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In search of the ηc
Volume 80B, number 3
PHYSICS LETTERS
1 January 1979
IN SEARCH OF THE r/c G. EILAM i , B. MARGOLIS and S. RUDAZ 2 Physics Department, McGill University, Montreal, Canada Received 12 October 1978
We argue that the X(2.88) detected in 7r-p ~ ")'3'+ n at 40 GeV/c cannot be the ~c' We discuss the possibility that a q~c~ state is produced there, probably the same state discovered in radiative decay of the J/~O.Only at much higher energies is the 7?c expected to dominate over q~cE in the 7r-p interaction. We also discuss coherent photoproduction and find that four quark state production would dominate over rlc.
It is well known that identification o f the X(2.83) detected in J / i -~ 7X ~ 777 [1] as the r/c presents severe problems for the charmonium picture [2]. From the experimental results [1 ] for the branching ratios B(J/t~ ~ 7 X ) B ( X ~ 77 ) = (1.2 -+ 0.5) X 10 - 4 and [3] B(J/~ ~ 7X) < 1.7% one deduces B(X -->3'7) > 7 X 10 - 3 to be compared with B(r/c ~ 7 7 ) ~ 1.2 X 10 - 3 as computed in the charmonium picture using the two gluon mechanism for the hadronic decay of the rlc, [4] and assuming a s (3 GeV) ~ 0.2. Furthermore, an unusually large hyperfine splitting is required for an r/c o f 2.83 GeV; it seems that r/c should be very close to tile J/if, with mass difference of the order o f its total width [2,5], thus making it extremely difficult to detect. An attractive way out of the r/c puzzle has been recently suggested [6]. Using an analogy from lighter quarks spectroscopy, it was suggested that around 2.8 GeV two degenerate cEq~states exist, one with I = 0 and the other with I = 1. These states are analogous to the S* and 6 which are jPC = 0 ++ objects with MS* = M 8 = 980 MeV and 1 = 0,1 respectively, and are probably the lowest lying sgq~states [7]. Following ref. [6] we denote the c~-qqstates by S c and 8 c. It is interesting to note [6] that these cEq~states are just I Permanent address: Physics Department, Technion-Israel Institute of Technology, Haifa, Israel. 2 Present address: Laboratory of Nuclear Studies, Cornell University, Ithaca, New York. 306
below the lowest 1 cc state in analogy with the s~'q~ states below the ¢. Such a four q u ~ k O+ state can be decomposed into VV, PP, ~ . ~ and P • P , where an arrow indicates a color octet. Although the VV recoupling coefficient may be smaller than the other three coefficients [7], the VV--} 3'3' decay mode is the only one which does not involve gluons and we expect it to dominate over the other three decay modes * 1. It is therefore reasonable to take P(6 e -~ 77) ~" 9F(Sc -~ 77), reflecting the fact that the VV pair for 8 c involves a cEvector meson and a p-like meson, whereas for the S c the combination is ffw. The relationship between the 77 widths then follows from VMD coupling strength considerations, and the state observed in J / i -* 3'X is expected to be the 6 c [6]. Recently a 2.88 GeV state has been detected in 7r-p --->77 + n at Plah = 40 GeV/c, with a r r - p ~ x n B ( X -->3'7) ~ ( 2 -+ 1) X 10 -34 cm 2 [8]. Can the X b e the r/c? It is shown here than an r/c can definitely not be produced with the reported cross section. We then explore the possibility that the same ccqq that was detected in J / i ~ 7X is the state observed in the 40 GeV/c experiment. Estimates are given for the cross section for both the c~q~ states and the tic in charge exchange. Let us first estimate the small angle cross section for 7r-p ~ r/c n by invoking well established Regge ,1 Such an argument may be more doubtful for the s~q~ states since a s is not that small there.
