Baryon-baryon scattering and SU(6)

Volume 17, number 3

PHYSICS

LETTERS

15 July 1965 --__ M.Goldberg, M.Gundzik. S. Leitner, M.Primer, P. L. Connolly, E. L. Hartz, K. W. Lai, G. W. London, N. P. Samios and S.S.Yamamoto, Phys. Rev. Letters 13 (1964) 249. AaeheniBerlin-Birmingham-Bonn-Hamburg-LondonMUnchenCollaboration.. Phvsics Letters 11 (1964) _ . 16’7. R.H.Dalitz and D.G.Sutherland, Preprint (1964) ‘IX and q mixing and some radiative meson decay

two pions and assuming a mixing between the T = 0 singlet and octet vector mesons represented by the angle 0. Using the total width of rpequal to 3.1 MeV [ 121 our experiment leads to a mixing angle 0 = 45’ in agreement with that given by the mass rule [ 91. The observed transition of the cp meson into pn and 3n is not in agreement with the predictions of the SU6 symmetry scheme [lo]. We wish to thank the crew of the 81 cm Saclay hydrogen bubble chamber, the physicists and technicians of CERN who helped to perform this experiment, Prof. R. H. Dalitz and Dr. A. Muller for helpful discussions, and finally our scanning and measuring teams for their untiring efforts.

a. 9. 10. 11.

References 1. J.Goldberg and J.M.Perreau, CERN Report 63-12. 2. G. R. Kalbfleisch, 0. I.Dahl and A. Rittenberg, Phys. Rev.Letters 13 (1934) 349. 3. P.M.Dauber, W.E.Slater, L.T.Smith, D.H.Stork and H.K.Ticho, Phys.Rev.Letters 13 (1964)449.

12.

processes. G.A.Smith, J.S.LindseyandJ.J.Murray, UCRL 11430. J. B. Bronzan and F. E.Low, Phys. Rev.Letters 12 (1964) 522. J. J.Sakurai, Phys.Rev.132 (1963) 434. F. Gursey, A. Pais and L. A. Radicati, Phys. Rev. Letters 13 (1964) 299; H. J.Lipkin, Phys.Rev.Letters 13 (1964) 590. P.Schlein, W. E .Slater, L. T.Smith, D.H.Stork and H. K. Ticho, Phys. Rev. Letters 10 (1963) 368; K.W.Lai. P.L.Connolly. E.L.Hart. G.W.London. G.C.Moneti, R.R.Rau,-N.P.Samios, I.O.Skilli. corn. S.S.Yamamoto. M.Goldberg. M.Gundzik. J. LeKner and S. Lich&n, Bull. Am. Phys. Sot .9 (1964) 22. N.Gelfsno, D.Miller, M.Nussbaum, J.Ratau, J. Schultz, J. Steinberger, T.H. Tan, L. Kirsch and R.Plano, Phys.Rev. Letters 11 (1963) 433.

*****

BARYON-BARYON

SCATTERING

AND SU(6)

*

D. CLlNE and M. OLSSON Department

of Physics,

University

of Wisconsin

Received 26 May 1965

The purpose of this note is to compare with experiments some predictions of SU(6) symmetry for non-relativistic baryon-baryon scattering, particularly for channels where there are no known bound states or absorption effects. The comparisons will be restricted to s-wave initial and final states and to low centre-of-mass kinetic energies. The cases in which SU(6) has worked particularly well have been mainly restricted to static properties [l] while agreement of various cross section predictions has not been consistent [2]. However, the presence of large mass splitting, absorption effects and nearby resonances may be partially responsible for the lack of agreement in cross section predictions. For this reason we have chosen what is perhaps the cleanest cross section prediction of SU(6) to compare with experiment. This note will compare the predictions of SU(6) with the 340

available experimental data for low energy NN, hp and C+p scattering. The theoretical calculations of the relevant SU(6) relations have been carried out by Barger and Rubin [3] &id also by Suzuki [ 41. At present the only accurate determination of the low energy Ap parameters results from the analysis of hyperfragment data. The low energy Ap parameters obtained from hyperfragment data for several recent analyses [5-81 are shown in table 1. The Ap parameters thus determined in the various analyses are quite consistent, and are also in substantial agreement with the directly measured Ap cross section [9, lo]. Using the SU(6) amplitude relationships of * Work supportedby the U . S. Atomic Energy Commission under Contract No. AT(ll-l)-881.

