Nucleon-antinucleon annihilation into two pseudoscalar mesons: quark rearrangement versus quark annihilation

Nuclear Physics B244 (1984) 349-358 ~'. North-Holland Publishing Company

NUCLEON-ANTINUCLEON ANNIHILATION INTO TWO PSEUDOSCALAR MESONS: QUARK REARRANGEMENT VERSUS QUARK ANNIHILATION Carl B. DOVER" Dtt'tsion ~h" Physique Thf'orique* *. lnstitut de Pttt'.~tqlw .¥uclbatre. ~1406 ()twa i ('c¢h'x. l)am e

Pat, I M. FISHBANE*'* Dtrision de Ptosique Fhborique**. lnstttut de Pl¢v.~iqlw Nucl&ure. ~)140o Orsav ('e~h' ~. France PhlVSic~"Deparmlent t, Unit'er~iO" of Virginia ('harh~tte.wtlle. ILq 22~)01. US,! Received 15 FcbruaD 1984 (Revised 28 May 1984)

We investigate the interference between planar and rearrangement mechanism,,, in the quark model for two pseudo.scalar annihilation modes of the N ~ .,,',stem. Both mechanism: seem to be n c c c s s a ~ even to partially undcrsland the data.

Nucleon-antinucleon (NN) annihilation, even at threshold, is intrinsically a short-range process involving significant overlap of the N and N. One therefore expects that quark degrees of freedom play here a crucial role, and that consideration of the symmetries and dynamics of quarks will yield a more fundamental understanding of such processes than a conventional picture expressed in terms of hadron degrees of freedom (baryon exchange for N ~ annihilation, for example). Several theoretical approaches to N N annihilation based on the quark model already exist in the literature. In the 1960's, three-meson modes N N - - , M~M2M 3 were discussed in the context of a pure SU(6) quark rearrangement model [1 ]. Later, more phenomenological flexibility was allowed [2] (initial state distortion factors and meson coupling constants), and a global fit to all three meson branching ratios was obtained. This was interpreted [2] as support for the dominance of pure rearrange-

-

-

-

_

_

* On leavc from Brookhavcn National LaboratoD', Upton. New York: supported in part by the US l)cpartmcnt of Energy under contract number DE-AC02-76Ctt(~}016 ** l.aboratoire Associ6 au CNRS. ***Supported in part by the US National Science Foundation under grant number PHY-8100257.

~ Permanent address. 349

350

C.B. Douer, P.M. Fishhane / N~ annihilation

ment processes. However, in ref. [3], an alternative model was discussed in terms of creation and annihilation of quark pairs. There has also been some discussion of two-meson annihilation modes in the quark model [4,5]. For instance, Genz [4] concludes that planar graphs (no crossing of quark lines) dominate rearrangement processes (one crossing), a conclusion which we dispute below. In a conventional -baryon exchange picture, a reasonable phenomenological description of the NN --) M~M 2 modes has been achieved [6], at the expense of a number of assumptions on coupling constants, form factors, etc. An important lesson of this work is that initial state distortion effects (primarily absorption into channels other than two mesons) are extremely important, reducing the Born approximation (BA) estimates by two orders of magnitude. These effects have significant dependence on the spin-isospin -{ S, I } of the N N pair, and illustrate the danger of comparing even ratios of squared transition amplitudes ITNR_M.M2[ 2 in BA (i.e. obtained from counting quark graphs) to ratios of observed cross sections for different { S, I }. In the present paper, as much as possible, we emphasize ratios of cross sections for the same initial -{ L, S, I }, where L = initial NN orbital angular momentum, in order to obtain more reliable tests of the quark annihilation mechanism itself. An extensive review of microscopic approaches to N ~ annihilation has recently appeared [7]. -The two-meson annihilation modes NN --, M~M 2, where M~ and M 2 and both pseudoscalars (~r,r/,,/',K,~), offer a particularly attractive case for the study of interference effects between different annihilation mechanisms, because of the quan-turn number selection rules which prevail. Working near the NN threshold renders the theoretical task simpler, since particular partial waves (S or P or both) are singled out, as shown in table 1. -On the quark level, the process NN -", MxM 2 can occur in a variety of ways, as depicted in fig. 1. We focus our attention on the "rearrangement" (R) and "planar" (P) diagrams of figs. la and b. The most crucial assumption in evaluating an -N N --, MxM 2 transition amplitude from the graphs of fig. 1 concerns the nature of the QO annihilation and creation vertices (the "dots"). In principle, these vertices are determined by the lagrangian of quantum chromodynamics (QCD). However,

