ELS EV I ER

UCLEAR PHYSICS

Nuclear Physics B (Proc. Suppl.) 56A (1997) 303-310

PROCEEDINGS SUPPLEMENTS

Annihilation into Channels with Strangeness and the OZI Rule Violation

V.E. Markushin

Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

Two-step mechanisms in the N/~ r annihilation and their role in the OZI rule violating reactions are discussed. In particular the two meson rescattering mechanism for ~r~b channel including all off-shell effects is typically two orders of magnitude bigger than the OZI tree level expectation and explains the observed ratio t~Tr/wr in the annihilation at rest. The rates for the final states including photons, 7w and 7~b, can be explained in the vector dominance model. The observed rate for p/~ --~ 7w is suppressed due to destructive interference between the intermediate p and w states while the interference in pl~ -+ ~,~b is required to be constructive leading to a large ratio 7¢/7w.

1. I N T R O D U C T I O N

In the nucleon-antinucleon annihilation near threshold, the channels with strangeness con- tribute only a few percent [1], nevertheless, the corresponding reactions are of big importance be- cause they provide new information on reaction mechanisms, proton structure, and exotic states. Of special interest are the processes resulting in the violation of the Okubo-Zweig-Iizuka (OZI) rule [2-4]. The recent experiments at LEAR have been very successful in providing the data on this subject [5-18]. A characteristic feature of the low energy p/5 annihilation is an abundant production of the ~b mesons in some channels (¢r, ¢7, CP, ¢irTr, ¢w, ¢¢) which is expected to be OZI sup- presses on the tree level because the ~b is domi- nantly a gs configuration.

Because the OZI rule can be dynamically bro- ken, it is important to understand whether the effects observed in the p~6 annihilation can result from known mechanisms of the OZI violation.

Two-step processes with ordinary haxtrons as intermediate doorway states have been considered long ago and were shown to be important already in unitarity approximation (see [19] and refer- ences therein). In the case of N N annihilation two meson doorway mechanisms have been stud- ied for various final states containing ¢ mesons in pi6 and pd reactions which violate the OZI rule [20-27]. Another way of violating the OZI rule is production of flavor mixed or exotic (glueballs, hybrids) intermediate states, an approach which

0920-5632/97/$17.00 © 1997 Elsevier Science B.M All rights reserved. Pll: S0920-5632(97)00292-2

will not be discussed here. Furthermore, one can link the OZI rule violation to the nucleon struc- ture by introducing an intrinsic gs component as in [28] (see also [29] and references therein for further details).

The goal of this paper is to review recent the- oretical results concerning the evaluation of con- ventional two step mechanisms for p/~ -+ CX as an explanation of the OZI rule violation. 'New physics' should be introduced only if these expla- nations fail. For earlier reviews we refer to [30,31].

2. T H E OZI R U L E A N D F L A V O R M I X - I N G

The OZI rule [2-4] states that processes with disconnected quark lines in initial or final states are suppressed. For the heavy quarks (c, b, t) this suppression is a consequence of the asymptotic freedom of QCD because the coupling constant a,(q2) becomes small, therefore the creation of a quark-antiquark pair is a perturbative process. The case of strange quarks belongs to the non- perturbative domain and involves more compli- cated dynamics.

One reason for the OZI rule violation is the flavor mixing in ordinary (nonexotic) hadrons. In QCD with massless u, d, s quarks the hadrons would form SU(3) multiplets, with the OZI sup- pression mechanism being trivially avoided for the states which are a superposition of all pos- sible configurations. In reality the s quark is sig- nificantly heavier than the u and d quarks, and

304 EE. Markushin /Nuclear Physics B (Proc. Suppl.) 56A (1997) 303-310

the SU(3) symmetry is broken. In particular, the physical states w and ¢ are the superpositions of the SU(3) singlet w~ and octet ws states [2,32]:

\s in{3 cos19 J ( wi ) (1)

u f i + d d + s g w ~ ~ wx -- ~ -- q~-{- sg (2)

ws = q q - sg (3)

where q~ = (u~ + dd)/v~. The so called ideal mixing corresponds to a complete decoupling of the gs and ~q components:

