States in Su(6) Theory

VOLUME 14,NUMBER9 PHYSICAL REVIEW LETTERS 1 MARCH 1965 *Work supported by the National Science Foundation. 1 M. Sugawara and A. Tubis, Phys. Rev. (to be published). 2 F. T. Meiere and M. Sugawara, to be published. 3 For example, J. S. Ball and D. Y. Wong [Phys. Rev. Letters 7_, 390 (1961)] point out that a far-away pole in the P-wave amplitude is indispensable in obtaining a resonance in the pion-pion problem. Recently, in their bootstrap approach to the pion-nucleon problem, K. Huang and F. E. Low [Phys. Rev. Letters 13., 596 (1964)] emphasize the necessity of introducing a sub- traction into the partial-wave dispersion relation in order to obtain a bootstrap solution. 4 M. Sugawara and A. Tubis, Phys. Rev. 130, 2127 (1963). 5 The existence of a pair of zeros implies that A(oS) cannot vanish at infinity. In the case of the fastest approach of A(u>) to zero, however, A{u>) becomes pure real at infinity because <5(°°) is then 7r or 0. Therefore, A{oo) cannot satisfy an unsubtracted dispersion relation. In the case when A(u>) approaches a finite pure imaginary limit, A{oS) can still satisfy an unsubtracted dispersion relation, as is discussed by M. Sugawara and A. Kanazawa, Phys. Rev. 123, 1895 (1961). 6 The argument below is essentially the same as that given by M. Sugawara and A. Tubis, Phys. Rev. Let- ters £, 355 (1962). 7 If A{oo) is not even with respect to the sign change in w, AM is no longer real on the imaginary axis and, therefore, the preceeding argument concerning a pair of zeros on the imaginary axis no longer holds. 8 J. Hamilton and W. S. Woolcock, Rev. Mod. Phys. 35, 737 (1963). ERRATA Y = 2 STATES IN SU(6) THEORY. Freeman J. Dyson and Nguyen-huu Xuong [Phys. Rev. Let- ters 13, 815 (1964)]. Experiment on IT "-D scattering at 140 MeV 1 shows a large ratio of inelastic to elastic scattering, indicating that many angular momenta contribute. The peak at 170 MeV (£* = 2160 MeV) is, therefore, not to be understood as belonging to a particular SU(6) representation. On the contrary, it seems to provide evidence that the splitting between SU(6) representation 490 and 1050 is small compared with the "SU(6)- violating" splitting between octet and decimet states of the single baryons. In this case, the hypothesis advanced in the second paragraph of our Letter is not valid. We thank Dr. R. Hof- stadter for referring us to the experimental paper quoted above, and Dr. S. Treiman and Dr. W. Alles for criticism. 1 E. G. Pewitt, T. H. Fields, G. B. Yodh, J. G. Fetkovich, and M. Derrick, Phys. Rev. 131, 1826 (1963). STUDY OF EXCHANGE INTEGRAL OF CRYS- TALLINE 3 He AT 0°K. L. H. Nosanow and William J. Mullin [Phys. Rev. Letters 14, 133 (1965)]. There is a typographical error in Eq. (12). It should read V.. = v..-(ti 2 /2mf. 2 )(f..V. 2 f..-V.f..- V / ). V V ij 13 i 13 ii3 i ij 339

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Transcript of States in Su(6) Theory

VOLUME 14,NUMBER9 P H Y S I C A L R E V I E W L E T T E R S 1 MARCH 1965

*Work supported by the National Science Foundation. 1M. Sugawara and A. Tubis , Phys . Rev. (to be pub

l i shed) . 2 F . T. Meie re and M. Sugawara, to be published. 3 F o r example , J . S. Ball and D. Y. Wong [Phys . Rev.

L e t t e r s 7_, 390 (1961)] point out that a fa r -away pole in the P - w a v e ampli tude i s indispensable in obtaining a r esonance in the pion-pion prob lem. Recently, in the i r boo ts t rap approach to the pion-nucleon problem, K. Huang and F . E. Low [Phys . Rev. L e t t e r s 13., 596 (1964)] emphas ize the necess i ty of introducing a subt rac t ion into the pa r t i a l -wave d ispers ion rela t ion in o r d e r to obtain a boots t rap solution.

4M. Sugawara and A. Tub i s , Phys . Rev. 130, 2127 (1963).

5The exis tence of a pa i r of ze ros impl ies that A(oS) cannot vanish at infinity. In the case of the fas tes t a p

proach of A(u>) to z e r o , however , A{u>) becomes pure r ea l at infinity because <5(°°) is then 7r or 0. The re fo re , A{oo) cannot satisfy an unsubt rac ted d i spers ion re la t ion . In the case when A(u>) approaches a finite pure imag i na ry l imi t , A{oS) can stil l satisfy an unsubtrac ted d i s pers ion re la t ion , a s i s d i scussed by M. Sugawara and A. Kanazawa, Phys . Rev. 123, 1895 (1961).

6The argument below is essent ia l ly the same a s that given by M. Sugawara and A. Tubis , Phys . Rev. Le t t e r s £, 355 (1962).

7If A{oo) i s not even with r e spec t to the sign change in w, A M is no longer r ea l on the imaginary axis and, t he re fo re , the preceeding a rgument concerning a pa i r of z e ros on the imaginary ax is no longer holds .

8 J . Hamilton and W. S. Woolcock, Rev. Mod. P h y s . 35, 737 (1963).

ERRATA

Y = 2 STATES IN SU(6) THEORY. Freeman J . Dyson and Nguyen-huu Xuong [Phys. Rev. Letters 13, 815 (1964)].

Experiment on IT "-D scattering at 140 MeV1

shows a large ratio of inelastic to elastic scattering, indicating that many angular momenta contribute. The peak at 170 MeV (£* = 2160 MeV) is, therefore, not to be understood as belonging to a particular SU(6) representation. On the contrary, it seems to provide evidence that the splitting between SU(6) representation 490 and 1050 is small compared with the "SU(6)-violating" splitting between octet and decimet states of the single baryons. In this case, the hypothesis advanced in the second paragraph of our Letter is not valid. We thank Dr. R. Hof-stadter for referring us to the experimental paper quoted above, and Dr. S. Treiman and Dr. W. Alles for criticism.

1 E. G. Pewit t , T. H. F ie lds , G. B. Yodh, J . G. Fetkovich, and M. D e r r i c k , Phys . Rev. 131, 1826 (1963).

STUDY OF EXCHANGE INTEGRAL OF CRYSTALLINE 3He AT 0°K. L. H. Nosanow and William J . Mullin [Phys. Rev. Letters 14, 133 (1965)].

There is a typographical error in Eq. (12). It should read

V.. = v..-(ti2/2mf.2)(f..V.2f..-V.f..- V / ). V V ij 13 i 13 ii3 i ij

339