- Email: [email protected]
B-meson trigger at high energies in e+e− annihilation
Volume 107B, number 1,2
PHYSICS LETTERS
3 December 1981
B-MESON TRIGGER AT HIGH ENERGIES IN e+e - ANNIHILATION
M.J. PUHALA 1, Z.J. REK 2, Bing-Lin YOUNG and Xue-Tian ZHU 3 Department o f Physics and Ames Laboratory, Iowa State University, A rues, IA 50011, USA Received 24 July 1981
We propose a method of identifying B meson events at high energies in e+e- annihilation. This model independent method involves a cut in the transverse momentum (k±) of prompt leptons from B decays. The shape of the k± distribution is independent of e+e- energy. A criterion for the signal of B events can be established, taking into account charm contamination and the effect of primordial transverse momentum smearing.
Recently, particles with overt b o t t o m , the B mesons, have been seen at CESR [1]. Due to the large hadron multiplicity and the possible neutral mesons involved in the decay of the B's, the conventional methods of observing resonant structure become extremely difficult. In fact, it is through the energy spectrum o f electrons produced through the semileptonic decay mode that the existence of the B is inferred. The following factors make this m e t h o d workable at the T(4S) resonance: first, the production cross section of BB is comparable, and therefore not lost, to the dominant background o f c h a r m - a n t i c h a r m meson p r o d u c t i o n ; s e c o n d , at the BB threshold the energy spectrum of electrons from B's is well separated from the D contribution. A comparison of the lepton production on and off the T(4S) gives an unequivocal signal that high mass particles are produced. This state of affairs does not persist at high energies. Unfortunately, the present statistics o f PETRA and PEP are not good enough to infer the existence of BB (or B'B, etc.) above the T(4S) energy simply b y examining R. It is natural to ask if there exists an alternative method to deduce the production o f BB in PETRA and PEP. Further, the study of the p r o m p t lepton energy I Ames Laboratory Postdoctoral Fellow. 2 On leave of absence from Warsaw University Branch at Bialystok, Poland. 3 Visiting scientist at Iowa State University from Zhejiang University, Hangzhou, Zhejiang, The People's Republic of China.
spectrum, which was effective at the T(4S), cannot be used to identify B meson events at high energies. This can be seen by noticing that at x/s-= 30 GeV, the charm contribution swamps the direct b o t t o m semileptonic decay contribution b y a factor o f 4 : 1, due to comparable semileptonic branching ratios. In addition, the B and D contributions resemble each other as a result o f the softening effects of the m o m e n t u m distribution of the B's. At first sight, it might seem that the b o t t o m production is completely obscured far above the BB threshold; however, we have found that this is not the case, and that there is a simple, model-independent method to identify a clean sample o f b o t t o m events at PETRA and PEP. The physical picture is quite simple. In the rest flame o f a decaying meson, the unpolarized lepton m o m e n t u m distribution is spherically symmetric, bounded b y a sphere of radius R k , where R k is roughly half the mass of the meson. If the decaying meson occurs in the jet of a fragmenting quark, the transverse m o m e n t u m distribution o f the lepton relative to the jet axis is bounded by a cylinder of radius R k , ignoring effects due to primordial transverse momentum. It follows that high mass particles produce high transverse m o m e n t u m leptons separable from those arising from low mass decays. Since the effects o f the primordial transverse m o m e n t u m become less important for high mass particles, the above picture remains unaltered for the case o f B mesons. Our method then, is based on the simple fact that the b o t t o m con119
Volume 107B, number 1,2
PHYSICS LETTERS