Oi = arctan v / l / 2 = 35.3 ° ~ ¢ = sg (4) ¢ o - - - - q ~

The Gell-Mann-Okubo mass formula with octet-singlet mixing gives the mixing angle 19 ~, 390 [33]. The mixing angle can also be obtained from the partial widths of the w and ~b decays into e+e -

rw.,+e- . r¢-+e+e- - tan2 19 (5) M~ M~

leading to 19 = 37.1 °. Since 19 ¢ 19i the OZI forbidden processes in-

volving the ~ production can go via the sg - q{ mixing. The corresponding amplitudes are ex- pected to be proportional to the deviation from the ideal mixing (O - 19i) 2 .~ (1 - 4.2) • 10 -3 for O - 19i ~ 1.80 - 3.7% The OZI rule violation on the level of the flavor mixing is usually called nondramatic. Compared to the level given by the w - ~b mixing, the low energy pl0 annihilation into the "r~b, 7r~b, and ¢~ channels appears to be rather dramatic exceeding it by 1-2 orders of magnitude. This problem will be discussed in detail in the fol- lowing sections.

3. T H E OZI R U L E V I O L A T I O N IN T H E pfi A N N I H I L A T I O N I N T O T W O V E C - T O R M E S O N S

Table 1 shows the summary of the experimen- tal da ta on the pfi -+ 1- + 1- reactions at rest (the annihilation in liquid target predominantly occurs in the S-wave, in gaseous targets both the

Table 1 The experimental branching ratios for p~ annihi-

lation at rest into pw, ww, 7w, PC, we, 7~b, chan- nels.

Reaction BR p/~ ---} pw 5.4(6). 10 -2

3.0(7). 10 -2 6.4(11). IO 2.3(2)- 10 -2

p p ---+ 6060

pl6--r 7w

p~-~ PC

pr~ --r 7¢

3.32(34). 10 -~ 1.4(6). 10 -2

6.8(18) . 10 -5 3 .4 (8 ) -10-"

4.4(12). 10 -4 3.4(10). 10 -4 3.7(9). 10 -4 6.3(23). 10 -4 3.0(11)-10 -4 4.2(14). 10 -4 5.3(22)- 10 -4 2.9(14). 10 -4 1.7(4)-10 -5

Condition Ref. gas. [6]

s [6] P [6]

liq. [34] liq. [8] liq. [36] liq. [7] gas. [5]

gas. /LX [5] is0 [5] 3pj [5] liq. [35] gas. [5]

gas. /LX [5] is0 [5] 3ps [5]

liq. [11]

S and P waves contribute; the LX trigger in gas mainly corresponds to the P-wave annihilation).

The vector dominance model (VDM) can be used to connect the amplitude of the reaction pP --+ 7X with the amplitudes for p~ ---r pX and pfi -d, coX [37,21,7,8]. The final states of interest for the OZI rule violation correspond to X = ¢, w.

The VDM relation has the form (see Fig. 1)

7 ~ m p GT,o = 7¢v G ~ F ~ + --~--~-,_,~, o~ (6) 1712 m w

7w-t f , ~ ,

p

where the amplitudes Gab correspond to the final states ab and the coupling constants 7~p and 7 ~ are related by

2 e = 0.054m~ . (8) 7~p = 37~p = m p

The form-factors Fab (p~) describe the off-shell behavior of the p~ -+ ab ver- tex, they are normalized by the condition F~(rn~) = F~(m~) = F~,(m~) - Fp~,(m~) - 1.

V.E. Markushin/Nuclear Physics B (Proc. Suppl.) 56A (1997) 303 310 305

O) O~ CO

Figure 1. The ampli tudes of the reactions pj5 J r 7w and p~6 -} ~/¢ in the vector dominance model.

Since the final states have well defined C-par i ty C = +1, the allowed initial pi0 states are ZS 0 and 3p j . Our analysis will be focused on the S-wave annihilation, therefore only the 1S0 state contributes. The corresponding partial width is

r o b - c h P h 4~r (9)

where Pab is the CMS m o m e n t u m of the particles a and b in the final state.

