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The positive excess of μ mesons at high energies
Nuclear Physics 74 (1965) 619--624; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or m i c r o f i l m without written permission from the publisher
T H E P O S I T I V E E X C E S S O F bl M E S O N S AT H I G H E N E R G I E S L. COHEN University of Southampton, England G. N. FOWLER and P. POULOPOULOS University of Newcastle upon Tyne, England Received 31 December 1964 Abstract: Experimental data on the positive excess of # mesons at high energy are compared with theoretical predictions based on a Monte Carlo calculation of the parent ~ meson production process supplemented by a contribution from isobars. It is found that some isobar contribution is essential to fit the experimental data. 1. Introduction
D a t a on the positive excess of ~ mesons at energies in excess o f 10 GeV have steadily accumulated in the last decade and have recently been extended beyond 50 GeV by A s h t o n et al. 1), H a y m a n and Wolfendale 2) and K a m i y a et al. 3). At the same time progress in our understanding o f rc and K meson production processes has made possible an interpretation of the # meson data in terms o f reasonably realistic models whose details are verifiable at lower energies. In the following we repoxt some results of a Monte Carlo calculation o f the ~+/rrratio at production essentially equivalent to the # + / # - ratio at production apart from a change in the energy scale, using the Poisson multiplicity distribution and the energy spectra given by Cocconi et al. 4). In addition to this "pionisation" contribution we have allowed for the effect o f isobar production using the model o f Contogouris et al. 5), averaged over an incident spectrum which we have assumed to be o f the form n(Ep) = A E p 3. 2. The Pionisation Contribution The procedure used has been to fix the incident nucleon energy t and to determine from energy considerations the m a x i m u m n u m b e r Nmax o f pions which can be produced by this nucleon assuming that the m i n i m u m energy of a pion is v1 " ½(1 + Ep) ~ GeV. In practice Nmax has been restricted to be 10. The probabilities of n = 0, 1, 2 . . . Nmax pions produced in this event are then evaluated with the distribution function
S(n, Ep) -
~ne-~
n! with
~=E~.
* We use units in which h = c = Mp = 1. 619
L. COHEN et al.
620
A Monte Carlo procedure has been used to find the actual number of pious for this event and then used again to find the numbers of ~+, re- and n ° assuming equal probabilities of pp and pn collisions using the usual isobaric spin weighting factors. The energies of the pions produced are then evaluated again by a Monte Carlo method using dn(E,0 _ 0.36 E~e_E./r ' dE~ T with
(1)
T = 0.36 Ep
for 7r mesons of each sign of charge, and we have considered first generation pions only but allowed the nucleons to initiate further events. This has been carried out for incident protons of energies of 60, 110, 160 and 210 GeV. The results have been weighted according to the incident spectrum and combined with due allowance for staffs°
N~+ T4t
T i
i
J
Ir 08 L~
I 10
.......
I lO0
j 1000
log E~ (GeV) Fig. 1. T h e e n e r g y d i s t r i b u t i o n o f t h e p o s i t i v e excess o f # m e s o n s at p r o d u c t i o n .