Volume 80B, number 3
PHYSICS LETTERS
pole phenomenology [9]. The only exchange possible in r?c production is the A 2 trajectory, with OZI violation in the meson vertex. We can therefore write ,2 2
° n - p ~ r l c n B(rlc ~ 3'3') _ gncA2 rrB (*lc -~ 3"3") On_p__,r/nB(r / ~ 3'3')
2 gnA2,rB(rl ~ 3"3")
-n,
(1)
where both cross sections are at the same energy. Converting coupling constants to widths one obtains
(
1 R = ~ \ M ~ A 2 ]l !\ ~-~nc !/
F ( A 2 ~ 7/n)a(r/ --*3'3')
' (2)
where kA2 and knc are the momenta in the decays A 2 --* ryr and r/c ~ A2rr respectively. Using Mnc ~ 3 GeV and the experimental values [10] for F ( A 2 rln) and B ( r / ~ 3'3') and the parameterization [11 ] On-p__,nnB(r/-+ 3'3') = 2.85 X 10 -28 Pl~b1.46 cm 2 we find
o _p_.~c~B(~ c --, 3'3') = 8.7 X 10 -34 F(r/c ~
(3)
3'3')B(nc -+ A27r)Plal'46cm 2 ,
where Plab is in GeV/c and P(r/c -+ 3'3') is in keV. If the state found in the 40 GeV/c experiment is ~c, then F07c ~ 3'3')B(~c ~ A2n) = 50 keV. The branching ratio of acE state into q~mesons is a few percent, at most 4% [10]. Therefore we arrive at the completely unreasonable value P(r/c ~ 3'3') ~ 1 MeV, to be compared with the prediction [4] 12a2e~ IR(0) I 2 ['(r/c ~ 3'3') =
~- 10 k e V ,
(4)
where R ( 0 ) i s the radial wave function at the origin, and eQ is the charge of the c quark. After rejecting the possibility of an ~c production at 40 GeV/c with the reported cross section we now try to answer the question: Are the cgq~ states responsible for such a high cross section? A 6 c would be produced via 77 and B exchange, while the S~ production results from the exchange of n and A 1 trajectories. It is difficult to deduce reliable estimates for the coupling constants of four quark states. Nevertheless it is ¢2 The mixing of r/1 and 77a gives a factor of order 1. Most of our estimates are order of magnitude estimates.
1 January 1979
clear that if a four quark state is produced at 40 GeV/c with the reported cross section, its width to 3'3' should be o f the order o f 1 MeV. Is this possible? Although the 3'3' widths of the s-gq~states ~ and S* have not been directly measured, a recent estimate [12] gives P(5 3"),) = 550 -+ 270 keV. This estimate is based on a pole model for the measured decay r~ -+ n3'3'; it is assumed that 6 is exchanged between the r~ and n. It is instructive to compare this large width of the s-gq~state with the width for 1S s-gdecay to 3'3', F(r/s ~ 3'3') ~ 0.5 keV, based on eq. (4) where eQ is now the charge o f the s quark (note that IR (0) l 2/M 2 is practically independent of the mass o f the decaying object [13] ). It is therefore not unreasonable to expect that P(6c ~ 3 ' 7 ) could be similar to I'(~ ~ 3'3') i.e. of the order of a few hundred keV or 1 MeV. Why should a four quark state have such a large decay width to two photons? We first consider its decay to two vector mesons. Let M4 and M 2 denote four quark and two quark mesons, respectively. Let us consider the coupling constant for M4 -~ M 2 + M 2 without any OZI violation, such as g2 . , g 2 p etc. In the QCD framework one expects thatCt*h°ese coupling constants will be much larger than those for M 2 ~ M 2 + M 2 [7,14] 2 2 gM4M2M2 :gM2M2M2 = 1 :~s/Tr . (5) In other words, an M4 meson just falls apart. In such a picture one can account [14] for the large width o f the e, which is assumed to be a u ~ d J s t a t e , as compared with the p width (both decay mainly to mr). It is therefore not surprising, using a VMD argument, that a large value for g~14V V will lead to a large 3'3' width , a . Let us now assume that 5 c is seen in the experiment at 40 GeV/c, and employ the B or r/trajectories for which a -w - 0 . 3 + 0.9t. We then find
O~r-p~cnB(6
c ~ 3 ' 3 ' ) ~ 2 . 9 × 10-30Pla2"6 cm 2 • (6)
For S c production the power should be similar, if n exchange is suppressed by the experimental cut off as in ref. [8] (only events with It I > 0.1 (GeV/c) 2 were scanned, to get rid of the 3'3' background which seems
4:3 For 6 c '* 73' it means a decay mainly through its 0¢ component, and according to the model presented here we expect a width of few MeV for 5c ~ p~. For a partial list of 6c and Sc decays see ref. [6]. 307