tribution can be clearly separated from the charm contribution when a judicious cut in transverse momentum, k±, is performed [2]. Let us describe the physical content of our model. First, the incident e+e - pair annihilates through a single photon or Z 0, producing a pair of heavy quarks (cg or bb). They subsequently fragment into heavy mesons (D or B) containing the appropriate heavy quarks, possessing a fraction Z of the momentum of the original quark, and a primordial transverse momentum q± with respect to the quark jet axis. The meson decays semileptonicaUy, and the resulting energy and transverse momentum distributions of the leptons are computed. Here, we confine ourselves to the case of electrons for the sake of illustration. The differential semfleptonic decay rates d I ' / d E are computed in the rest frame of the D or B meson by using free-quark V - A amplitudes for the following direct decay processes: b ~ c e - V e, b ~ u e - Ue, c se- re, and ~ ~ d e - Pe" The relative proportions of the above are obtained from fits [3] to the Kobayashi -Maskawa [4] mixing parameters. The masses of the quarks are chosen to correspond to the masses of physical particles in an obvious fashion, so that m b = 5.2 GeV, rn c = 1.87 GeV, m s = 0.5 GeV, m u = m d = 0.14 GeV. We assume effective branching ratios of 12% for B ~ e - X [1] and D ~ e - X [5]. We also consider the contributions from the semileptonic cascades
3 December 1981
we estimate that the average multiplicity is (n) 4. Our conclusions concerning the high k± electroi~ distributions will be insensitive to the precise details of the cascade;moreover, our cascade electron energy distribution is consistent with that of ref. [ 1 ]. We parametrize the q2 distribution by a gaussian of the form e x p ( - q 2 / 2 t2)?We favor t H = 0.45 GeV/c to agree with fits [7] to the PETRA results. For definiteness, we take the longitudinal momentum distribution to be of the Feynman-Field type [8], D ( Z ) = 1 - a + 34(1 - Z) 2, where a = 0.57 [9]. A calculation of the electron energy spectrum for x/s-= 31 GeV shows that the effects of bottom production are obscured by the electrons from D decays. The possibility of identifying the B improves greatly if one measures the prompt electron cross section, doe/dk±, where k± is the component of the observed electron's momentum perpendicular to the quark jet axis. In fig. 1, we show dae/dk ± for t H = 0.45 GeV/c. The direct decays of B mesons dominate the high k± region of the plot. This result is independent of s at large s, and B contribution grows relative to charm as s approaches the Z 0 pole. We point out that the shapes of the k± distributions depend only on t H and the rest frame energy distributions for B ~ e - ~X and D ~ e - p-X. If we experimentally determine the electron energy spectra at the 4" for the D and at the T(4S) for the B, the only model dependence that remains at high k I is due to the pri=
(1) L e-X
-~ e - X ,
and the hadronic cascade 1~-~ g + hadrons
,
llO
1,5
1
5O
(2)
-+e-X We neglect r lepton cascade contributions due to phase space suppression and the softness of the resulting electron distribution. The energy distribution of the in (2) is estimated by assuming that the B nonleptonic decay proceeds entirely via B ~ D + nzr. In order to obtain an analytic form for this distribution we made additional approximations: (a) the matrix elements are momentum independent; (b) the pions are massless; (c) the pion multiplicity is Poisson like. From fits to multiplicities in low energy e+e data [6] using the maximum available kinetic energy, 120
i
~
20
b2
•
0
,~
0.5
x,
2,0
k.L(GeV/c) Fig. 1. Prompt electron transverse m o m e n t u m distribution with respect to the jet axis, d a e / d k l , for x/s = 31 GeV. Curve A, total; c u r v e B, b o t t o m contribution; curve C. charm; c u r v e D, cascade.
Volume 107B, number 1,2 Oi
PHYSICS LETTERS
I
~1 Fig. 2. (a) Left axis: fraction of total direct electrons from bottom with transverse momentum greater than k±. Right axis: integrated electron cross section for transverse momentum greater than kL at xfs = 31 GeV. Solid line: t H = 0.45 GeV/c. Dashed line: t H = 0.8 GeV/c. (b) Contamination from charm ha all electrons with transverse momentum greater than k1. Curve A, t H = 0.45 GeV/c; curve B, t H = 0.8 GeV/c.