Volume 1’7, number 3

PHYSICS

Table 1 Ap low energy scattering parametere derived in various hyperfragment analyeea.

Singlet

Ref.

Singlet

scattering length (fm)

5

-(2.25 ” $2)

6

-(3.6

+ 3.6 _ ls8)

7

-(4.6

; ;I$

8

-(2.89 “, 8.:;)

.

.

effective range (sn)

Triplet eoattering length (W

Triplet effective range W

LETTERS

loo0 700 500 400

1.97 f 0.14 0.51 f 0.09 3.62 f 0.35

300

0.53 f 0.12

200

N2 1.7 f 0.1

N5

15 July 1965

0.53 f 0.11 3.66 f 0.65

1.94 f 0.08 0.71 f 0.06 3.75 f 0.22

r; _g 100 b

Unilarity ----

Barger and Rubin [3], the Ap and Z’p scattering lengths may be expressed in terms of the well known nucleon-nucleon scattering lengths [ll] +~(?a&-&)=-

50

Limil

Ref. (5)

-_---

Ref. (6)

.. .... . ..

Ref. (f)

.*.*...=

Ref. (6)

9*2fm

lztA=$,@as N - 5u$=-5.4kO.8

fm

fz! =a k =*a:=-10*2fm, where ai z and G: x are the Ap and C+p elastic scatteri$ lengths fbr the singlet spin state and triplet spin states, respectively. The error reflects the apparent charge-independence violation in nucleon-nucleon singlet scattering [ll]. These predictions for the Ap parameters have the same sign v the actual Ap scattering lengths in table 1 but are several times too large. It has been argued that good agreement should not be expected because of the existence of the bound nucleon-nucleon triplet state and nearly bound singlet state [4]. It is interesting to note that the predicted Ap and Z?p scattering lengths are negative, indicating the absence of a bound state (using the nucleon-nucleon scattering lengths as input). We now examine the relationship between two scattering processes which have some particularly simple aspects. The processes are Ap and C+p elastic scattering near threshold where the kinetic energy is much less than the particle masses. Both of these channels are purely elastic (i.e., no open or nearby inelastic competing processes), and have no known bound states. In SU(6) any baryon-baryon scattering amplitude is specified by two complex energy dependent parameters [3]. The known Ap parameters of table 1 define the singlet and triplet s-wave Ap scattering amplitudes and thus can be used to predict the other baryon-

20

t 0.0

ICiO

2bo

360

Pz (MeV/c) Fig. 1. SU(6) prediction for Z’p elastic scattering using aa imput the low energy Ap parameters given in table 1. The I;+ momentum is for the laboratory system. The references for the theoretical curves are the same as in table 1. The plotted experimental point is a weighted average of the data given in ref. 14. For comparison, the error in the predicted C’p cross section using the Ap parameters of ref. 8, at 160 MeV/c C+ momentum, is 90 mb.

baryon scattering states. In particular, we may predict the s-wave Z+p elastic cross section as is shown in fig. 1, [12,13]. This figure shows that the predicted Z+p cross section exceeds the experimental cross section [14] by a considerable margin. Thus we see that even in this favourable case a straight forward application of SU(6) to reaction amplitudes gives less than satisfactory results. It is hard to imagine that the kinematic difference due to the different E and A masses could account for such a large discrepancy with the SU(6) predictions [15]. We wish to thank V. Barger and M. Rubin for illuminating discdssions. 1. M.Beg and A.Pais, Phys.Rev. 137 (1965) B1514. Contains a review of semi-strong and some electromagnetic symmetry breaking properties. Decuplet maa8 splitting has also been calculated,

341

Volume 17, number 3 -. -

PHYSICS

T.Kuo and T.Yao, Phys.Rev.Letters 14 (1965) 79; A. Dolgov, L. Okun, I. Pomersnchuk and V. Solovyev, Phvsics Letters 15 11965) 84: and has been found in agreement with experiment, ‘G. Pjerrou, P. Schlein, W.Slater. L.Smith. D.Stork and H.Ticho. Phvs. Rev. Letters 14 (1965) 275 and M. Olsson, ‘Phys. Rev.Letters 14 (1965) 118. 2. K. Johnson and S.Treiman, Phys. Rev. Letters 14 (1965) 189: R. Good and Nguyen-huu Xuong, Phys. Rev. Letters 14 (1965) 191 have looked at elastic meson-barvon scattering.

