Nonleptonic kaon decay

M. A. Ahmed

doi:10.1103/PhysRevD.32.671

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Nonleptonic kaon decay

M. A. Ahmed

Physics Department, Kuwait University, Kuwait

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Phys. Rev. D 32, 671 – Published 1 August, 1985

DOI: https://doi.org/10.1103/PhysRevD.32.671

Abstract

Current-algebra methods are used to analyze K→2π decays. A study is made of the effects of terms which are usually made to vanish by the soft-pion procedure. For this purpose the pions are treated symmetrically and massless pions, $k^{2}$ = $q^{2}$ =0, are considered as an alternative to soft ones. Detailed numerical estimates are made for the various contributions arising from ‘‘left-left’’ and ‘‘left-right’’ operators.

References (25)

For a recent review see R. D. C. Miller and B. H. J. McKellar, Phys. Rep. 106, 169 (1984).
M. K. Gaillard and B. W. Lee, Phys. Rev. Lett. 33, 108 (1974); G. Altarelli and L. Maiani, Phys. Lett. 52B, 351 (1974).
K. G. Wilson, Phys. Rev. 179, 1499 (1969).
M. A. Shifman, A. I. Vainshtein and V. J. Zakharov, Nucl. Phys. B120, 315 (1977). See also A. I. Vainshtein, V. J. Zakharov and M. A. Shifman, Zh. Eksp. Teor. Fiz. 72, 1275 (1977) [Sov. Phys. JETP 45, 670 (1977)].
J. F. Donoghue, E. Golowich. W. A. Ponce and B. R. Holstein, Phys. Rev. D 21, 186 (1980) and references to previous work cited therein.
T. DeGrand, R. Jaffe, K. Johnson and J. Kiskis, Phys. Rev. D 12, 2060 (1975).
T. Tanuma, S. Oneda and K. Terasaki, Phys. Rev. D 29, 444 (1984); K. Terasaki, S. Oneda, and T. Tanuma ibid. 29, 456 (1984) K. Terasaki and S. Oneda, ibid. 29, 466 (1984).
S. Oneda and S. Matsuda, Phys. Lett. 37B, 105 (1971).
B. H. J. McKellar and M. D. Scadron, Phys. Rev. D 27, 157 (1983).
M. A. Ahmed and G. G. Ross, Phys. Lett. 61B, 287 (1976); see also M. D. Scadron, ibid. 95B, 123 (1980).
For a review of these methods see, e.g., D. Bailin, Weak Interactions (Hilger, London, 1982); R. E. Marshak, Riazuddin, and C. P. Ryan, Theory of Weak Interactions in Particle Physics (Academic, New York, 1969); for a recent review, see M. D. Scadron, Rep. Prog. Phys. 44, 213 (1981).
S. Weinberg, Phys. Rev. Lett. 16, 879 (1966).
H. Georgi and H. D. Politzer, Phys. Rev. D 9, 416 (1974); D. J. Gross and F. Wilczek, ibid. 9, 980 (1974).
See, for example, S. Weinberg, in I. I. Rabi Festchrift (Academy of Sciences, New York, 1978). For a review and extensive list of references see J. Gasser and H. Leutwyler. Phys. Rep. 87C, 77 (1982).
See, for example, Weinberg, (Ref. 14).
This is similar to the equivalence relationship for the case of PCAC and the pion field: $m_{π}$ ${}^{2}F_{π}$ φ ${}_{π^{i}}$ = i m hat ψ bar $γ_{5}$ $τ^{i}$ psi, where ψ = ( ${}_{d}^{u}$ ) and m hat is the common u- and d-quark mass. See, for example, T. D. Lee, Particle Physics and Field Theory (Harwood, New York, 1981).
T. Tanuma, Ph. D. Thesis, University of Maryland, 1983.
M. K. Gaillard and B. W. Lee, Phys. Rev. D 10, 897 (1974).
M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B147, 385 (1979). In this reference the authors discuss the validity of the vacuum-intermediate-state-dominance technique.
S. L. Glashow and S. Weinberg, Phys. Rev. Lett. 20, 224 (1986); M. Gell-Mann, R. Oakes and B. Renner, Phys. Rev. 175, 2195 (1986). See also M. D. Scadron cited in Ref. 12 above.
See Gasser and Leutwyler, Ref. 14.
Particle Data Group, Rev. Mod. Phys. 56, S1 (1984).
Y. Dupont and T. N. Pham, Phys. Rev. D 29, 1368 (1984).
J. F. Donoghue, Phys. Rev. D 30, 1499 (1984).
B. Gavela, A. Le Yaouanc, L. Oliver, O. Pene and J. C. Raynal, Phys. Lett. 148B, 225 (1984).