From (6-9) and neglecting the mass difference of the w and p mesons the following result for the branching ratios is derived [37]

= (10)

~ ~ e ~ 2 ~

= (11)

. = Fp,+gVBR---ffO--~r.~¢e-- _ _ \ P . * ]

where /3x is the relative phase between the two terms corresponding to pX and wX intermediate states (X = ~, ¢).

3.1. R e a c t i o n pi6 -+ 7w Using the experimental branching ratios

BR(Vco)/BR(pw) = (2.3 + 1.1) • 10 -3 and BR(ww)/BR(pw) = 1.1 =t: 0.3 [6-8] one gets

+ (0 .49± I -- 0 .49±0 .13 (12)

I f F ~ o ~ F ~ ~ 1, then j3~ ~ r , i.e. there is a destructive interference between the p and w intermediate states with isospin I = 1, 0 in the total ampli tude of the reaction pl~ "-} 7w. The result of the analysis by the Crystal Barrel Col- laboration [7] obtained with a model formfactor [38] is cos#~ = -0 .60 + 0.18.

3.2. R e a c t i o n p/3 -+ 7¢ Using the experimental branch-

ing ratios BR(7¢) /BR(p¢) = 0.05 =t: 0.025 and SR(w~b)/BR(p¢) = 1.6 -I- 1.1 [5,11] one gets

I = 1 .1+0 .3 (13)

If Fp¢ ~, F~0¢ ~, 1, then the data can be explained by a constructive interference between the p and ¢0 terms. The effect of the formfactor in this case can be more significant than for the 7w final s tate because of a larger difference in the final mo- menta: Pp~ = 0.28 GeV/c and P~¢ = 0.66 GeV/c (compare with the case p/5 --+ pw,Tw : P~0 = 0.53 GeV/c and Pw~o-- 0.78 GeV/c) .

The analysis done in [8] arrived at the conclu- sion that the VDM prediction is too small to de- scribe the experimental data. This conclusion, however, strongly depends on the model formfac- tot [38]. If we use the following formfactor

A2 + P;~ (14) Fp¢(p~) - A2 + p2(p~)

where P(p~) is the CMS m o m e n t u m of the par- ticles in the final state, and a similar one for the we vertex, than for A = 1 GeV/c the suppression factor is Fp~(0) = 0.75 and the VDM relation (13) holds true for cos /~ ~ 1.

Thus the relative phases of the intermediate terms I = 0, 1 for the two reactions pp --} 7w, "y¢ are different, and this agrees with the observation that w - ¢ mixing cannot be the dominant mech- anism of the ¢ production. Indeed, the OZI rule violation in the Cw and Cp channels, given by the ratios BR(f)w)/BR(ww) ~ SR(¢p) /BR(wp) ,~ 10 -2 , seems to exceed the level expected from the deviation from the ideal mixing, 1 ( e - e i ) 2 0.4. lO -2, but is not dramatic . Thus a seemingly

I T h e e s t i m a t i o n can vary if the f inal s t a t e phase space fac tor is t aken into accoun t .

306 I4E. Markushin/Nuclear Physics B (Proc. Suppl.) 56A (1997) 303-310

drastic violation of the OZI rule observed in the ratio BR(7¢)/BR(Tw) = 0.24 =t: 0.09 [7,11,12] re- sults from partial cancellation of the two terms I = 0, 1 for the 7w channel and the constructive interference between the intermediate states for the 7~b channel. Therefore the core problem lies in the explanation of the p~ -+ pC and p/~ -+ we reactions which will be discussed in Sec. 7.

4. T W O - S T E P M E C H A N I S M AS D Y - N A M I C A L B R E A K I N G O F T H E O Z I R U L E

Reactions which are OZI forbidden in a tree approximat ion can proceed via two-step mecha- nisms without a violation of the OZI rule at the individual steps [19,39-41]. Before discussing this mechanism in the p/5 annihilation we briefly illu- minate it by the example of the ¢ -~ pTr decay.