l
- ~','x,~x
,\
.8
3 December 1981
co)
q
2
® Ill-
mordial q±. The effects of the value of t H on the electron distribution from direct decays are summarized in fig. 2. We define daq~e aq~e(k±)-=- ; ~ dk±, k±
J¢ 1~-.4
F(k±) =
.2
Ob__.e(kl) Ob.~e(k± = 0 ) '
q = b, c,
(3)
(4)
Oc~e(k±) l(k±) ~ Ob~e(k±) + Oc~e(k±) . I 0.5
1 1.5
1.0
2.0
kx ( Ge V/C) ,
I
1
.4¢
(b)
.30
A
i.-4 .20
30
-
O. 5
I 1.0
~'~
kL (GeV/C }
I 1.5
2.0
(5)
If we consider k± > 1.0 GeV/c, the inclusion of the cascade electrons will have a negligible effect on the above quantities. In fig. 2a, we show a plot of Ob~e(k±) and F(k±) versus k~ for t H = 0.45 GeV/c (solid line) and t H = 0.8 GeV/c (dashed line). We see that Ob_,e(k±) is quite independent of t H over the range considered. This is due to the fact that the B meson is very massive, and large transverse m o m e n t a correspond to relatively low velocities with respect to the jet axis. In fig. 2b, we show I(k±), given by (5). We see that the contamination due to D decays depends more strongly on t H at low k± due to the greater velocity range of D's. Choosing a cut of k± > 1.2 GeV/c gives a 98% pure sample of B mesons corresponding to a cross section of about 2 pb for t H = 0.45 GeV/c (7pb, including e -+, /r+). In the context of QCD, soft gluon emission is responsible for generating the primordial q±. Consequently, we expect that t H for D and B mesons, which contain heavy quarks, is less than that for ordinary hadrons. As a result, we feel that the choice t H = 0.45 GeV/c may already be too large. As a check of the stability of our result against variations in tH, we tried t H = 0.8 GeV/c and found an 80% pure sample of events, as shown in fig. 2b. Our calculation indicates that any large excess of electrons over the predicted b o t t o m contribution at high transverse momentum, say k I 121
Volume 107B, number 1,2
PHYSICS LETTERS
> 1.5 GeV/c, is difficult to explain in terms of any primordial distribution. There are, however, other effects increasing I(k±), in particular the misidentification of the jet axis caused by unobserved neutral particles and the presence of 3-jet events due to hard gluon emission. We find that it is not essential that 3jet events be excluded. Our most pessimistic estimates of these effects lead to 70% pure b o t t o m sample. Due to limited space we postpone the discussion of details to a forthcoming publication. In addition to enabling us to isolate a relatively clean sample of B meson events, we can utilize the t H insensitivity of the B electrons to extrapolate the observed high kz cross section, Ob__,e(k±)lexp, to obtain the cross section for b o t t o m production, o b : Ob = Ob~e(ki)[exp/BeF(k±).
(6)
In the above, B e is the branching ratio for B mesons into direct electrons. As this formula holds below the top threshold, we can investigate the coupling of b quarks to the Z 0 by studying the s dependence of o b, provided the top quark is sufficiently massive [ I 0 ] . We summarize by pointing out that we have an efficient m e t h o d for isolating a relatively pure sample of B meson events; for instance, for k i > 1.2 GeV/c we keep over 50% of all direct electrons from B decay. We can extrapolate the observed cross section in a model independent fashion to determine the production cross section for bottom. We point out that although the D's have been isolated above the if" by looking for high transverse m o m e n t u m hadrons [2], that m e t h o d is impractical in the case of the B. The semi-leptonic
122
3 December 1981
mode will provide dependable, quantitative results. Details of the present work and several applications, in particular the study of the Z 0 - 7 asymmetry in the hadronic channel, will be presented elsewhere. This work was supported b y the US Department of Energy, contract No. W-7405-Eng-82, Office of Basic Sciences (KA-01-01), Division o f High Energy Physics and Nuclear Physics.
References [1] C. Bebek et al., Phys. Rev. Lett. 46 (1981) 84; K. Chadwick et al., Phys. Rev. Lett. 46 (1981) 88. [2] V.D. Barger, T. Gottshalk and R.J.N. Phillips, Phys. Rev. D16 (1977) 746; see also, J.D. Bjorken, Phys. Rev. D17 (1978) 171; A. Ali, Z. Phys. C1 (1979) 25; G.G. Hanson, SLAC-PUB-2118 (1978). [3] R.E. Shrock, S.B. Treiman and L.L. Wang, Phys. Rev. Lett. 42 (1979) 1589; V.D. Barger, W.F. Long and S. Pakvasa, Phys. Rev. Lett. 42 (1979) 1585. [4] M. Kobayashi and K. Maskawa, Prog. Theor. Phys. 49 (1973) 652. [5] W. Bacino et al., Phys. Rev. Lett. 45 (1980) 329. [6] R. Brandelik et al., Phys. Lett. 89B (1980) 418. [7] R. Brandelik et al., Phys. Lett. 86B (1979) 243. [8] R.D. Field and R.P. Feynman, Nucl. Phys. B126 (1978) 1. [9] S.L. Wu and S. Yamada, Proc. XXth Intern. Conf. on High energy physics, eds. L. Durand and L. Pondrom (1981) pp. 604, 616. [10] M.J. Puhala, Z.J. Rek and B.L. Young, Phys. Rev. D23 (1981) 89.