Volume 80B, number 3
PHYSICS LETTERS
to be dominated by rr exchange 4-4. Even for 6 c this experimental cut off can result in a slightly different power, but we consider eq. (6) adequate for order of magnitude estimates. The cross section in eq. (6) has to be compared with
oTr-p--.ncnB(rlc~3`7)
= 3.5 X 10-34Plab1"46 cm 2 (7)
as deduced from eq. (3) with the optimistic values B(r/c ~ A27r) = 0.04, I"(77c ~ 7 7 ) = 10 keV. Therefore it is not very difficult to observe the r~c in the decay J/ff ~ 3`r/c since its mass is so close to the J / ¢ mass (and it may even be slightly higher than the J / ¢ [5,16], but its low width into 73` means that it will start dominating the n - p ~ 77 + n cross section (with M,r.r ~ 3 GeV only at/°lab of a few thousand GeV/c. In a r r - p -+ "/3' + n experiment at Fermilab energies (elab ~ 300 GeV/c) one expects from eqs. (6) and (7) that cgq~ production will be higher than tic production by about an order of magnitude. Therefore the only way to search for the r/c there is to be able to use the expected mass difference of about 200 MeV between the rTc and the degenerate 6 c and S c, i.e to have good resolution in the -/3' spectrum, and to design an experiment that can measure cross sections times branching ratio down to 5 × 10 -38 cm 2 as expected for r/c at 400 GeV/c* s Photoproduction experiments are hopeless for searching for the r/c, since cEq~ will dominate at all energies. Consider for example 3'T ~ 3'3' + T at M ~ ~ 3 GeV,. where T is an isoscalar nucleus. Since cE pair production is involved, most of the contribution will come from the incoming photon conversion into J / ~ . The only exchange possible for both S c and % production outside the Primakoff peak, is the co trajectory (6 c will be suppressed, since it has I = 1). Thus the energy dependence of both processes is expected to be the same, with ~c production much be,4 It is possible that the one pion exchange background reported in ref. [8] is actually an S* production via one pion exchange. , s In principle one can distinguish between 0- and 0÷ states by detecting the polarization states of the two photons [151.
308
1 January 1979
low the S c ~ue to: a) P(S c ~ 77) N P(r/c
77)- b)
gs~o ~g.~cOWis expected, as discussed above, for M4 ~ M 2 + M 2 c o m p a r e d w i t h M 2 ~ M 2 + M 2. To summarize, we have found that it is difficult but possible to detect the rlc in strong production, We would like to thank C. Leroy for helpful discussions. After completion of the manuscript we received a preprint [16] where it is also shown, using arguments from A 2 exchange, that r~c should have an unreasonable width of 1 MeV into 3'7 to account for the 40 G e V / c cross section. However the interpretation of the results in terms of four quark states, the possibility of enhancing the relative r/c signal by performing experiments at higher energies, and the clean signal for ccqq expected in photoproduction are not discussed there.
References [1] W. Braunschweig et al., Phys. Lett. 67B (1977) 243. [2] For reviews see: K. Gottfried, in: Proc. Intern. Symp. on Lepton and photon interactions at high energies, ed. F. Gutbrod (DESY, Hamburg, 1977) p. 667; V.A. Novikov et al., Phys. Rep. 41C (1978) 1. [3] C.J. Biddick et al., Phys. Rev. Lett. 38 (1977) 1324. [4] R. Barbieri, R. Gatto and R. K6gerler, Phys. Lett. 60B (1976) 183. [5] M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Phys. Lett. 77B (1978) 80. [6] H.J. Lipkin, H.R. Rubinstein and N. Isgur, Weizmann Inst. preprint WLS-78/23 Ph. [7] R.L. Jaffe, Phys. Rev. D15 (1977) 267. [8] W.D. Apel et al., Phys. Lett. 72B (1978) 500. [9] For a review see: A.C. Irving and R.P. Worden, Phys. Rep. 34C (1977) 118. [10] C. Bricman et al. Phys. Lett. 75B (1978) 1. [11] O.I. Dahl et al., Phys. Rev. Lett. 37 (1976) 80. [12] G.K. Greenhut and G.W. Intemann, Phys. Rev. D18 (1978) 231. [13] J.D Jackson, in: Proc. Summer Institute on Particle physics, ed. M.C. Zipf (SLAC, 1976) p. 147. [14] S.O. Holmgren and M.R. Pennington, Phys. Lett. 77B (1978) 304. [ 15 ] W.R. Frazer, Elementary particles (Prentice-Hall, 1966) p. 31. [16] A. Yu, Khodjamirian, Yerevan preprint EFI/28(6)/78.