4.1. T h e O Z I r u l e v i o l a t i o n ¢ --+ prr d e c a y The width of the ¢ --4 prr decay due to the w - ¢

mixing is given by the est imate

.2 p3 r , ~ _ ~ p . ~ ( o - o , ) 2 ~ p " ~ - ~ " ~ 0.16 MeV (15)

12~r

where g ~ . / 4 ~ = 20.6 GeV -2 [42] and P ~ _ . . is the CMS m o m e n t u m of the particles in the fi- nal state. This is significantly smaller than the experimental value l~¢_~p. = 0.57 MeV. The lat- ter can be explained by the two step mechanism ¢ -+ K/~" --+ plr [45,46].

u,d

¢ K** : s

u,d

All the vertices are OZI allowed in this two step

process. A simple est imate of the ampli tude can be obtained in the unitari ty approximation when

the intermediate particles K /~ are on the mass shell. It gives the imaginary par t of the ampli tude which is of the right order of magni tude, but for a quant i ta t ive agreement the real par t is essential, and the full calculation of the h~dronic loops is needed [45,46].

4.2. Lipkln cancellations in hadronic loops Since two-step (one-loop) mechanisms tend to

be large, one faces the problem of avoiding too large corrections to the OZI rule [19,39-41,43,44]. It turns out that cancellations between various in- termediate states can suppress the two step cor- rections in some cases.

The effect of cancellations for the mass op- erator in the meson nonets is demonstra ted in Table 2 showing the relative sign of the vari- ous kaonic intermediate states contributing to the real part of the mixing ampli tude in different JPC channels [44]. Nearly perfect cancellation between the K K , K*/~, K/~*, K*/ (* terms ex- plains a small deviation from the ideal mixing for jPC = 1 - - , 2 ++ , 3 - - mesons, while no cancella- tion occurs in the scalar sector where the mixing is known to be large.

Table 2 The relative sign of various intermediate states

in the hadronic loop contr ibuting to the q q - sg mixing [44] and the corresponding deviation from the ideal mixing (0 - e i ) (deg).

j/-'G"

1 - - 2++ 3---- 1 + - 1++ 0 - + 0++

K K KK* K ' K K ' K * O - O i

+ - - + 0.7 - 3.4 + - - + 7 - 9 + - - + 6 - 7 0 - - + ,-, 18 0 - - + ,-, 26 0 - - + 45 - 58 + 0 0 + ,~ 36

A special case is the mass region above one and only one OZI allowed channel threshold. In this case the corresponding loop has an imaginary part which cannot be canceled by other terms. Therefore, with a sufficiently strong coupling to a single OZI allowed channel, dynamical breaking of the OZI rule can occur. The decay ~b --~ prr is a

EE. Markushin/Nuclear Physics B (Proc. Suppl.) 56A (1997) 303-310 307

pb K

(a)

0.8

~0 0.4

p ' K ~ 0.2

(b) 0

Figure 2. Two-step mechanisms in p/~ -+ ¢ + X.

~IB S" 2.0 . (a)

/ .

/ Im

"X.~Re -0.2 0"0:2 0:4 0:6 0:8 ; i.2

K [ G e V / c ]

particular example of this effect. In the following section we consider how the two-step mechanism works in the case of pi6 annihilation.

5. T W O M E S O N D O O R W A Y R E S C A T - T E R I N G M E C H A N I S M IN p/~ -+ ¢7r

The OZI rule violation in the p/~ -+ ¢7r at rest is rather strong: B R ( p p ~ ¢Tr ) /BR(pp ~ oa~r) = 0.0964-0.015 [8,11,12]. The two-step mechanisms in pi6 -+ ¢ + X were studied in [21-25,27]. The most important intermediate states are KI~* - K ' [ ¢ and pp, since they provide the maximum combined strength of the vertex functions (Fig.2). In the pp case the strong annihilation step [47] (a hundred times bigger than the 7r¢ branching ratio) is followed by the strong pzrlr vertex and the CpTr vertex of moderate strength. In the K/~* case the annihilation step is a factor of 10 weaker [48], but it is followed by maximum strength for the remaining vertices in the second step.