• Combined experimental results (MacKeown and Wolfendale 6)); © Monte Carlo calculation (i.e. pionisation only); the full line represents the theoretical result (Monte Carlo plus pionisation). tical errors and the points obtained are displayed in fig. 1. The rather large errors on the points will be much reduced when a faster computer is available but it will be seen that the Monte Carlo points are systematically below the experimental results. This agrees with the results of MacKeown and Wolfendale 6) and Hayman 7) when large fluctuations in multiplicity are not included. 3. The Isobar Contribution
For the energy distribution of pions produced through isobar decay we shall use the model described in detail by Contogouris et al. 5) in which the isobar is produced through the exchange of a Pomeranchon. The result is
ddE~ a ~ _ ~'p log F I ½ S f-M-'2 dm*D(m*)(vp~?)- 1,
(2)
#
MESON
621
EXCESS
where Et is a product of vertex factors, e'p the slope of the Pomeranchon trajectory at t = 0, D the shape of the resonance, s is the square of the total energy in the c.m. system, v the isobaric velocity in the lab. system, p~ is the pion momentum in the rest system of the isobar and 7 = ( 1 - v 2 ) -~. We have approximated D ( m * ) by a 3 function at a mass of 1690 MeV. The pions produced by the incident nucleons then have a spectrum which is given to the required accuracy at the energies of interest by , dnt(E,) = ~ ' n I =_
dE~
A da,~ E~ E3 dE,~
dEp,
where M * is the isobar mass, E~ the pion energy in the laboratory system and E* the pion energy in the rest system of the isobar. The ratio R is then given by t+
,,~ AA
'+
R = npi°n +O'q~¢ ~:nl n'pi-on+ 0.07 x n } - '
(3)
t+ where np~on is the pionisation contribution, n} ± the contribution from an isobar of
isobaric spin ½ and we allow for the incident neutron flux in both the isobar and pionisation contributions. I f we assume that the pionisation cross section is equal to the total cross section then ~: may be taken to be Fx/C(p evaluated in units of the total cross section and is to be adjusted to give the best fit with the experimental results. The combined results for x = 0.03 are shown in fig. 1 as the full curve and compared with the experimental results; it should be noted that the value of x is uncertain by at least a factor of 2 because of the error on the Monte Carlo points. The fit we find is not particularly good, but this depends on the details of the isobar production model, and in view of the errors on both experimental and Monte Carlo points it does not seem worthwhile at this state to use a more elaborate model. It may be worth remarking that this value of ~¢is in agreement as to order to magnitude with the result of Contogouris et al. for the ½, ~ - nucleon isobar. We make this comparison here merely to establish that the isobar contribution we require is of the order of magnitude which might be expected to occur in fact. The question of which isobar might actually be involved is discussed further below.
4. Discussion Several authors have analysed the positive excess of/~ mesons along similar lines, in particular Yash Pal and Peters 8), Ramana Murthy 9) and MacKeown and Wolfendale 6). Yash Pal and Peters took the extreme view that all the positive excess is produced by isobar decay, i.e. that the pionisation contribution is negligible at the energies of interest. This requires that the T -- 3 isobars must be included otherwise the ratio is automatically 6.7 (see (3)). The isobars included are shown in table 1.
622
L. COHENet
al.
At lower energies the positive excess is attributed to the energetic pions produced through the decay of the ½, z2- isobar to the ground state via the 3, 2~+ state (transitions 2 and 3 of table 1). This gives a value of/~+/#- in agreement with experiment until TABLE 1 Isobar decay s c h e m e s contributing to the positive excess of # m e s o n s
I
J
]683 1510
1 6 +
. 938
the meson energy becomes sufficiently large for nuclear interactions in the atmosphere to compete with the decay. When this happens the contribution from the ½, ~+ isobar should be included (transition 4 of table 1) and only the decay modes which have no intermediary pion need be considered. This means that the process which is important is N* ~ K + + A I~/t+ + v. The experimental results for energies in excess of 20 GeV require a contribution of 2-4 % of the total flux from this mode, as we should expect. There is however an important objection to this approach which depends upon the observation that all isobars which are likely to be produced with reasonable frequency should arise through the exchange o f a Pomeranchon. From this it follows that isobars with spin > ~2 cannot be produced at least in the forward direction (which is the only important direction at high energies). This would seem to exclude the K meson producing mechanism. So far as the production of the ½, -~- isobar is concerned this is likely to be inhibited for reasons discussed in ref. 5) but the cross section derived therein is still of the order of 1 mb which might be adequate to account for the data. However according to the experimental results given by Glashow and Rosenfeld ao), the ratio of the partial widths for the two transitions of table 1 marked 1 and 2 is greater than 8 This implies that a pionisation contribution is required to give agreement with experiment. This approach has been followed by Ramana Murthy under the rather restrictive assumptions that a given constant fraction of the primary energy is shared equally by all the pions emitted in the forward direction in the c.m. system and that the mean number of pions produced is constant independent of primary energy. The results are given for one value of E~ only. MacKeown and Wolfendale have used the energy spectrum 1) and a multiplicity
/Z MESON EXCESS
623
distribution which is consistent with the assumption ½n~E~ = flEp in the laboratory system where fl is a constant fixed from experiment. They predict a p+/#- ratio from pionisation alone which is somewhat less than that found in the present work. The main reason for this is their use of a mean multiplicity ~ = 2.8 Ep+. These authors find a fit to the experimental data only when an enhanced contribution from events involving the production of a single n meson is introduced.