TABLE 1 Selection rules for two pscudoscalar annihilation modes of the p~ system in L = 0, 1 states

Channel MIM 2 ,'~ * '~I"

wowo,)))),)1)),,)),~, ~0~,

~0~,

K 4 KKsKt. KsKs, KtK t.

Allowed p~)state -"¢-1.2s- ILj 33 S I , 13 I:)0. 2

~3F().2 ~3 P o , 2

~S~,3~S>13Po.2,33Po.2 13S1,33S 1

t 3Po.>33Po,2

C.B, Do~er, P.M. Fishbane / N~ anmhtlation

(a)

(b)

(c)

(d)

351

Fig. 1. Quark graphs contributing to the annihilation process N,q - , M~ M 2. Graph (a) is referred to as ""rearrangement'" and graph (b) as "' planar" (no crossing of quark lines) in thc text. Graph (c) combines somc featurcs of (a), i.e. one crossing of quark lines, and (b), i.e. three quark-antiquark (QUa) annihilation verticcs (indicated by dots). Graph (d) corresponds to the cxchange of a Q~i~ system, and is neglected here (as are disconnected diagrams). Graph (c) has the same spin structure as (a) and can bc considcrcd to bc lumped together phenomcnologically with the latter. Graphs with zero or two Q ~ vertices do not contribute to the process N ~ ~ M~M 2. but rather to the Ngl ~ M~M_~M 3 channels.

near the N ~ threshold, these vertices are "soft", and therefore the applicability of perturbative QCD techniques is unclear. Here we make the simplest assumption, namely that the Q 0 vertex is flavor independent, possesses the quantum numbers of the vacuum (~3P0 in LS coupling), and occurs with some phenomenological vertex strength 3'. The annihilation and creation of Q 0 pairs is thus assumed to proceed without changing the spin, isospin or momentum of the other quark lines, which are taken to be true spectators. If other quantum numbers are assumed for the effective vertices (for instance 13S1 as in the most naive one gluon exchange picture), the spectator assumption would not be consistent (spin flip of quark lines would have to be included). This "3P0 model" has enjoyed considerable phenomenological success in the description of meson and baryon decays [8]. (Early applications of the 3Po model are due to Micu in ref. [8].) Decay widths, phases and polarizations are accounted for in terms of a universal value of y ([9], see fig. 2 for a collection of "y values for different decays). This remarkable success must be tempered by the fact that, in the available meson and baryon decays, selection rules severely limit the quantum numbers of the QO vertex: in decays, an 3S1 vertex is not allowed, unless the effective operator allows for spin-flip and non-zero momentum transfer, while in NN annihilation various combinations of S- and P-wave vertices are allowed at threshold. For instance in fig. lb, the vertex patterns (left to right) SSP or PPP both yield an N ~ ~ M~M 2 transition from L = 0 to l = 1 (l = orbital angular momentum -