PHYSICS LETTERS
3 December 1981
B-MESON TRIGGER AT HIGH ENERGIES IN e+e - ANNIHILATION
M.J. PUHALA 1, Z.J. REK 2, Bing-Lin YOUNG and Xue-Tian ZHU 3 Department o f Physics and Ames Laboratory, Iowa State University, A rues, IA 50011, USA Received 24 July 1981
We propose a method of identifying B meson events at high energies in e+e- annihilation. This model independent method involves a cut in the transverse momentum (k±) of prompt leptons from B decays. The shape of the k± distribution is independent of e+e- energy. A criterion for the signal of B events can be established, taking into account charm contamination and the effect of primordial transverse momentum smearing.
Recently, particles with overt b o t t o m , the B mesons, have been seen at CESR [1]. Due to the large hadron multiplicity and the possible neutral mesons involved in the decay of the B's, the conventional methods of observing resonant structure become extremely difficult. In fact, it is through the energy spectrum o f electrons produced through the semileptonic decay mode that the existence of the B is inferred. The following factors make this m e t h o d workable at the T(4S) resonance: first, the production cross section of BB is comparable, and therefore not lost, to the dominant background o f c h a r m - a n t i c h a r m meson p r o d u c t i o n ; s e c o n d , at the BB threshold the energy spectrum of electrons from B's is well separated from the D contribution. A comparison of the lepton production on and off the T(4S) gives an unequivocal signal that high mass particles are produced. This state of affairs does not persist at high energies. Unfortunately, the present statistics o f PETRA and PEP are not good enough to infer the existence of BB (or B'B, etc.) above the T(4S) energy simply b y examining R. It is natural to ask if there exists an alternative method to deduce the production o f BB in PETRA and PEP. Further, the study of the p r o m p t lepton energy I Ames Laboratory Postdoctoral Fellow. 2 On leave of absence from Warsaw University Branch at Bialystok, Poland. 3 Visiting scientist at Iowa State University from Zhejiang University, Hangzhou, Zhejiang, The People's Republic of China.
spectrum, which was effective at the T(4S), cannot be used to identify B meson events at high energies. This can be seen by noticing that at x/s-= 30 GeV, the charm contribution swamps the direct b o t t o m semileptonic decay contribution b y a factor o f 4 : 1, due to comparable semileptonic branching ratios. In addition, the B and D contributions resemble each other as a result o f the softening effects of the m o m e n t u m distribution of the B's. At first sight, it might seem that the b o t t o m production is completely obscured far above the BB threshold; however, we have found that this is not the case, and that there is a simple, model-independent method to identify a clean sample o f b o t t o m events at PETRA and PEP. The physical picture is quite simple. In the rest flame o f a decaying meson, the unpolarized lepton m o m e n t u m distribution is spherically symmetric, bounded b y a sphere of radius R k , where R k is roughly half the mass of the meson. If the decaying meson occurs in the jet of a fragmenting quark, the transverse m o m e n t u m distribution o f the lepton relative to the jet axis is bounded by a cylinder of radius R k , ignoring effects due to primordial transverse momentum. It follows that high mass particles produce high transverse m o m e n t u m leptons separable from those arising from low mass decays. Since the effects o f the primordial transverse m o m e n t u m become less important for high mass particles, the above picture remains unaltered for the case o f B mesons. Our method then, is based on the simple fact that the b o t t o m con119
Volume 107B, number 1,2
PHYSICS LETTERS