The scalar invariant amplitude has the form (see [27] for details)

+oo G(s) = i / K d K A ( K , s ) F ~ (16)

Et(K) (EIu---EI(I£-) + ie)' 0

where A ( K , s ) is the spectral density shown in Fig.3 and F~ is the form-factor describing the

• -, 1.2

~__o.g

< 0.6 1 o .-- 0.3

-0.3

• ( b )

Re

_0.60 . . . . . . . . . . . . . . . . . . . . . . . 0.2 0.4 0.6 0.8 1 1.2

K [ G e V / c ]

Figure 3. The spectral density A ( K , s) at thresh- old, s = 4m~, vs. momentum K: (a) the K ' K - case, (b) the pp-case. The unitarity approxima- tion amplitude To = A ( K v , s) is marked by the full dots. The two curves for the imaginary part plotted in (a) correspond to different values of the form-factor parameter Ab (indicated in units of GeV) describing the t-channel exchange in the second step [27]. The dotted lines in (b) corre- spond to a Breit-Wigner propagator for the p me- s o n .

308 VE. Markushin/Nuclear Physics B (Proc. Suppl.) 56A (1997) 303-310

Table 3 Branching ratio for pfi(aS1) ~ ¢~r ° in the unitari ty approximat ion (UA) and with the off-mass shell

effects taken into account (l-loop) in comparison with experiment [11]. The form-factor parameters A= and Ab [27] are in GeV.

Theory

UA Ab = oo Ab = 1.2

l- loop Aa = 1.5, Ab = 1.2 Aa = 2.0, Ab = 1.2 Aa = 2.0, Ab = 1.5

K * K 3.0 x 10 -4

0.63 x 10 -4 0.55 x 10 -4 0.69 x 10 -4 1.59 x 10 -4

Two step mechanism

PP 2.0 x 10 -4

0.33 x 10 -4 0.53 x 10 -4 0.53 X 10 -4 0.85 x 10 -4

incoherent 5.0 x 10 -4

0.96 x 10 -4 1.09 x 10 -4 1.22 x 10 -4 2.44 x 10 -4

Crystal Barrel Collab. (5.5 4-0.7) x 10 -4

m a x i m u m 9.9 x 10 -4 1.87 x 10 -4 2.16 x 10 -4 2.40 x 10 -4 4.60 x 10 -4

combined off-mass-shell effects for the interme- diate state.

The results of the one loop calculations are compared with the unitari ty approximation and the experimental da ta in Table 3. The relative sign of the Kff,* and pp terms is not known. In the case of constructive interference the two step mechanism is in a good agreement with the data. Lipkin cancellations are not likely for this reac- tion [27].

Apar t from annihilation at threshold the en- ergy dependence carries potentially important in- formation on the OZI rule violation. The en- ergy dependence of the two step mechanism for p f -+ Czr has been est imated in [24]. The pre- dictive power in this case suffers from too many unknown parameters.

6. T W O M E S O N R E S C A T T E R I N G M E C H A N I S M IN pfi -~ ¢¢

This reaction was studied in [20] in the uni- tari ty approximation. The most impor tant inter- mediate state is K/-~ (Fig.4) for it has the maxi- m u m coupling to the final state. Notice that the ¢¢ production via the w - ¢ mixing is strongly suppressed: a p ~ , ~ . . , ¢ ¢ / ~ p ~ , ~ --- (O - Oi) 4 "~ 10 -5 . The calculations of the two-step mecha- nism have correct magni tude in comparison with the experiment [15] as shown in Fig.5. More da ta concerning the energy dependence of the ¢¢ pro- duction would be very helpful for a further test of the mechanism considered.

Figure 4. The K/~ rescattering mechanism in pp--+ ~¢

, . - - 2.5 :d . v 2

1.5

1

0.5

0 ' ' ' ' 1 ' ' ' ' 1 . . . . I . . . .

2.1 2.2 2.3 2.4 2.5

EcM s (GeV)

Figure 5. The energy dependence of the pfi --+ ~bff cross section calculated for the two step mecha- nism shown in Fig.4 [20]. Experimental da ta from [15].

V.E. Markushin/Nuclear Physics B (Proc. Suppl.) 56A (1997) 303 310 309

Table 4 The relative probabilities for the ~bp, w p and

¢~r+Ir-,wTr+~r - channels in the p16 annihilation vs. antiproton momentum (in units 10-3).

p~(GeV/c) o (gas) 0 (gas/LX) 0 (liq.) 0.76 1.2 2.3 3.6

6.3 4- 1.6 7.5 4- 2.4

9 + 5

22 :i: 13

s R ( , , + , - ) sa(,o,~+,~-) Ref.

