryon or baryon in the final state together with the P or P.

Bj(hd) -*c + d+u + d->c + d+u + d + (ss) + (uu) -•

— P" + A (2.5a)

Bd(b3)-tc + d + ii + d->c + d + u + d + (ss) + (uu) -> -P° + \ (2.56) B+(bu) -> c + u + u + d-> c + u + u + d + (ss) + (dd~) -» - P° + (S)+ (2.5c) B~(bu) ->c + u + fi + d-tc + u + u-td+ (si) + (.dd) -> ->£° + £- (2.5d)

The branching ratio in this case is expected to be lower than for the Ba because of the 5X'(3) flavor symmetry breaking in the creation of the strange quark pair, and because the additional mass of the strange baryon in the final state reduces phase spare.

-5 Equal numbers of b quarks and b antiquarks are produced in all reactions. This particle-antiparticle symmetry should be reasonably well preserved in P production, since it is broken only by the small asymmetry effect of pickup of b quarks by quarks from the initial hadron state to make beautiful baryons. Thus the P should be produced almost as frequently as the P in hadronic experiments, and the antinucleon signature of the P makes it the favored choice with the lowest background, 3. WEAK DECAYS OF THE PENTAQUARK The most favored signature for the decay is from the mode

+ p° _^ + 7r- +p_+ K + K~ +7T" +p (3.1)

This could appear as the decay of an off-shell DB together with a proton and give a peak in the invariant mass of the ir~p system. The signature should be fairly clean, since there should be very little — TT background in the invariant mass neighborhood of the Dg One would expect the branching ratio for this decay to be comparable to the branching ratio for the Ds —* 4> + n~ decay. The decay (3.1) is produced by the standard spectator diagram in which the anticharmed quark decays via the Cabibbo allowed transition c-* s + d+u (3.2) Spectator diagrams produce a state of five quarks and two antiquarks which can either rearrange to combine into two mesons and a baryon, fragment into states with more hadrons, or annihilate one quark-antiquark pair to produce a meson-1 aryon state. There is no reliable estimate of the relative probabilities of rearrangement, fragmentation or annihilation of such a seven-body system. One might obtain a crude estimate from the analogous case of the six-quark system produced by riucleon-antinucleon annihilation at rest, where rearrangement produces three-meson states, fragmentation produces states of more mesons and annihilation produces two-meson states. All three mechanisms seem to be observed. In addition to the spectator diagrams, there are annihilation diagrams, exchange diagrams and penguin diagrams, all of which lead first to a state of four quarks and an antiquark. The relative contribution of these diagrams is still an open question for the decay of normal quark-antiquark mesons. Even more uncertainty arises from the presence of three additional quarks in the P, all of which can participate in one of these diagrams. This might suggest that such diagrams are more important in the P than in meson decays, d and s quarks can annihilate against the c to make a W~ boson; the u quark can exchange a W^ with the c. All of these quarks can exchange a gluon with the antiquark in a penguin diagram. These diagrams are of special interest for detectors which are particularly sensitive to the two-body final states formed from four quarks and an antiquark. We now consider these diagrams in detail. The annihilation diagrams for the Cabibbo allowed and suppressed transitions are:

c + s -» W~ -> ii + d (3.3a)

- 6 - c + s —> W~ —> u + s (3.36) i + d-* W~ -* u + d (3.3c)

These lead to the final states for P decay

P°->u + u+d + d + u->p+ir- (3.4a)

P° — u + u + d + s + u->p+K~ (3.46) where the hadroiiic final states chosen are the most favorable for a detector of two charged particles. The exchange diagrams for the Cabibbo allowed and suppressed transitions are: c + u -» i + d (3.5a) c + u ->d + d (3.56) c + u -> S + s (3.5c) These lead to the final states for P decay

P° -» u + s + d + d + S -. E~ + K+ (3.6a)

P°->u + a + d+d + J — ST +7T+ (3.66) P° -tu + d + t + 3 + a — =.- + K+ (3.6c) The penguin diagrams produce the same quark transitions (3-3b) and (3.3c) as the Cabibbo-suppressed annihilation diagrams, raid lead to the same hadronic final state (3.4b).