tribution can be clearly separated from the charm contribution when a judicious cut in transverse momentum, k±, is performed [2]. Let us describe the physical content of our model. First, the incident e+e - pair annihilates through a single photon or Z 0, producing a pair of heavy quarks (cg or bb). They subsequently fragment into heavy mesons (D or B) containing the appropriate heavy quarks, possessing a fraction Z of the momentum of the original quark, and a primordial transverse momentum q± with respect to the quark jet axis. The meson decays semileptonicaUy, and the resulting energy and transverse momentum distributions of the leptons are computed. Here, we confine ourselves to the case of electrons for the sake of illustration. The differential semfleptonic decay rates d I ' / d E are computed in the rest frame of the D or B meson by using free-quark V - A amplitudes for the following direct decay processes: b ~ c e - V e, b ~ u e - Ue, c se- re, and ~ ~ d e - Pe" The relative proportions of the above are obtained from fits [3] to the Kobayashi -Maskawa [4] mixing parameters. The masses of the quarks are chosen to correspond to the masses of physical particles in an obvious fashion, so that m b = 5.2 GeV, rn c = 1.87 GeV, m s = 0.5 GeV, m u = m d = 0.14 GeV. We assume effective branching ratios of 12% for B ~ e - X [1] and D ~ e - X [5]. We also consider the contributions from the semileptonic cascades
3 December 1981
we estimate that the average multiplicity is (n) 4. Our conclusions concerning the high k± electroi~ distributions will be insensitive to the precise details of the cascade;moreover, our cascade electron energy distribution is consistent with that of ref. [ 1 ]. We parametrize the q2 distribution by a gaussian of the form e x p ( - q 2 / 2 t2)?We favor t H = 0.45 GeV/c to agree with fits [7] to the PETRA results. For definiteness, we take the longitudinal momentum distribution to be of the Feynman-Field type [8], D ( Z ) = 1 - a + 34(1 - Z) 2, where a = 0.57 [9]. A calculation of the electron energy spectrum for x/s-= 31 GeV shows that the effects of bottom production are obscured by the electrons from D decays. The possibility of identifying the B improves greatly if one measures the prompt electron cross section, doe/dk±, where k± is the component of the observed electron's momentum perpendicular to the quark jet axis. In fig. 1, we show dae/dk ± for t H = 0.45 GeV/c. The direct decays of B mesons dominate the high k± region of the plot. This result is independent of s at large s, and B contribution grows relative to charm as s approaches the Z 0 pole. We point out that the shapes of the k± distributions depend only on t H and the rest frame energy distributions for B ~ e - ~X and D ~ e - p-X. If we experimentally determine the electron energy spectra at the 4" for the D and at the T(4S) for the B, the only model dependence that remains at high k I is due to the pri=
(1) L e-X
-~ e - X ,
and the hadronic cascade 1~-~ g + hadrons
,
llO
1,5
1
5O
(2)
-+e-X We neglect r lepton cascade contributions due to phase space suppression and the softness of the resulting electron distribution. The energy distribution of the in (2) is estimated by assuming that the B nonleptonic decay proceeds entirely via B ~ D + nzr. In order to obtain an analytic form for this distribution we made additional approximations: (a) the matrix elements are momentum independent; (b) the pions are massless; (c) the pion multiplicity is Poisson like. From fits to multiplicities in low energy e+e data [6] using the maximum available kinetic energy, 120
i
~
20
b2
•
0
,~
0.5
x,
2,0
k.L(GeV/c) Fig. 1. Prompt electron transverse m o m e n t u m distribution with respect to the jet axis, d a e / d k l , for x/s = 31 GeV. Curve A, total; c u r v e B, b o t t o m contribution; curve C. charm; c u r v e D, cascade.
Volume 107B, number 1,2 Oi
PHYSICS LETTERS
I
~1 Fig. 2. (a) Left axis: fraction of total direct electrons from bottom with transverse momentum greater than k±. Right axis: integrated electron cross section for transverse momentum greater than kL at xfs = 31 GeV. Solid line: t H = 0.45 GeV/c. Dashed line: t H = 0.8 GeV/c. (b) Contamination from charm ha all electrons with transverse momentum greater than k1. Curve A, t H = 0.45 GeV/c; curve B, t H = 0.8 GeV/c.