[5,6] [5,6]

7.0 ± 1.4 [34] 10.0 ± 2.4 [49]

11 _q [5o1 21 ± 5 [51]

[501

7. T H E OZI V I O L A T I O N IN pi~ -~ ~b~r + ~'-, Cp, Cw

Table 4 summarizes the experimental data on the OZI rule violation in the ¢~r+Tr - and Cp channels at different energies. The OZI rule vi- olation in these channels is not dramatic com- pared with the level given by the w - ¢ mixing ( e - e i ) 2 ,,, 4 • 10 -3. The measured branching ratios for the reactions p/~ --+ ~bp, Cw at rest are given in Tab. 1. The OZI rule violation in the channel, BR(¢~)/BR(~) = (19 :t: 7). 10 -a (liq- uid) [8,35], is comparable with the effect in the ep channel.

The two-step mechanisms with two particles in the intermediate state were considered in the unitarity approximation in [23] where the calcu- lated branching ratios for the ep and ew channels were found to be almost two orders of magnitude smaller than the data. The off-mass-shell cor- rections have not yet been calculated for these processes. It is also not excluded that the inter- mediate states with more than two particles (like pp~r, K*.f£1r in the case of ep) are important.

8. C O N C L U S I O N

Two step mechanisms play an important role in the observed violations of the OZI rule in the p/5 annihilation at low energies. - The two meson rescattering mechanisms for ~p -+ ~r¢ including all off-mass-shell effects have a size almost two orders of magnitude bigger than the OZI tree level expectations, in agreement with

the measured branching ratios at rest. The K* rescattering mechanism does not request any un- explained OZI violation for the individual vertices in the diagrams. - The ~ production in the p/~ annihilation at v ~ < 2.5 GeV can be explained by the two step mechanism with the intermediate state K/~'. - The ~7/w7 ratio in the pl~ annihilation at rest can be explained by the VDM. The (p -+ 7) + (w -~ 7) interference is destructive for w7 and construc- tive for ~b 7.

Thus the most drastic violations of the OZI rule can be explained by the known mechanism of rescattering. In particular no substantial s$ com- ponent in the nucleon is required. Further studies of the OZI rule breaking due to two step correc- tions in other annihilation channels (~p, ¢~r~,¢w) and the energy dependence of the ~ production would be very desirable.

A C K N O W L E D G E M E N T S

The author would like to thank M.P. Locher and S. von Rotz for fruitful collaboration and O. Gorchakov, F. Leo, and M. Sapozhnikov for useful discussions.

R E F E R E N C E S

1. Compilation of Cross Sections, III: p and fi induced reactions, CERN-HERA-84-01, CERN, 1984.

2. S. Okubo, Phys. Lett. 5 (1963) 165. 3. G. Zweig, CERN Preprint 8419 / TH-412

(1964). 4. I. Iizuka, Progr. Theor. Phys. Suppl. 37

(1966) 21. 5. J. Reinfenrbther, et al. Phys. Lett. B267

(1991) 299. 6. P. Weidenauer, et al., Phys. Lett. B267

(1991) 299. 7. C. Amsler et al., Phys. Lett. B311 (1993)

371. 8. C. Amsler et al., Z. Phys. C58 (1993) 175. 9. K. Braune, Nucl. Phys. A558 (1993) 269c. 10. M.A. Faessler et al., Phys. At. Nucl. 57 (1994)

1693.

310 V.E. Markushin/Nuclear Physics B (Proc. Suppl.) 56A (1997) 303-310

11. C. Amsler et al., Phys. Lett. B346 (1995) 363.

12. U. Wiedner, Proc. III Conf. on Low Energy Antiproton Physics, Bled, 1994, Eds. G. Ker- nel, P. Kri~.an, M. Miku~., World Sci., 1995, p. 319.

13. V.G. Ableev et al., Phys. At. Nuclei 57 (1994) 1716.

14. V.G. Ableev et al., Phys. Lett. B334 (1994) 237.

15. M. Macri et al., . Proc. of the Second Bi- ennial Conference on Low-Energy Antipro- ton Physics, Courmayeur, Italy, 1992, Eds. C. Guaraldo, F. Iazzi, A. Zenoni, North- Holland, Amsterdam, 1993, p.27c.