-

C B. Dm,er, P.M. Ft~hhane / N ~ atmihilation

352

in final state; if n~ and n 2 are pseudoscalars, we have AL = IL - II = 1 from parity conservation). If we allow S-vertices, additional amplitudes are introduced for the planar graphs of fig. lb. Here we adopt the vertex pattern PPP and record the resulting predictions. Later, when better data become available from the low-energy antiproton ring (LEAR) facility at CERN, one may be forced to introduce an effective S-wave Q ~ vertex as well. Note that the rearrangement graph (fig. la) does not contribute to the L = 0 to 1 = 1 transition but only to the L = 1 to 1 = 0 reaction (for a P vertex). An S-wave vertex producing no momentum transfer q to a "spectator" quark only gives L = 0 to / = 0 , violating parity conservation for N ~ --, PS + PS. To obtain an L = 0 to l = 1 transition, an operator S . (o, × q,) is required, where S is the spin of the Q ~ pair and i labels another quark, but this goes beyond the pure "spectator" model considered here. In the absence of such a "non-spectator" 3S~ vertex, ratios of L = 0 cross sections ( p~ --, ~r ~~r , K ~ K ) onl.v test the planar graphs, while for L = 1 (p~)~ two neutral PS) one can sec the interference between planar and rearrangement graphs. Our calculation now proceeds as follows: we first write down the T-matrix elements for the rearrangement and planar graphs, which are of the form ( M , M , _ iTr~lpp ) = ~ - . ~ E ( _ ) . , . ]

(¢) u :4) M., 1%e~ 04,,.~.,,, ) 1 .... R

(1)

DZ

for fig. la and ~-

3

= ( ' ( ~ Y)

( - )0,-,,,', ,,,.... , (~M,q,M.,q,,,2~f'I~pq~q~,,~"~,.~"')l,ti.,,..,,..,

E I ) t O l ~ O | ~"

(2) for fig. lb, where we have used the fact that the L S coupling coefficient for the 3Po 7 ( - ) .... t . The vacuum has the spin-flavor structure vertices is ( l m l - ml00 ) = V.'-i"' 0,.~

=

X" =

¢'T-~ x"' ( u~ + d d + si)

,

TT

m=l

.,q-_ t ~,2~T,l,+ ST)

m=O

,1, ,1,

m=

t

(3) -1,

i.e., the product of an SU(3) flavor singlet and an S = 1 wave function of z-component m. The color recoupling factor is implicitly included in 7. The quantities I,,R, and 1t rPL or/'. ~1,1" are overlap integrals of the p, ~, M~ and M~- wave functions with factors of e,,-Y~,,,(kq-kq) for each 3Po vertex (kq + k q = 0 is assumed). In a particular model, for instance the harmonic oscillator, one could evaluate the

C.B. Dover, P.M. l-Tshhane / N.~ annihilation

353

integrals I r~ and I t" explicitly. While --this is appropriate for decays [8], where the momentum release is limited, the NN--, M~M~ case generally involves a large m o m e n t u m q (of order of m N) in the final state, even when the initial momentum k is small. Thus I ~ and I t" may exhibit considerable sensitivity to the choice of wave functions. We leave I ~ and I t" as parameters, and emphasize qualitative features which are independent of their values. Note that for SU(6) wave functions, eqs. (1) and (2) involve the coupling of spin and orbital angular momentum, so that the amplitudes for N ~ ~ M~M~ do not factorize into a product of spin, flavor and orbital matrix elements, as has sometimes been assumed *. For any choice of m-values, one can easily enumerate all spin-flavor labellings of the graphs in fig. 1. Using standard SU(6) wave functions *~' for the N, ~ and mesons, one obtains weight factors for planar and rearrangement graphs, after projection onto each channel M~ M~. For the ~/and r/' mesons, we use the wave functions [11]

,> = ½[lu#> + IdaT> -T- v~ls~>],

(4)

a form which is consistent with the usual pseudoscalar mixing angle -11 °. In our work we sample only the non-strange components. As mentioned above, the rearrangement graph (fig. la) with a 3P0 vertex does not contribute to the L = 0 to l = 1 transitions. For these cases, we thus test the validity of SU(6) recoupling for planar graphs only, assuming that the graphs of fig. lc can be neglected. For example, defining a reduced cross section *** 6 = o/q 2~" ~, we predict Opl~__~K'K

