# Implications of Current Algebra for η Decay— A Summary

## 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 Adler^{1} and Weissberger^{2} 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 processes^{3} and in giving some details of nonleptonic decays.^{4} Hara and Nambu^{4} 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.

## Keywords

Matrix Element Current Algebra Pseudoscalar Meson Dalitz Plot Axial Vector Current## Preview

Unable to display preview. Download preview PDF.

## References

- 1.
- 2.
- 3.C. G. Callan and S. B. Treiman,
*Phys. Rev. Letters***16**: 153 (1966).MathSciNetADSCrossRefGoogle Scholar - 4.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).ADSCrossRefGoogle Scholar - 5.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).ADSGoogle Scholar - 6.S. Weinberg,
*Phys. Rev. Letters***17**: 616 (1966); N. N. Khuri,*Phys. Rev*.**153**: 1477 (1967).ADSCrossRefGoogle Scholar - 7.Columbia Berkeley-Purdue-Wisconsin-Yale Collaborators,
*Phys. Rev*.**149**: 1044 (1966).CrossRefGoogle Scholar - 8.
- 9.W. Bardeen, L. S. Brown, B. W. Lee and H. T. Nieh,
*Phys. Rev. Letters***18**: 1170 (1967).ADSCrossRefGoogle Scholar - 10.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).ADSCrossRefGoogle Scholar - 11.F. Crawford and L. R. Price,
*Phys. Rev*.**167**: 1339 (1968); also Aditya Kumar and R. Ramachadran, T.I.F.R. preprint (unpublished).ADSCrossRefGoogle Scholar - 12.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.ADSGoogle Scholar - 13.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).ADSCrossRefGoogle Scholar