PHYSICS LETTERS
1 January 1979
IN SEARCH OF THE r/c G. EILAM i , B. MARGOLIS and S. RUDAZ 2 Physics Department, McGill University, Montreal, Canada Received 12 October 1978
We argue that the X(2.88) detected in 7r-p ~ ")'3'+ n at 40 GeV/c cannot be the ~c' We discuss the possibility that a q~c~ state is produced there, probably the same state discovered in radiative decay of the J/~O.Only at much higher energies is the 7?c expected to dominate over q~cE in the 7r-p interaction. We also discuss coherent photoproduction and find that four quark state production would dominate over rlc.
It is well known that identification o f the X(2.83) detected in J / i -~ 7X ~ 777 [1] as the r/c presents severe problems for the charmonium picture [2]. From the experimental results [1 ] for the branching ratios B(J/t~ ~ 7 X ) B ( X ~ 77 ) = (1.2 -+ 0.5) X 10 - 4 and [3] B(J/~ ~ 7X) < 1.7% one deduces B(X -->3'7) > 7 X 10 - 3 to be compared with B(r/c ~ 7 7 ) ~ 1.2 X 10 - 3 as computed in the charmonium picture using the two gluon mechanism for the hadronic decay of the rlc, [4] and assuming a s (3 GeV) ~ 0.2. Furthermore, an unusually large hyperfine splitting is required for an r/c o f 2.83 GeV; it seems that r/c should be very close to tile J/if, with mass difference of the order o f its total width [2,5], thus making it extremely difficult to detect. An attractive way out of the r/c puzzle has been recently suggested [6]. Using an analogy from lighter quarks spectroscopy, it was suggested that around 2.8 GeV two degenerate cEq~states exist, one with I = 0 and the other with I = 1. These states are analogous to the S* and 6 which are jPC = 0 ++ objects with MS* = M 8 = 980 MeV and 1 = 0,1 respectively, and are probably the lowest lying sgq~states [7]. Following ref. [6] we denote the c~-qqstates by S c and 8 c. It is interesting to note [6] that these cEq~states are just I Permanent address: Physics Department, Technion-Israel Institute of Technology, Haifa, Israel. 2 Present address: Laboratory of Nuclear Studies, Cornell University, Ithaca, New York. 306
below the lowest 1 cc state in analogy with the s~'q~ states below the ¢. Such a four q u ~ k O+ state can be decomposed into VV, PP, ~ . ~ and P • P , where an arrow indicates a color octet. Although the VV recoupling coefficient may be smaller than the other three coefficients [7], the VV--} 3'3' decay mode is the only one which does not involve gluons and we expect it to dominate over the other three decay modes * 1. It is therefore reasonable to take P(6 e -~ 77) ~" 9F(Sc -~ 77), reflecting the fact that the VV pair for 8 c involves a cEvector meson and a p-like meson, whereas for the S c the combination is ffw. The relationship between the 77 widths then follows from VMD coupling strength considerations, and the state observed in J / i -* 3'X is expected to be the 6 c [6]. Recently a 2.88 GeV state has been detected in 7r-p --->77 + n at Plah = 40 GeV/c, with a r r - p ~ x n B ( X -->3'7) ~ ( 2 -+ 1) X 10 -34 cm 2 [8]. Can the X b e the r/c? It is shown here than an r/c can definitely not be produced with the reported cross section. We then explore the possibility that the same ccqq that was detected in J / i ~ 7X is the state observed in the 40 GeV/c experiment. Estimates are given for the cross section for both the c~q~ states and the tic in charge exchange. Let us first estimate the small angle cross section for 7r-p ~ r/c n by invoking well established Regge ,1 Such an argument may be more doubtful for the s~q~ states since a s is not that small there.