If the P is a loosely-bound Ds — p bound 3tate, the detaya nay resemble those of the unbound D. with a spectator proton. There would be no contribution from - exchange diagrams (3.5-3.6) which involve a W exchange be ween the Da and the proton. However, the annihilation transitions (3.3a-3.3b) can occur within the Ds and lead to the two-body final states (3.4a-3.4b) whose counterparts in the unbound Ds decay are forbidden by energy and momentum conservation. In the bound case, the D8 can decay by annihilation into an off-shell pion or kaon, which then scatters on shell by exchanging momentum with the spectator proton. There may be an appreciable suppression here because of the high momentum transfer required. 4. COLOR-SPACE CORRELATIONS AT THE WAVE FUNCTION TAIL The searches for the pentaquark and for the H dibaryon are complicated by the inability of models to provide reliable theoretical estimates for experimentnl production. The important part of the multiquark wave function relevant, to production processes is the tail at large distances where the pentaquark wave function appears as a quark- antiquark cluster separated from a three-quark cluster or the H wave function appears as

- 7 two three-quark clusters and the distance between clusters is larger than the mean size of each cluster. The standard bag or potential model wave functions used to calculate binding neglect color-space correlations which are important here. We now note the following factors: 1. The short range two-body correlations are dominated by the one-gluon exchange Coulomb-like potential. 2. The OGE Coulomb potential between a quark and an antiquark is attractive in the color singlet state and repulsive in the color octet, 3. The coulomb energy will be much lower for the two-cluster system if both clusters are coupled to color singlets rather than to color octets. Thus the two-cluster tail of the wave function can be expected to have a different color structure from the central part of the wave function, and be dominated by color singlet clusters. The so-called "hidden color" components with clusters that are not color singlets can be expected to be strongly suppressed by these correlations over what is obtained from any fractional parentage expansion of the uncorrelated central part of the wave function. For an estimate we note that the standard color exchange OGE coulomb interaction can be written as

Vfcoui = w5^AI--AJ-/ry (4.1) where v is a strength parameter, A; denotes the color SU(3) generator for the i — th quark or antiquark and r,,- is the distance between particles i and j. We now assume that we have an overall color singlet state consisting of two clusters, denoted by a and b and that the expectation value (l/rij) is 1/r within each cluster and is 1/fi for any pair in different clusters. Then

vcoui = v Y, \t • \j/r+«£][>• h • (\ -}) = i>; ica jeb

= « £> • Xj/r + vAa • A;, • (i - i) (4.2a) i>j where A0 and A4 are the sums of the A operators within each cluster. This can be written in terms of the SU(3) casimir operators C(q) for the SU(3) quark triplet and C(a) = C(b) for the clusters a and b.

nvC(q) „, , (\ 1 \ Since C(g) = 16/3 and C(a) = 0 for a color singlet and 12 for a color octet, we obtain

Vcout(ociei ~ octet) — Vcoudsinglet — singlet) =

= IVCoUl{rnes

KCou,(m«on) = _!!£fo) (4.34) r is the color-electric energy of the two-body color singlet state (the meson) obtained from the first term on the right hand side of eq. (4.2b) by jetting n=2. Thus the additional color-electric energy required to introduce "hidden color" is of the order of ti;e color coulomb energy of a meson, which is appreciable. One can therefore expect these hidden color configurations to be suppressed. ACKNOWLEDGEMENT Discussions with D. Ashery, J. Lichtenstadt, J. Miller and S. Nussinov are gratefully acknowledged.

- 9 - References

1. Jechiel Lichtenstadt, these proceedings 2. Harry J. Lipkin, in Hadrons, Quarks and Gluons, Proceedings of the Hadronic Ses­ sion of the XXIInd Rencontre de Moriond, Edited by J. Tran Thanh Van, Editions Frontieres, Gif Sur Yvette - France (1987), p.691

3. Harry J. Lipkin, Phys. Lett. 195B, (1987) 484

4. C. Gignoux, B. Silvestre-Brac and J. M. Richard, Phys. Lett. B193 (1987) 323

5. Harry J. Lipkin, In Proceedings of the International Symposium on The Production and Decay of Heavy Flavors, Stanford (1987) Edited by Elliott D. Bloom and Alfred Fridman, Annals of the New York Academy of Sciences, Vol. 535 (1988) p.438

6. R. L. Jaffe, Phys. Rev. Lett. 38 (1977) 195

7. Harry J. Lipkin, in Hadron '87, Proceedings of the Second International Confer­ ence on Hadron Spectroscopy, KEK Tsukuba, Japan, edited by Y. Oyanagi, K. Takamatsu and T.Tsuru, KEK Report 87-7 (1987), p.363

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