%~,~,,',

-

= ~ ,

(5)

/=0 .

independent of the form of the overlap integrals 1 ~'. The simple result (5) reflects the * In rcf. [4] it is assumed that the matrix clement of N.~ ~ MIM 2 factorizes into spin and flavor terms. This is false, since the N and ~ wave functions in SU(6) do not factorize into a single product of spin and flavor parts, but rather arc sums of two such products (mixed symmetry), ttencc the conclusions of this paper on the dominance of planar graphs are invalidated. In ref. [3]. the transition pp (~S~) ---, ~" ' ,-r- is assumed to be forbidden, in analogy to the forbidden transition o --' ~r ' v in static" SU(6) (scc Close [10], eq. (6.8)). In reality, the spin and orbital matrix elements arc coupled, and hence static SU(6) is no longer thc relevant symmetry. For decays, as is wcll known [8], the 3Po model with m = 0 vertices is equivalent to the symmetry SU(61w rather than SU(6). In SU~,6) w, the transition p ~ ~--~r- is allowed, and hence the reaction p)( 33S l ) ~ ~'" rr- is also allowed. " * Note that the SU(6) wave functions of rcf. [2] have an incorrect sign of the C~Q ordering relative to the Q 0 part. This relative sign is fixed by the requirement of good G-parity, as discussed by Close [10]. " * * We use a phase space factor q2t~ l rather than q,..t, ~ as in ref. [4 I. Note that the use of such a threshold factor is not really justified, since q is large. However, the influence of this factor on ratios of reduced cross sections is modest, since / = 0 or 1 only. Although this prescription suffices for the present qualitative discussion, it should be replaced by one based on /R(q) and It,(q) at a later stage.

354

C.B. Dover, P.M. Fishbane / N ~ annihilation _

flavor independence of the QQ vertex after phase space is removed. Eq. (5) compares very favorably with the experimental value of about 7, ~ obtained by Bizzarri et al. [12]. (Note that by charge independence, we have equal cross sections for p~ -~ K" K and K°~°.) Note that the numerator in eq. (5) involves both I = 0, 1 while only I = 1 enters the denominator. This indicates that the isospin dependence due to initial state interactions does not produce qualitative changes in ratios of cross sections. For the L = 1 initial state, on the other hand, the rearrangement and planar graphs both contribute to the ~-+~r- channel, while only the planar graph produces K" K -, since the s~ pair must be created in the final state. We then find

°pl~"'"-

I1 ÷

IOx/yzl

2 ,

(6)

where x = i R / ] ~" (see eqs. (10) and (11)) is the ratio of overlap integrals 1 (color -factors included), after a "penalty factor" ~/~ "¢ for each Q ~ vertex has been ,/~ q,qremoved ~, ~ for flavor, ~/~ for spin, ~,~ from LS coupling). If ]x/y~l is of order unity, we see that the ratio (6) is suppressed by two orders of magnitude relative to eq. (5). Such a suppression has indeed been claimed experimentally by Bizzarri et al., who find [12] Op~ ~ K * K

_

%~ -~~ ,, --

= 10 -2 .

(7)

l.=l

The important contribution of the rearrangement graph of fig. la for ~r ~~r- provides a natural dynamical mechanism for this suppression. Note that if the rearrangement graph is neglected, the ratio of K + K - to ~r~~r- production is equal to ~-, independent of L, in qualitative disagreement with experiment. A large rearrangement process for the ~r~r channel also helps to explain a long-standing anomaly relating to sizable odd-L contributions to ~r 4~r in "at rest" experiments (a "precocious P-wave"). Devons et al. [13] give

Io d

= 0.4,

(8)