Volume 80B, number 3
PHYSICS LETTERS
pole phenomenology [9]. The only exchange possible in r?c production is the A 2 trajectory, with OZI violation in the meson vertex. We can therefore write ,2 2
° n - p ~ r l c n B(rlc ~ 3'3') _ gncA2 rrB (*lc -~ 3"3") On_p__,r/nB(r / ~ 3'3')
2 gnA2,rB(rl ~ 3"3")
-n,
(1)
where both cross sections are at the same energy. Converting coupling constants to widths one obtains
(
1 R = ~ \ M ~ A 2 ]l !\ ~-~nc !/
F ( A 2 ~ 7/n)a(r/ --*3'3')
' (2)
where kA2 and knc are the momenta in the decays A 2 --* ryr and r/c ~ A2rr respectively. Using Mnc ~ 3 GeV and the experimental values [10] for F ( A 2 rln) and B ( r / ~ 3'3') and the parameterization [11 ] On-p__,nnB(r/-+ 3'3') = 2.85 X 10 -28 Pl~b1.46 cm 2 we find
o _p_.~c~B(~ c --, 3'3') = 8.7 X 10 -34 F(r/c ~
(3)
3'3')B(nc -+ A27r)Plal'46cm 2 ,
where Plab is in GeV/c and P(r/c -+ 3'3') is in keV. If the state found in the 40 GeV/c experiment is ~c, then F07c ~ 3'3')B(~c ~ A2n) = 50 keV. The branching ratio of acE state into q~mesons is a few percent, at most 4% [10]. Therefore we arrive at the completely unreasonable value P(r/c ~ 3'3') ~ 1 MeV, to be compared with the prediction [4] 12a2e~ IR(0) I 2 ['(r/c ~ 3'3') =
~- 10 k e V ,
(4)
where R ( 0 ) i s the radial wave function at the origin, and eQ is the charge of the c quark. After rejecting the possibility of an ~c production at 40 GeV/c with the reported cross section we now try to answer the question: Are the cgq~ states responsible for such a high cross section? A 6 c would be produced via 77 and B exchange, while the S~ production results from the exchange of n and A 1 trajectories. It is difficult to deduce reliable estimates for the coupling constants of four quark states. Nevertheless it is ¢2 The mixing of r/1 and 77a gives a factor of order 1. Most of our estimates are order of magnitude estimates.
1 January 1979
clear that if a four quark state is produced at 40 GeV/c with the reported cross section, its width to 3'3' should be o f the order o f 1 MeV. Is this possible? Although the 3'3' widths of the s-gq~states ~ and S* have not been directly measured, a recent estimate [12] gives P(5 3"),) = 550 -+ 270 keV. This estimate is based on a pole model for the measured decay r~ -+ n3'3'; it is assumed that 6 is exchanged between the r~ and n. It is instructive to compare this large width of the s-gq~state with the width for 1S s-gdecay to 3'3', F(r/s ~ 3'3') ~ 0.5 keV, based on eq. (4) where eQ is now the charge o f the s quark (note that IR (0) l 2/M 2 is practically independent of the mass o f the decaying object [13] ). It is therefore not unreasonable to expect that P(6c ~ 3 ' 7 ) could be similar to I'(~ ~ 3'3') i.e. of the order of a few hundred keV or 1 MeV. Why should a four quark state have such a large decay width to two photons? We first consider its decay to two vector mesons. Let M4 and M 2 denote four quark and two quark mesons, respectively. Let us consider the coupling constant for M4 -~ M 2 + M 2 without any OZI violation, such as g2 . , g 2 p etc. In the QCD framework one expects thatCt*h°ese coupling constants will be much larger than those for M 2 ~ M 2 + M 2 [7,14] 2 2 gM4M2M2 :gM2M2M2 = 1 :~s/Tr . (5) In other words, an M4 meson just falls apart. In such a picture one can account [14] for the large width o f the e, which is assumed to be a u ~ d J s t a t e , as compared with the p width (both decay mainly to mr). It is therefore not surprising, using a VMD argument, that a large value for g~14V V will lead to a large 3'3' width , a . Let us now assume that 5 c is seen in the experiment at 40 GeV/c, and employ the B or r/trajectories for which a -w - 0 . 3 + 0.9t. We then find
O~r-p~cnB(6
c ~ 3 ' 3 ' ) ~ 2 . 9 × 10-30Pla2"6 cm 2 • (6)
For S c production the power should be similar, if n exchange is suppressed by the experimental cut off as in ref. [8] (only events with It I > 0.1 (GeV/c) 2 were scanned, to get rid of the 3'3' background which seems
4:3 For 6 c '* 73' it means a decay mainly through its 0¢ component, and according to the model presented here we expect a width of few MeV for 5c ~ p~. For a partial list of 6c and Sc decays see ref. [6]. 307