5. Conclusions
The calculations reported confirm the results of previous workers that a contribution from nucleon isobars (or large fluctuations in multiplicity) is required to accomlt for the positive excess o f / t mesons at energies greater than 50 GeV. With regard to the results at the highest energies we have not been able to find a value of ~: which gives a # + / # - ratio increasing with energy as rapidly as the experimental results appear to do. However the errors on these high energy points are so large that this may not be significant. As to the isobar which may be involved this could be the 1, ~- or the 1, 1 + (Px, l ) resonance first discussed by Feld and Layson 11) and subsequently by Bransden et al. ~2) and Auvil et al. ~3). We have in fact carried out the calculation for the latter case. The mass value of the P1, ~ resonance quoted by Feld and Layson used in (2) was above the K + production threshold but subsequent calculations 12, J3) indicate that the Feld and Layson mass value was probably too high and the correct value is below the K threshold. This could be important for muon energies > 100 GeV since in this region K mesons are expected to be an important source of # mesons. However it is not at present possible to say whether the observed positive excess at these energies is produced through K or rc decay. Future observations in inclined directions may throw some light on this problem * The conclusion therefore must be that the observed positive excess of # mesons requires a significant contribution from processes in which a small number of pions and possibly of K + mesons is produced. If the experimental increase in the p+/llratio for energies greater than 100 GeV is confirmed the most reasonable interpretation6) would seem to be that the increase is due mainly to the contribution of K mesons which should be important at these energies. This requires 14) a K + / K - ratio > 5 compared with an observed value at machine energies of 3 4 . Since one should expect this ratio to fail with increasing energy as is the case with rc+/rc - and since the K/Tr ratio as) is < 20 % it is difficult to see how a "kaonisation" process can account for an increase in the p+/#- ratio. Since it is difficult to find an isobar with spin < ~which is allowed by unitary symmetry and which has a K meson decay mode it may be that at high energy pions or resonant pion groups are created together with single t T h e a u t h o r s are i n d e b t e d to Dr. A. W. W o l f e n d a l e a n d P. K. M c K e o w n for this suggestion.
624
L. COHEN et al.
K + mesons (e.g. K* a n d C meson16)) in preference to multiple K +, K - p r o d u c t i o n . The pions are subsequently r e m o v e d by n u c l e a r interactions so that they do n o t dilute the positive excess. The authors are grateful to the staff of the C o m p u t i n g L a b o r a t o r y of the University o f Newcastle for their assistance with the c o m p u t a t i o n a n d to Dr. A. W. Wolfendale a n d Mr. P. K. M a c K e o w n for discussions. One of us (P.P.) wishes to t h a n k the Greek State Scholarship F o u n d a t i o n for a scholarship d u r i n g the tenure of which some of this work was carried out.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)
F. Ashton et al., Phys. Lett. 6 (1963) 259 P. J. Hayman and A. W. Wolfendale, Nature 195 (1962) 166 Y. Kamiya, W. Ueno, S. Sagisaka and Y. Sekido, Nuovo Cim. 30 (1963) 1 G. Cocconi, R. J. Kolster and D. H. Perkins, Lawrence Radiation Laboratory Report, High Energy Physics Study Seminars, No. 28, part 2 (1961) A. P. Contogouris, S. C. Frautschi and H. S. Wong, Phys. Rev. 129 (1963) 974 P. K. McKeown and A. W. Wolfendale, N.I.R.N.S. Conf. on High Energy Physics (1964) P. J. Hayman, Ph.D. Thesis, Durham Colleges, England (1962) J. Yash Pal and B. Peters, Conf. on Cosmic Ray Physics, Bristol (1962) P. V. Ramana Murthy, Nuovo Cim. 30 (1963) 762 J. Glashow and A. H. Rosenfeld, Phys. Rev. Lett. 10 (1963) 192 B. T. Feld and W. M. Layson, Proc. Int. Cong. on High Energy Physics, CERN (1962) p. 147 B. H. Bransden, R. G. Moorhouse and P. J. O'Donnell, N.I.R.N.S. preprint N.I.R.L./R/70(1964) P. Auvil, A. Donnachie, A. T. Lea and C. Lovelace, preprint (1964) P. K. McKeown, private communication (1964) J. L. Osborne, Nuovo Cim. 32 (1964) 816 B. C. Maglic, N.I.R.N.S. Conf. on High Energy Physics (1964)