l
- ~','x,~x
,\
.8
3 December 1981
co)
q
2
® Ill-
mordial q±. The effects of the value of t H on the electron distribution from direct decays are summarized in fig. 2. We define daq~e aq~e(k±)-=- ; ~ dk±, k±
J¢ 1~-.4
F(k±) =
.2
Ob__.e(kl) Ob.~e(k± = 0 ) '
q = b, c,
(3)
(4)
Oc~e(k±) l(k±) ~ Ob~e(k±) + Oc~e(k±) . I 0.5
1 1.5
1.0
2.0
kx ( Ge V/C) ,
I
1
.4¢
(b)
.30
A
i.-4 .20
30
-
O. 5
I 1.0
~'~
kL (GeV/C }
I 1.5
2.0
(5)
If we consider k± > 1.0 GeV/c, the inclusion of the cascade electrons will have a negligible effect on the above quantities. In fig. 2a, we show a plot of Ob~e(k±) and F(k±) versus k~ for t H = 0.45 GeV/c (solid line) and t H = 0.8 GeV/c (dashed line). We see that Ob_,e(k±) is quite independent of t H over the range considered. This is due to the fact that the B meson is very massive, and large transverse m o m e n t a correspond to relatively low velocities with respect to the jet axis. In fig. 2b, we show I(k±), given by (5). We see that the contamination due to D decays depends more strongly on t H at low k± due to the greater velocity range of D's. Choosing a cut of k± > 1.2 GeV/c gives a 98% pure sample of B mesons corresponding to a cross section of about 2 pb for t H = 0.45 GeV/c (7pb, including e -+, /r+). In the context of QCD, soft gluon emission is responsible for generating the primordial q±. Consequently, we expect that t H for D and B mesons, which contain heavy quarks, is less than that for ordinary hadrons. As a result, we feel that the choice t H = 0.45 GeV/c may already be too large. As a check of the stability of our result against variations in tH, we tried t H = 0.8 GeV/c and found an 80% pure sample of events, as shown in fig. 2b. Our calculation indicates that any large excess of electrons over the predicted b o t t o m contribution at high transverse momentum, say k I 121
Volume 107B, number 1,2
PHYSICS LETTERS
> 1.5 GeV/c, is difficult to explain in terms of any primordial distribution. There are, however, other effects increasing I(k±), in particular the misidentification of the jet axis caused by unobserved neutral particles and the presence of 3-jet events due to hard gluon emission. We find that it is not essential that 3jet events be excluded. Our most pessimistic estimates of these effects lead to 70% pure b o t t o m sample. Due to limited space we postpone the discussion of details to a forthcoming publication. In addition to enabling us to isolate a relatively clean sample of B meson events, we can utilize the t H insensitivity of the B electrons to extrapolate the observed high kz cross section, Ob__,e(k±)lexp, to obtain the cross section for b o t t o m production, o b : Ob = Ob~e(ki)[exp/BeF(k±).
(6)
In the above, B e is the branching ratio for B mesons into direct electrons. As this formula holds below the top threshold, we can investigate the coupling of b quarks to the Z 0 by studying the s dependence of o b, provided the top quark is sufficiently massive [ I 0 ] . We summarize by pointing out that we have an efficient m e t h o d for isolating a relatively pure sample of B meson events; for instance, for k i > 1.2 GeV/c we keep over 50% of all direct electrons from B decay. We can extrapolate the observed cross section in a model independent fashion to determine the production cross section for bottom. We point out that although the D's have been isolated above the if" by looking for high transverse m o m e n t u m hadrons [2], that m e t h o d is impractical in the case of the B. The semi-leptonic
122
3 December 1981
mode will provide dependable, quantitative results. Details of the present work and several applications, in particular the study of the Z 0 - 7 asymmetry in the hadronic channel, will be presented elsewhere. This work was supported b y the US Department of Energy, contract No. W-7405-Eng-82, Office of Basic Sciences (KA-01-01), Division o f High Energy Physics and Nuclear Physics.
References [1] C. Bebek et al., Phys. Rev. Lett. 46 (1981) 84; K. Chadwick et al., Phys. Rev. Lett. 46 (1981) 88. [2] V.D. Barger, T. Gottshalk and R.J.N. Phillips, Phys. Rev. D16 (1977) 746; see also, J.D. Bjorken, Phys. Rev. D17 (1978) 171; A. Ali, Z. Phys. C1 (1979) 25; G.G. Hanson, SLAC-PUB-2118 (1978). [3] R.E. Shrock, S.B. Treiman and L.L. Wang, Phys. Rev. Lett. 42 (1979) 1589; V.D. Barger, W.F. Long and S. Pakvasa, Phys. Rev. Lett. 42 (1979) 1585. [4] M. Kobayashi and K. Maskawa, Prog. Theor. Phys. 49 (1973) 652. [5] W. Bacino et al., Phys. Rev. Lett. 45 (1980) 329. [6] R. Brandelik et al., Phys. Lett. 89B (1980) 418. [7] R. Brandelik et al., Phys. Lett. 86B (1979) 243. [8] R.D. Field and R.P. Feynman, Nucl. Phys. B126 (1978) 1. [9] S.L. Wu and S. Yamada, Proc. XXth Intern. Conf. on High energy physics, eds. L. Durand and L. Pondrom (1981) pp. 604, 616. [10] M.J. Puhala, Z.J. Rek and B.L. Young, Phys. Rev. D23 (1981) 89.