Volume 80B, number 3
PHYSICS LETTERS
to be dominated by rr exchange 4-4. Even for 6 c this experimental cut off can result in a slightly different power, but we consider eq. (6) adequate for order of magnitude estimates. The cross section in eq. (6) has to be compared with
oTr-p--.ncnB(rlc~3`7)
= 3.5 X 10-34Plab1"46 cm 2 (7)
as deduced from eq. (3) with the optimistic values B(r/c ~ A27r) = 0.04, I"(77c ~ 7 7 ) = 10 keV. Therefore it is not very difficult to observe the r~c in the decay J/ff ~ 3`r/c since its mass is so close to the J / ¢ mass (and it may even be slightly higher than the J / ¢ [5,16], but its low width into 73` means that it will start dominating the n - p ~ 77 + n cross section (with M,r.r ~ 3 GeV only at/°lab of a few thousand GeV/c. In a r r - p -+ "/3' + n experiment at Fermilab energies (elab ~ 300 GeV/c) one expects from eqs. (6) and (7) that cgq~ production will be higher than tic production by about an order of magnitude. Therefore the only way to search for the r/c there is to be able to use the expected mass difference of about 200 MeV between the rTc and the degenerate 6 c and S c, i.e to have good resolution in the -/3' spectrum, and to design an experiment that can measure cross sections times branching ratio down to 5 × 10 -38 cm 2 as expected for r/c at 400 GeV/c* s Photoproduction experiments are hopeless for searching for the r/c, since cEq~ will dominate at all energies. Consider for example 3'T ~ 3'3' + T at M ~ ~ 3 GeV,. where T is an isoscalar nucleus. Since cE pair production is involved, most of the contribution will come from the incoming photon conversion into J / ~ . The only exchange possible for both S c and % production outside the Primakoff peak, is the co trajectory (6 c will be suppressed, since it has I = 1). Thus the energy dependence of both processes is expected to be the same, with ~c production much be,4 It is possible that the one pion exchange background reported in ref. [8] is actually an S* production via one pion exchange. , s In principle one can distinguish between 0- and 0÷ states by detecting the polarization states of the two photons [151.
308
1 January 1979
low the S c ~ue to: a) P(S c ~ 77) N P(r/c
77)- b)
gs~o ~g.~cOWis expected, as discussed above, for M4 ~ M 2 + M 2 c o m p a r e d w i t h M 2 ~ M 2 + M 2. To summarize, we have found that it is difficult but possible to detect the rlc in strong production, We would like to thank C. Leroy for helpful discussions. After completion of the manuscript we received a preprint [16] where it is also shown, using arguments from A 2 exchange, that r~c should have an unreasonable width of 1 MeV into 3'7 to account for the 40 G e V / c cross section. However the interpretation of the results in terms of four quark states, the possibility of enhancing the relative r/c signal by performing experiments at higher energies, and the clean signal for ccqq expected in photoproduction are not discussed there.
References [1] W. Braunschweig et al., Phys. Lett. 67B (1977) 243. [2] For reviews see: K. Gottfried, in: Proc. Intern. Symp. on Lepton and photon interactions at high energies, ed. F. Gutbrod (DESY, Hamburg, 1977) p. 667; V.A. Novikov et al., Phys. Rep. 41C (1978) 1. [3] C.J. Biddick et al., Phys. Rev. Lett. 38 (1977) 1324. [4] R. Barbieri, R. Gatto and R. K6gerler, Phys. Lett. 60B (1976) 183. [5] M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Phys. Lett. 77B (1978) 80. [6] H.J. Lipkin, H.R. Rubinstein and N. Isgur, Weizmann Inst. preprint WLS-78/23 Ph. [7] R.L. Jaffe, Phys. Rev. D15 (1977) 267. [8] W.D. Apel et al., Phys. Lett. 72B (1978) 500. [9] For a review see: A.C. Irving and R.P. Worden, Phys. Rep. 34C (1977) 118. [10] C. Bricman et al. Phys. Lett. 75B (1978) 1. [11] O.I. Dahl et al., Phys. Rev. Lett. 37 (1976) 80. [12] G.K. Greenhut and G.W. Intemann, Phys. Rev. D18 (1978) 231. [13] J.D Jackson, in: Proc. Summer Institute on Particle physics, ed. M.C. Zipf (SLAC, 1976) p. 147. [14] S.O. Holmgren and M.R. Pennington, Phys. Lett. 77B (1978) 304. [ 15 ] W.R. Frazer, Elementary particles (Prentice-Hall, 1966) p. 31. [16] A. Yu, Khodjamirian, Yerevan preprint EFI/28(6)/78.