T H E P O S I T I V E E X C E S S O F bl M E S O N S AT H I G H E N E R G I E S L. COHEN University of Southampton, England G. N. FOWLER and P. POULOPOULOS University of Newcastle upon Tyne, England Received 31 December 1964 Abstract: Experimental data on the positive excess of # mesons at high energy are compared with theoretical predictions based on a Monte Carlo calculation of the parent ~ meson production process supplemented by a contribution from isobars. It is found that some isobar contribution is essential to fit the experimental data. 1. Introduction
D a t a on the positive excess of ~ mesons at energies in excess o f 10 GeV have steadily accumulated in the last decade and have recently been extended beyond 50 GeV by A s h t o n et al. 1), H a y m a n and Wolfendale 2) and K a m i y a et al. 3). At the same time progress in our understanding o f rc and K meson production processes has made possible an interpretation of the # meson data in terms o f reasonably realistic models whose details are verifiable at lower energies. In the following we repoxt some results of a Monte Carlo calculation o f the ~+/rrratio at production essentially equivalent to the # + / # - ratio at production apart from a change in the energy scale, using the Poisson multiplicity distribution and the energy spectra given by Cocconi et al. 4). In addition to this "pionisation" contribution we have allowed for the effect o f isobar production using the model o f Contogouris et al. 5), averaged over an incident spectrum which we have assumed to be o f the form n(Ep) = A E p 3. 2. The Pionisation Contribution The procedure used has been to fix the incident nucleon energy t and to determine from energy considerations the m a x i m u m n u m b e r Nmax o f pions which can be produced by this nucleon assuming that the m i n i m u m energy of a pion is v1 " ½(1 + Ep) ~ GeV. In practice Nmax has been restricted to be 10. The probabilities of n = 0, 1, 2 . . . Nmax pions produced in this event are then evaluated with the distribution function
S(n, Ep) -
~ne-~
n! with
~=E~.
* We use units in which h = c = Mp = 1. 619
L. COHEN et al.
620
A Monte Carlo procedure has been used to find the actual number of pious for this event and then used again to find the numbers of ~+, re- and n ° assuming equal probabilities of pp and pn collisions using the usual isobaric spin weighting factors. The energies of the pions produced are then evaluated again by a Monte Carlo method using dn(E,0 _ 0.36 E~e_E./r ' dE~ T with
(1)
T = 0.36 Ep
for 7r mesons of each sign of charge, and we have considered first generation pions only but allowed the nucleons to initiate further events. This has been carried out for incident protons of energies of 60, 110, 160 and 210 GeV. The results have been weighted according to the incident spectrum and combined with due allowance for staffs°
N~+ T4t
T i
i
J
Ir 08 L~
I 10
.......
I lO0
j 1000
log E~ (GeV) Fig. 1. T h e e n e r g y d i s t r i b u t i o n o f t h e p o s i t i v e excess o f # m e s o n s at p r o d u c t i o n .
• Combined experimental results (MacKeown and Wolfendale 6)); © Monte Carlo calculation (i.e. pionisation only); the full line represents the theoretical result (Monte Carlo plus pionisation). tical errors and the points obtained are displayed in fig. 1. The rather large errors on the points will be much reduced when a faster computer is available but it will be seen that the Monte Carlo points are systematically below the experimental results. This agrees with the results of MacKeown and Wolfendale 6) and Hayman 7) when large fluctuations in multiplicity are not included. 3. The Isobar Contribution
For the energy distribution of pions produced through isobar decay we shall use the model described in detail by Contogouris et al. 5) in which the isobar is produced through the exchange of a Pomeranchon. The result is
ddE~ a ~ _ ~'p log F I ½ S f-M-'2 dm*D(m*)(vp~?)- 1,
(2)
#
MESON
621
EXCESS
where Et is a product of vertex factors, e'p the slope of the Pomeranchon trajectory at t = 0, D the shape of the resonance, s is the square of the total energy in the c.m. system, v the isobaric velocity in the lab. system, p~ is the pion momentum in the rest system of the isobar and 7 = ( 1 - v 2 ) -~. We have approximated D ( m * ) by a 3 function at a mass of 1690 MeV. The pions produced by the incident nucleons then have a spectrum which is given to the required accuracy at the energies of interest by , dnt(E,) = ~ ' n I =_
dE~
A da,~ E~ E3 dE,~
dEp,
where M * is the isobar mass, E~ the pion energy in the laboratory system and E* the pion energy in the rest system of the isobar. The ratio R is then given by t+
,,~ AA
'+
R = npi°n +O'q~¢ ~:nl n'pi-on+ 0.07 x n } - '
(3)
t+ where np~on is the pionisation contribution, n} ± the contribution from an isobar of