O'-p]~ ~ ~ . ~,- I c v e n L

from charge independence [Op~,_~..~,-I,,~o t.=26p~,,,, ,,] and a measurement of ~ p - , ~ r % °. Bassompierre et al. [14] cite a smaller value 0.12, but the recent experiment of Backenstoss et al. [15] (in quoting the p) branching ratio, these authors assume that the r/'0/cr%l ratio is ~, but only the sum of ~r°rt and rtr~ channels is measured experimentally) is consistent with eq. (8). Dris [16] has analyzed the "in-flight" data on p) -, ~r% ° at low momentum, and found a ratio

C.B. Dover, P.M. Fishbane / N~Vannihilation

355

consistent with eq. (8), with the 13P0 wave dominating 13p2.. The large deviation of eq. (8) from the naive "S-wave dominance" that one might expect at threshold can be understood as a combination of two effects: (a) a particularly deep and attractive real p~ potential in the 13P0 channel, arising from coherent central, quadratic spin-orbit and tensor terms from t-channel meson exchanges [17], and (b) a transition potential for p~ --, ~rrr which is also large in the t3P0 channel (compared to L = 0) due to the importance of the rearrangement process. As noted by Green et al. [18], the t3p0 QO vertex in fig. la is reflected in a maximal contribution to the 13P0 channel of the overall p) system. This viewpoint is also supported by a consideration of the ratio [19] O'-pl~ ~

KsKs+

KtKt.[odd

L

= 2 × 10 -2

(9)

O-pp ~ K,.Ksleven L

at rest, which is fully consistent with S-wave dominance. For strange particle final states the rearrangement graph is absent, so that there is no mechanism for a "precocious P-wave" in the ratio (9). Let us now consider other pseudoscalar modes, involving r/and r( mesons. Here the pattern of interference between planar and rearrangement graphs is different -from that for ~r~r or KK, so we obtain new information. Starting with initial spin configurations p'l'p $ and p ~'p ~" (which are added coherently) we can write down the amplitudes for each choice of m indices in eqs, (1) and (2). This gives rise to P eight distinct overlap integrals I.,.,,.,,, for planar graphs (we use here only the P _ P symmetries I,..,,.,,,- I,,,,,~,... and I.P,,.,,.,, = 1 -Pm . • m ' , -. m " ' which are independent of the choice of wave functions). For rearrangement graphs, there are two integrals I~ and I~R, but since these appear in the same linear combination in each PS + PS channel, we have only one effective phenomenological quantity denoted as 1 R. Defining two ratios x and y of rearrangement-to-planar amplitudes by x = iR/i,

y = ]~//rep,

(10)

where -

~~

-~~

]~

~

I~P=-]o~-±[~ -L~.o +~ll.o.i+~I~.o,o-~lo,o.-1 + 3 -1.1, "1 + ~l~lt, ]" ] .~ I ~ )~- - 3

~

-1,1,0

--~"

~ 5 ~ 4 ~ 1~I~,0,~--~I~,0.0--~I0.0. ~+71 L~,-~--~l~,

(11)

* In using a phase space factor q for L = 1 transitions, we in fact as.,,umc that the 3Po channel dominates other pseudoscalar channels as well (i.e. / = 0 rather than 1 = 2 as for 3P 2 ).

C.B. Dover. P.M. Fishhane / N.~ amtthilatum

356

we obtain*

O-pp .. ,,~ _ 1 ~pp_,,%.

1-

6x/g 2 2,

4 1-710~

#op-=% _ { z

1 +6y/'~

~

2 2,

iglOO7-,

(12)