[c1] For a recent review see R. D. C. Miller and B. H. J. McKellar, Phys. Rep. 106, 169 (1984).

[c2] M. K. Gaillard and B. W. Lee, Phys. Rev. Lett. 33, 108 (1974); G. Altarelli and L. Maiani, Phys. Lett. 52B, 351 (1974).

[c3] K. G. Wilson, Phys. Rev. 179, 1499 (1969).

[c4] M. A. Shifman, A. I. Vainshtein and V. J. Zakharov, Nucl. Phys. B120, 315 (1977). See also A. I. Vainshtein, V. J. Zakharov and M. A. Shifman, Zh. Eksp. Teor. Fiz. 72, 1275 (1977) [Sov. Phys. JETP 45, 670 (1977)].

[c5] J. F. Donoghue, E. Golowich. W. A. Ponce and B. R. Holstein, Phys. Rev. D 21, 186 (1980) and references to previous work cited therein.

[c6] T. DeGrand, R. Jaffe, K. Johnson and J. Kiskis, Phys. Rev. D 12, 2060 (1975).

[c7] T. Tanuma, S. Oneda and K. Terasaki, Phys. Rev. D 29, 444 (1984); K. Terasaki, S. Oneda, and T. Tanuma ibid. 29, 456 (1984) K. Terasaki and S. Oneda, ibid. 29, 466 (1984).

[c8] S. Oneda and S. Matsuda, Phys. Lett. 37B, 105 (1971).

[c9] B. H. J. McKellar and M. D. Scadron, Phys. Rev. D 27, 157 (1983).

[c10] M. A. Ahmed and G. G. Ross, Phys. Lett. 61B, 287 (1976); see also M. D. Scadron, ibid. 95B, 123 (1980).

[c11] For a review of these methods see, e.g., D. Bailin, Weak Interactions (Hilger, London, 1982); R. E. Marshak, Riazuddin, and C. P. Ryan, Theory of Weak Interactions in Particle Physics (Academic, New York, 1969); for a recent review, see M. D. Scadron, Rep. Prog. Phys. 44, 213 (1981).

[c12] S. Weinberg, Phys. Rev. Lett. 16, 879 (1966).

[c13] H. Georgi and H. D. Politzer, Phys. Rev. D 9, 416 (1974); D. J. Gross and F. Wilczek, ibid. 9, 980 (1974).

[c14] See, for example, S. Weinberg, in I. I. Rabi Festchrift (Academy of Sciences, New York, 1978). For a review and extensive list of references see J. Gasser and H. Leutwyler. Phys. Rep. 87C, 77 (1982).

[c15] See, for example, Weinberg, (Ref. 14).

[c16] This is similar to the equivalence relationship for the case of PCAC and the pion field: $m_{π}$ ${}^{2}F_{π}$ φ ${}_{π^{i}}$ = i m hat ψ bar $γ_{5}$ $τ^{i}$ psi, where ψ = ( ${}_{d}^{u}$ ) and m hat is the common u- and d-quark mass. See, for example, T. D. Lee, Particle Physics and Field Theory (Harwood, New York, 1981).

[c17] T. Tanuma, Ph. D. Thesis, University of Maryland, 1983.

[c18] M. K. Gaillard and B. W. Lee, Phys. Rev. D 10, 897 (1974).

[c19] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B147, 385 (1979). In this reference the authors discuss the validity of the vacuum-intermediate-state-dominance technique.

[c20] S. L. Glashow and S. Weinberg, Phys. Rev. Lett. 20, 224 (1986); M. Gell-Mann, R. Oakes and B. Renner, Phys. Rev. 175, 2195 (1986). See also M. D. Scadron cited in Ref. 12 above.

[c21] See Gasser and Leutwyler, Ref. 14.

[c22] Particle Data Group, Rev. Mod. Phys. 56, S1 (1984).

[c23] Y. Dupont and T. N. Pham, Phys. Rev. D 29, 1368 (1984).

[c24] J. F. Donoghue, Phys. Rev. D 30, 1499 (1984).

[c25] B. Gavela, A. Le Yaouanc, L. Oliver, O. Pene and J. C. Raynal, Phys. Lett. 148B, 225 (1984).

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Nonleptonic kaon decay

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