isobaric spin ½ and we allow for the incident neutron flux in both the isobar and pionisation contributions. I f we assume that the pionisation cross section is equal to the total cross section then ~: may be taken to be Fx/C(p evaluated in units of the total cross section and is to be adjusted to give the best fit with the experimental results. The combined results for x = 0.03 are shown in fig. 1 as the full curve and compared with the experimental results; it should be noted that the value of x is uncertain by at least a factor of 2 because of the error on the Monte Carlo points. The fit we find is not particularly good, but this depends on the details of the isobar production model, and in view of the errors on both experimental and Monte Carlo points it does not seem worthwhile at this state to use a more elaborate model. It may be worth remarking that this value of ~¢is in agreement as to order to magnitude with the result of Contogouris et al. for the ½, ~ - nucleon isobar. We make this comparison here merely to establish that the isobar contribution we require is of the order of magnitude which might be expected to occur in fact. The question of which isobar might actually be involved is discussed further below.
4. Discussion Several authors have analysed the positive excess of/~ mesons along similar lines, in particular Yash Pal and Peters 8), Ramana Murthy 9) and MacKeown and Wolfendale 6). Yash Pal and Peters took the extreme view that all the positive excess is produced by isobar decay, i.e. that the pionisation contribution is negligible at the energies of interest. This requires that the T -- 3 isobars must be included otherwise the ratio is automatically 6.7 (see (3)). The isobars included are shown in table 1.
622
L. COHENet
al.
At lower energies the positive excess is attributed to the energetic pions produced through the decay of the ½, z2- isobar to the ground state via the 3, 2~+ state (transitions 2 and 3 of table 1). This gives a value of/~+/#- in agreement with experiment until TABLE 1 Isobar decay s c h e m e s contributing to the positive excess of # m e s o n s
I
J
]683 1510
1 6 +
. 938
the meson energy becomes sufficiently large for nuclear interactions in the atmosphere to compete with the decay. When this happens the contribution from the ½, ~+ isobar should be included (transition 4 of table 1) and only the decay modes which have no intermediary pion need be considered. This means that the process which is important is N* ~ K + + A I~/t+ + v. The experimental results for energies in excess of 20 GeV require a contribution of 2-4 % of the total flux from this mode, as we should expect. There is however an important objection to this approach which depends upon the observation that all isobars which are likely to be produced with reasonable frequency should arise through the exchange o f a Pomeranchon. From this it follows that isobars with spin > ~2 cannot be produced at least in the forward direction (which is the only important direction at high energies). This would seem to exclude the K meson producing mechanism. So far as the production of the ½, -~- isobar is concerned this is likely to be inhibited for reasons discussed in ref. 5) but the cross section derived therein is still of the order of 1 mb which might be adequate to account for the data. However according to the experimental results given by Glashow and Rosenfeld ao), the ratio of the partial widths for the two transitions of table 1 marked 1 and 2 is greater than 8 This implies that a pionisation contribution is required to give agreement with experiment. This approach has been followed by Ramana Murthy under the rather restrictive assumptions that a given constant fraction of the primary energy is shared equally by all the pions emitted in the forward direction in the c.m. system and that the mean number of pions produced is constant independent of primary energy. The results are given for one value of E~ only. MacKeown and Wolfendale have used the energy spectrum 1) and a multiplicity
/Z MESON EXCESS
623
distribution which is consistent with the assumption ½n~E~ = flEp in the laboratory system where fl is a constant fixed from experiment. They predict a p+/#- ratio from pionisation alone which is somewhat less than that found in the present work. The main reason for this is their use of a mean multiplicity ~ = 2.8 Ep+. These authors find a fit to the experimental data only when an enhanced contribution from events involving the production of a single n meson is introduced.