where z = ( ] y / ~ ) 2 = (x/y)2. Since the non-strange parts of the rt and ~' wave functions are identical, the same results hold for ~' channels: for instance ~op-~ ~"0' = Op~.~,o,, etc. T h e rtr//~'% "° ratio is measured to be about ~ at threshold (see ref. [14]). of order ~ at 1.2 G e V / c and unity at 1.8 G e V / c [20]. For x/y: = - 1 , consistent with a 10 -2 suppression in eq. (6), we would obtain a ~rt/~r°~r ° ratio of ~ from eq. (12). Note that for x = 0 (no rearrangement), we would obtain a ratio of ~. Either value of x is p r o b a b l y consistent with this data. Thus it is important to measure the ~rt/~r%r ° ratio precisely near threshold, in order to obtain another constraint on x. This is a task for L E A R . Note that both rt'O and ~r%r° come from the same ~3P0.2 p~ state, so the effects of initial state interactions on their ratio are minimized. T o understand the ~r°r//~r%r ° ratio is m o r e delicate, since there exist two independent ratios x and y. Moreover, here we are c o m p a r i n g states of different isospin, so that initial state interactions could appreciably change the ratio. There is some limited data on the ratio:

_

( 0.4

R -= -°vr'~""n ~ 1 15 op~ ~ ,,o,,o 1

" a t rest" [21]** " a t rest" [15] Pl~b = 1.2-1.8 G e V / c [20].

(13)

T h e available experimental results for R " a t rest" differ by almost a factor of 40! It is clearly i m p o r t a n t to remeasure R at LEAR. One might be tempted to explain any energy dependence in R, if it exists, by invoking an L = S = 1 = 1 " b a r y o n i u m " state near the N N threshold, but such an object would also tend to make the ratio (6) large, in contrast to experiment, unless it is magically decoupled from the K * K channel. -

-

* Care is required in order to respect the requirements of Bose-Einstein statistics. If we treat identical particles ( w % o or rlrl, for instance) as distinguishable, and draw quark graphs with two orderings, say p~ ~ ~r°(1)~r°(2) or ~,°(2)'n'°(1). we must divide 6 by 2 at thc end. *~' These results for the ratio ~'°'~/~r%r ° and rl~O/~%r ° are contained in [22].

C.B. Do~,er, P.M. Fishhane / N~ annihilation

357

From eq. (12), one finds

R=

{~ ~z

(rearrangement only) (planar only).

(14)

It is then clear that the model with rearrangement graphs alone is in disagreement with experiment. In the planar limit the ratio depends strongly on both the relative ~p phases* and magnitudes of the overlap integrals 1,,,,,,,,... With seven independent amplitudes it is clear that it is possible to fit the ratio (13), but a very delicate ~p cancellation of the combination of I,,,,~.,,,, appearing in I~~, so that z is large, is required to obtain a large value of B. The simplest assumption, namely that the overlap integrals ],,,c,,z" are all the same order of magnitude, gives z of order 1. Thus both planar and rearrangement limits tend to give R << 1. A large value of R would represent a genuine puzzle for the simple type of quark model considered here. Note in passing that if we had restricted our attention to m = m ' = m" = 0 only, we obtain again z = 1. The m 4:0 vertices are known to be important in decays: m = 5-1 is necessary to obtain a non-zero decay rate for B --, ~ with a polarized B-meson [81. If we now introduce the effects of planar-rearrangement interference, we tend to diminish the ~r°r//~r°rr ° ratio, since I1 + lOx/yZl 2 must be large in order to understand the suppression of the K ' K /~r'~r- ratio for L = 1, as in eq. (6). Another possibility presents itself, outside the context of this model. The transition N ~ --, N~ will be very strong, due to the coherent effect of ~r and O exchange [18]. and the resulting N3, configuration feeds only the I = 1, i.e. ~.o~, channel. In this way R could be enhanced. Within the context of our model, i.e. fig. 1, it appears that there is no natural way to make both the ~'°r//~r°~r° and t~"o~.o-.,o.,O./r,, r,, ~ . ~ ratios large. In summary, the branching ratios for N ~ annihilation into two pseudoscalar mesons are very revealing of interference effects between planar and rearrangement mechanisms in the quark model. We would like to thank members of the lnstitut de Physique Nucl6aire at Orsay for their hospitality during our visits, and to acknowledge useful discussions with J.M. Richard, R. Vinh Mau, as well as members of the Orsay particle theory group (A. Le Yaouanc, L. Oliver, O. P6ne and J.C. Raynal) on aspects of the ~P0 model. References 11] H. Rubinstein and H. Stern, Phys. Lett. 21 (1966) 447; J. Harte. R. Socolow and J. van dcr Mculen. Nuovo C i m 49 (1967) 555

