Abstract
In calculations involving pions, the use of equal time commutation relations for the currents together with PCAC (Partial Conservation of Axial Vector Current) principle for the pion field operator has had some success over the last couple of years. Most spectacular among these is the calculation of Adler1 and Weissberger2 giving the weak axial vector renormalization g A in terms of the total crosssection in π-N scattering. Subsequently, the current algebra was found successful in relating various leptonic K-decay processes3 and in giving some details of nonleptonic decays.4 Hara and Nambu4 applied these techniques to successfully predict the energy spectrum of the unlike pion in the K → 3π decay. There is a lot of similarity between η → 3π and K → 3π decays, and it is natural to expect that similar mechanism explain both processes. However, the current algebra techniques that were so successful in K decays have not had a similar effect in η decays. We shall see that some of the difficulties will be traced to the ambiguity in the various extrapolations possible from the soft pion limit (where the current algebra makes definite predictions) to the physical pions. In this talk we shall review briefly the various approaches and then suggest an extrapolation procedure that we think best explains the π-decay process.
Presented at the Sixth Anniversary Symposium, The Institute of Mathematical Sciences, Adyar, Madras, India, January, 1968.
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References
S. L. Adler, Phys. Rev. Letters 14: 1051 (1965).
W. I. Weissberger, Phys. Rev. Letters 14: 1047 (1965).
C. G. Callan and S. B. Treiman, Phys. Rev. Letters 16: 153 (1966).
Y. Hara and Y. Nambu, Phys. Rev. Letters 16: 875 (1966); D.K. Elias and J. C. Taylors, Nuove Cimento 44 518(1966); S. K. Bose and S. N. Biswas Phys. Rev. Letters 16: 330 (1966): H. D. I. Aberbanel, Phys. Rev. 153: 154 (1967).
R. Ramachandran, Nuovo Cimento 47A: 669 (1967); S. K. Bose and A. M. Zimerman, Ibid 43A: 1165 (1966); R. Graham, S. Pakvasa, and L. O’Rafea-ataigh, Ibid 48A: 830 (1967).
S. Weinberg, Phys. Rev. Letters 17: 616 (1966); N. N. Khuri, Phys. Rev. 153: 1477 (1967).
Columbia Berkeley-Purdue-Wisconsin-Yale Collaborators, Phys. Rev. 149: 1044 (1966).
D. G. Sutterland, Phys. Letters 23: 384 (1966).
W. Bardeen, L. S. Brown, B. W. Lee and H. T. Nieh, Phys. Rev. Letters 18: 1170 (1967).
J. A. Cronin, Phys. Rev. 161: 1483 (1967); (see also) S. Weinberg, Phys. Rev. Letters 18: 188 (1967); J. Schwinger, Phys. Letters 24B: 473 (1967); Phys. Rev. Letters 18: 923 (1967); 19: 1154 (1967); and 19: 1501 (1967).
F. Crawford and L. R. Price, Phys. Rev. 167: 1339 (1968); also Aditya Kumar and R. Ramachadran, T.I.F.R. preprint (unpublished).
S. Baltay et al., report on preliminary data at the International Theoretical Physics Conference on particles and Fields, Rochester, September, 1967, (unpublished) give a value of 1.55 ± 0.25; S. Buniatov et al., Phys. Letters 25B: 560 (1967) give R = 1.38 ± 0.15. C. Baglin et al., preprint (presented at the APS Spring meeting, Washington, 1967) report 1.3 ± 0.4.
W. A. Dunn and R. Ramachandran, Phys. Rev. 153: 1558 (1967) Similar result for τ and τ′ decays was first noted by N. Khuri and S. B. Treiman, Phys. Rev. 119:1115(1960).
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Ramachandran, R., Kumar, A. (1969). Implications of Current Algebra for η Decay— A Summary. In: Ramakrishnan, A. (eds) Symposia on Theoretical Physics and Mathematics 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7673-6_4
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