5. Conclusions
The calculations reported confirm the results of previous workers that a contribution from nucleon isobars (or large fluctuations in multiplicity) is required to accomlt for the positive excess o f / t mesons at energies greater than 50 GeV. With regard to the results at the highest energies we have not been able to find a value of ~: which gives a # + / # - ratio increasing with energy as rapidly as the experimental results appear to do. However the errors on these high energy points are so large that this may not be significant. As to the isobar which may be involved this could be the 1, ~- or the 1, 1 + (Px, l ) resonance first discussed by Feld and Layson 11) and subsequently by Bransden et al. ~2) and Auvil et al. ~3). We have in fact carried out the calculation for the latter case. The mass value of the P1, ~ resonance quoted by Feld and Layson used in (2) was above the K + production threshold but subsequent calculations 12, J3) indicate that the Feld and Layson mass value was probably too high and the correct value is below the K threshold. This could be important for muon energies > 100 GeV since in this region K mesons are expected to be an important source of # mesons. However it is not at present possible to say whether the observed positive excess at these energies is produced through K or rc decay. Future observations in inclined directions may throw some light on this problem * The conclusion therefore must be that the observed positive excess of # mesons requires a significant contribution from processes in which a small number of pions and possibly of K + mesons is produced. If the experimental increase in the p+/llratio for energies greater than 100 GeV is confirmed the most reasonable interpretation6) would seem to be that the increase is due mainly to the contribution of K mesons which should be important at these energies. This requires 14) a K + / K - ratio > 5 compared with an observed value at machine energies of 3 4 . Since one should expect this ratio to fail with increasing energy as is the case with rc+/rc - and since the K/Tr ratio as) is < 20 % it is difficult to see how a "kaonisation" process can account for an increase in the p+/#- ratio. Since it is difficult to find an isobar with spin < ~which is allowed by unitary symmetry and which has a K meson decay mode it may be that at high energy pions or resonant pion groups are created together with single t T h e a u t h o r s are i n d e b t e d to Dr. A. W. W o l f e n d a l e a n d P. K. M c K e o w n for this suggestion.
624
L. COHEN et al.
K + mesons (e.g. K* a n d C meson16)) in preference to multiple K +, K - p r o d u c t i o n . The pions are subsequently r e m o v e d by n u c l e a r interactions so that they do n o t dilute the positive excess. The authors are grateful to the staff of the C o m p u t i n g L a b o r a t o r y of the University o f Newcastle for their assistance with the c o m p u t a t i o n a n d to Dr. A. W. Wolfendale a n d Mr. P. K. M a c K e o w n for discussions. One of us (P.P.) wishes to t h a n k the Greek State Scholarship F o u n d a t i o n for a scholarship d u r i n g the tenure of which some of this work was carried out.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)
F. Ashton et al., Phys. Lett. 6 (1963) 259 P. J. Hayman and A. W. Wolfendale, Nature 195 (1962) 166 Y. Kamiya, W. Ueno, S. Sagisaka and Y. Sekido, Nuovo Cim. 30 (1963) 1 G. Cocconi, R. J. Kolster and D. H. Perkins, Lawrence Radiation Laboratory Report, High Energy Physics Study Seminars, No. 28, part 2 (1961) A. P. Contogouris, S. C. Frautschi and H. S. Wong, Phys. Rev. 129 (1963) 974 P. K. McKeown and A. W. Wolfendale, N.I.R.N.S. Conf. on High Energy Physics (1964) P. J. Hayman, Ph.D. Thesis, Durham Colleges, England (1962) J. Yash Pal and B. Peters, Conf. on Cosmic Ray Physics, Bristol (1962) P. V. Ramana Murthy, Nuovo Cim. 30 (1963) 762 J. Glashow and A. H. Rosenfeld, Phys. Rev. Lett. 10 (1963) 192 B. T. Feld and W. M. Layson, Proc. Int. Cong. on High Energy Physics, CERN (1962) p. 147 B. H. Bransden, R. G. Moorhouse and P. J. O'Donnell, N.I.R.N.S. preprint N.I.R.L./R/70(1964) P. Auvil, A. Donnachie, A. T. Lea and C. Lovelace, preprint (1964) P. K. McKeown, private communication (1964) J. L. Osborne, Nuovo Cim. 32 (1964) 816 B. C. Maglic, N.I.R.N.S. Conf. on High Energy Physics (1964)