* Indeed the relative phase of terms of this general type play,', a crucial role in the case of meson or baD'on decay vertices [8]. where it has its origin in the coupling of intrinsic spin and orbital motion. The inclusion of recoil effects breaks the static SU(6) symmetry in which the matrix element in question (in our case N ~ ~ M~ M 2) factorizes into a spin-flavor and an orbital part.

358

C.B. Dot,er, P.M. Fishbane / N~ anmhilation

[2] M. Maruyama and T. Ueda, Nucl. Phys. A364 (1981) 297; Phys. Lett. 124B (1983) 121: M. Maruyama, Prog. Theor. Phys. 69 (1983) 937 [3] S. Furui, A. Faessler and S.B. Khadkikar, T'obingen preprint (1983) [4] H. Genz, Phys. Rev. D28 (1983) 1094 [5] A.M. Green, J.A. Niskanen and S. Wycech, Helsinki preprint HU-TFT-83-63 (1983) [6] B. Moussallam, Nucl. Phys. A407 (1983) 413: thesis, University of Paris (1980) unpublished [7] A.M. Green and J.A. Niskanen, to appear in International review of nuclear physics, ed. T.T.S. Kuo, vol. II (World Scientific, Singapore, 1984) [8] A. Le Yaouanc, L. Oliver, O. Pene and J.C. Raynal, Phys. Rev. D8 (1973) 2223; D9 (1974) 1415: D l l (1975) 1272; M. Chaichian and R. KiSgerler, Ann. of Phys. 124 (1980) 61; G. Busetto and L. Oliver, Z. Phys. C20 (1983) 247; L. Micu, Nucl. Phys. B10 (1969) 521; R. Carlitz and M. Kislinger, Phys. Rev. D2 (1970) 336; E. Colglazier and J. Rosner, Nucl. Phys. B27 (1971) 349 [9] J.P. Ader, B. Bonnier and S. Sood, Nuovo Cim 68A (1982) 1 [10] F.E. Close, An introduction to quarks and partons (Academic Press, New York, 1979) table 4.2 [11] N. Isgur, Phys. Rev. 13 (1976) 122 [12] R. Bizzarri ct al., Nuovo Cim. B69 (1974) 307 [13] S. Devons et al., Phys. Rev. Lett. 27 (1971) 1614 [14] G. Bassompicrre et al., Proc. 4th European Antiproton Symp. Barr, Strasbourg, ed. A. Fridman, vol. I (CNRS, Paris, 1979) p. 139 [15] G. Backenstoss et al., Nucl. Phys. B228 (1983) 424 [16] M. Dris, in Proc. Fourth Int. Syrup. on ~ N Interactions, Syracu~, 1975, ed. T. Kalogeropoulos, vol. II, p. 21 [17] W.W. Buck, C.(i. Dover and J.M. Richard, Ann. of Phys. 121 (1979) 47 [18] A.M. Green, J. Niskanen and S. Wycech, Phys. Lett. in press [19] R. Armenteros et al., Phys. Lett. 17 (1965) 344; C. Baltay et al., Phys. Rev. Lett. 15 (1965) 532, 597 (E) [20] E. Eisenhandler and C. De Matzo et al., in Proc. 3rd Int. Symp. on Antinucleon-Nucleon interactions, Stockholm, July 1976, ed. G. Ekspong and S. Nilsson, (Pergamon, New York, 1977) pp. 91 and 139; R.S. Dulude et al., Phys. Left. 79B (1978) 329 [21] T. Kalogeropoulos, private communication [22] J. Skelly, thesis (1971) unpublished