3. 4. 5. 6. 7. 8.

V. Barger and M. Rubin, Phys. Rev, Letters 14 (1965) 713; J. Carter, J. Coyne and S. Meskov, Phys. Rev. I,etters 14 (1965) 523; T.Binford, D.Cline and M.Olsson, Phys.Rev. Letters 14 (1965) 715 have examined several inelastic meson-baryon cross section equalities. V. Barger and M. Rubin, to be published. M. Suzuki, Nuovo Cimento, to be published. There is a disagreement among the triplet state relationships given by M. Suzuki and by V . Barger et al. B. W.Downs and R.H.Dalitz, Phys.Rev. 114 (1959) 593. J. J. DeSwart and C .Dullemond, Ann. Phys. (New York) 19 (1962) 458. K.Diehich, H. J.Mang and R. Folk, Nucl. Phys. 50 (1964) 177. R.C.Herndon, Y.C.TangandE.W.Scbmid, UCRL-12037, to be published.

LETTERS

-_

~---

15 July 1965

9. B.Sechi-Zorn, R. A. Burnstein, T. B. Day, B.Kehoe and G. A. Snow, Phys. Rev. Letters 13 (1964) 282 and G. Alexander, U.Karehorn, A.Shapora, G.Yekutieli, R.Engelmann, H.Filthuth, A.Fridman and A.Minguzzi-Ranzi, Phys.Rev.Letters 13 (1964) 484. N.W.Reay, J.T.Reed, T.Yama10. A.C.Melissinos, ouchi, E. Sacharidis, J. J. Lindenbaum, S.Ozaki and L. C. L.Yuan, Phys. Rev. Letters 14 (1965) 604. 11. See, for example, R. P. Haddock, R.M.Salter Jr. , M. Zeller, J.B. Czirr and D.R.Nygren, Phys. Rev. Letters 14 (1965) 318 and references to previous work contained therein. 12. The SU(6) prediction for I;“p scattering in fig. 1 is for s-wave scattering only. The existence of pwave in the zp scattering makes the disagreement with the SU(6) prediction greater. The effects of the Coulomb interaction are negligible at the p momentum for which the comparison of theory and experiment is made. 13. The SU(6) prediction of ref. 3 gives the same singlet and triplet scattering amplitude in pp elastic scattering. 14. R.A.Burnstein, T.B.Day, B.Kehoe, H.A.Rubin, B. Sechi-Zorn and G. A. Snow. Bull. Am. Phvs.Soc. 9 (1964) 642 and R. A. Burnstein, private communication; H.G.Dosch, R. Engelmann, H.Filtuth, V.Hepp, E. Kluge and A. Minguzzi-Ranzi, Physics Letters 14 (1965) 162. 15. Relativistic effects should also be small since the mean value of v/c for the p is 0.13 for the experimental data.

*****

GROUP

SU (12)

AS A GENERALIZATION OF AND SPIN SYMMETRIES

THE

SYMPLECTIC

D. G. FAKIROV, B. V. STRUMINSKY and I. T. TODOROV Joint Laboratory

Institute for Nuclear Research of Theoretical Physics, Dubna,

USSR

Received 9 June 1965

The success of the group W(6) [l-5] uniting the group of internal symmetries SU(3) and the spin group SU(2) put aside attempts to extend

the SU(3) scheme in the framework of purely internal symmetries. Meanwhile it is not clear to what degree the success of the SU(3) is related to the specific properties of the above mentioned group and its subgroup 6U(3). In the present note it is shown that if the group of the third rank Sp(6) considered in refs. 6-8 is taken as the internal symmetry group after uniting it with the spin group according to the scheme leading from SU(3) 9 SU(2) to SU(6) [e.g. 91 we 342

may get all the basic results obtained in the SU(6) scheme. In this case, in place of SU(6) there appears a 143-parametric unitary group * SU(12). Along with classified particles and resonances, the multiplets of SU(12) (as well as the Sp(6) multiplets) lead to new resonances for which the considered scheme predicts definite properties. The * Note that in a recent paper [lo], where the compact groups with the number of parameters not exceeding

140 are analysed it is shown that among these groups there is no one, but the SU(6) itself, leading to the same physical results as the group SU(6).