16. R.T. Jones, Proc. III Conf. on Low Energy Antiproton Physics, Bled, 1994, Eds. G. Ker- nel, P. Kri~,an, M. Miku~, World Sci., 1995, p. 326.

17. U. Wiedner, Talk at LEAP-96, this volume. 18. V. Lucherini, Talk at LEAP-96, this volume. 19. H.J. Lipkin, Nucl. Phys. B244 (1984) 147. 20. Y. Lu, B.S. Zou, and M.P. Locher, Z. Phys.

A345 (1993) 207. 21. M.P. Locher, Yang Lu, and B.S. Zou, Z. Phys.

A347 (1994) 281. 22. M.P. Locher and Yang Lu, Z. Phys. A351

(1994) 83. 23. D. Buzatu and F.M. Lev, Phys. Lett. B329

(1994) 143. 24. D. Buzatu and F.M. Lev, JINR preprint, E4-

94-158, Dubna, 1994. 25. D. Buzatu and F.M. Lev, Phys. Rev. C51

(1995) R2893. 26. D. Buzatu and F.M. Lev, Phys. At. Nucl. 58

(1995) 480. 27. O. Gortchakov, M.P. Locher, V.E. Marku-

shin, and S. yon Rotz, Z. Phys. A353 (1996) 447.

28. J. Ellis, M. Karliner, D.E. Kharzeev, M.G. Sapozhnikov, Phys. Lett. B353 (1995) 319.

29. T. Gutsche, G.D. Yen, A. Faessler, Talk at LEAP-96, this volume.

30. M.P. Locher, Proc. III Conf. on Low Energy Antiproton Physics, Bled, 1994, Eds. G. Ker- nel, P. Kri~an, M. Miku~, World Sci., 1995, p. 38.

31. M.G. Sapozhnikov, Proc. III Conf. on Low

Energy Antiproton Physics, Bled, 1994, Eds. G. Kernel, P. Kri~an, M. Miku~, World Sci., 1995, p. 355.

32. J. Arafune, M. Fukugita, and Y. Oyanagi, Phys. Lett. 70B (1977) 221.

33. Review of Particle Properties, Phys. Rev. D54 (1996) 98.

34. R. Bizzari et al., Nucl. Phys. B14 (1969) 169. 35. R. Bizzari et al., Nucl. Phys. B27 (1971) 140. 36. M. Bloch, G. Fontaine and E. Lillestol, Nucl.

Phys. B23 (1970) 221. 37. B. Delcourt, J. Layssac, and E. Pelaquier,

Proc. of the Workshop on Physics at LEAR with Low Energy Antiprotons, Erice 1982, Plenum, New York, 1984, p.305.

38. F. yon Hippel and C. Quigg, Phys. Rev. D5 (1972) 624.

39. H.J. Lipkin, Phys. Lett. B179 (1986) 278. 40. H.J. Lipkin, Nucl. Phys. B291 (1987) 720. 41. H.J. Lipkin, Phys. Lett. B225 (1989) 287. 42. M. Gell-Mann, D. Sharp, and W. Wagner,

Phys. Rev. Lett. 8 (1962) 261. 43. P. Geiger and N. Isgur, Phys. Rev. Lett. 67

(1991) 1066. 44. H.J. Lipkin and B.S. Zou, Phys. Rev. D53

(1996) 6693. 45. J. Pasupathy, Phys. Rev. D12 (1975) 2929;

J. Pasupathy and C.A. Smith, Phys. Lett. 61B (1976) 469.

46. R. Tegen and J. Willrodt, Nuovo Cimento 43A (1978) 495.

47. A. Cieply, M.P. Locher, and B.S. Zou, Z. Phys. A345 (1993) 41.

48. B. Conforto et al., Nucl. Phys. B3 (1967) 469. 49. A.M. Cooper et al., Nucl.Phys. B146 (1978)

1. 50. R.A. Donald et al., Phys.Lett. B61 (1976)

210. 51. C.K. Chen et al., Nucl.Phys. B130 (1977)

269.