Low-Energy Axial-Vector Form Factors for <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>K</mi></mrow><mrow><mi>e</mi><mn>4</mn><mn></mn></mrow></msub></mrow></math></span> Decay Based on Broken Chiral Symmetry

B. R. Wienke; N. G. Deshpande

doi:10.1103/PhysRevD.5.725

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Low-Energy Axial-Vector Form Factors for $K_{e 4}$ Decay Based on Broken Chiral Symmetry

B. R. Wienke^* and N. G. Deshpande

Department of Physics, Northwestern University, Evanston, Illinois 60201

^*Present address: Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87544.

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Phys. Rev. D 5, 725 – Published 1 February, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.725

Abstract

We present an analysis of $K_{e 4}$ decay, particularly the process, $K^{+} \to π^{+} π^{-} e^{+} ν$ , using the techniques of current algebra and the $(3^{*}, 3) \oplus (3, 3^{*})$ -breaking model. The axial-vector form factors with explicit dependence on the chiral-symmetry parameters are obtained at the points $k^{2} = p^{2} = q^{2} = 0$ and $k^{2} = m_{K}^{2}$ , $p^{2} = q^{2} = 0$ and predictions compared with experimental rates and distributions. Discussion and comparison of our results with other recent analyses are also given. In particular, we find that $f_{K} = f_{π}$ and $f_{κ} = 0$ gives good over-all agreement with the experimental rate, the fitted form factors, and the experimental distributions although small breakings in $\frac{f_{K}}{f_{π}}$ and somewhat larger breakings in $\frac{f_{κ}}{f_{π}}$ are not ruled out.

References (13)

C. G. Callan and S. B. Treiman, Phys. Rev. Letters 16, 153 (1966) S. Weinberg, ibid. 17, 336 (1966) A. K. Mohanti and R. E. Marshak, Nuovo Cimento 52A, 467 (1967) ibid.54A, 213(E) (1968) R. Dutt, K. C. Gupta, and J. S. Vaishya, Phys. Rev. 175, 1884 (1968) A. Q. Sarker, ibid. 176, 1959 (1968) ibid.176, 1971 (1968) S. N. Biswas, R. Dutt, and K. C. Gupta, Ann. Phys. (N.Y.) 52, 366 (1969) S. N. Biswas, R. Dutt, P. Nanda, and L. K. Pandit, Phys. Rev. D 1, 1445 (1970) S. C. Chhajlany, L. K. Pandit, and G. Rajasekaran, 2, 1934 (1970) R. Dutt and R. Majumdar, Phys. Rev. 184, 1950 (1968) I. S. Gerstein and H. J. Schnitzer, ibid. 175, 1876 (1968) S. P. de Alwis, Phys. Rev. D 1, 213 (1970)
S. Weinberg, Phys. Rev. Letters 16, 879 (1966)
I. S. Gerstein and H. J. Schnitzer, Phys. Rev. 170, 1638 (1968)
N. Cabibbo, Phys. Rev. Letters 10, 531 (1963)
N. Cabibbo and A. Maksymowicz, Phys. Rev. 137, B438 (1965) A. Pais and S. B. Treiman, ibid. 168, 1858 (1968)
I. S. Gerstein and H. J. Schnitzer, Phys. Rev. 170, 1638 (1968)
S. Weinberg, Phys. Rev. Letters 18, 507 (1967)
M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968) P. R. Auvil and N. G. Deshpande, ibid. 183, 1463 (1969)
A. Q. Sarker, Phys. Rev. 176, 1971 (1968)
K. Kawarabayashi and M. Suzuki, Phys. Rev. Letters 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966)
R. W. Birge et al., Phys. Rev. 139, B1600 (1965)
R. P. Ely et al., Phys. Rev. 180, 1319 (1969)
F. A. Berends, A. Donnachie, and G. C. Oades, Nucl. Phys. B3, 569 (1967)

[c1] C. G. Callan and S. B. Treiman, Phys. Rev. Letters 16, 153 (1966) S. Weinberg, ibid. 17, 336 (1966) A. K. Mohanti and R. E. Marshak, Nuovo Cimento 52A, 467 (1967) ibid.54A, 213(E) (1968) R. Dutt, K. C. Gupta, and J. S. Vaishya, Phys. Rev. 175, 1884 (1968) A. Q. Sarker, ibid. 176, 1959 (1968) ibid.176, 1971 (1968) S. N. Biswas, R. Dutt, and K. C. Gupta, Ann. Phys. (N.Y.) 52, 366 (1969) S. N. Biswas, R. Dutt, P. Nanda, and L. K. Pandit, Phys. Rev. D 1, 1445 (1970) S. C. Chhajlany, L. K. Pandit, and G. Rajasekaran, 2, 1934 (1970) R. Dutt and R. Majumdar, Phys. Rev. 184, 1950 (1968) I. S. Gerstein and H. J. Schnitzer, ibid. 175, 1876 (1968) S. P. de Alwis, Phys. Rev. D 1, 213 (1970)

[c2] S. Weinberg, Phys. Rev. Letters 16, 879 (1966)

[c3] I. S. Gerstein and H. J. Schnitzer, Phys. Rev. 170, 1638 (1968)

[c4] N. Cabibbo, Phys. Rev. Letters 10, 531 (1963)

[c5] N. Cabibbo and A. Maksymowicz, Phys. Rev. 137, B438 (1965) A. Pais and S. B. Treiman, ibid. 168, 1858 (1968)

[c6] I. S. Gerstein and H. J. Schnitzer, Phys. Rev. 170, 1638 (1968)

[c7] S. Weinberg, Phys. Rev. Letters 18, 507 (1967)

[c8] M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968) P. R. Auvil and N. G. Deshpande, ibid. 183, 1463 (1969)

[c9] A. Q. Sarker, Phys. Rev. 176, 1971 (1968)

[c10] K. Kawarabayashi and M. Suzuki, Phys. Rev. Letters 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966)

[c11] R. W. Birge et al., Phys. Rev. 139, B1600 (1965)

[c12] R. P. Ely et al., Phys. Rev. 180, 1319 (1969)

[c13] F. A. Berends, A. Donnachie, and G. C. Oades, Nucl. Phys. B3, 569 (1967)

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Low-Energy Axial-Vector Form Factors for $K_{e 4}$ Decay Based on Broken Chiral Symmetry

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Low-Energy Axial-Vector Form Factors for Ke4 Decay Based on Broken Chiral Symmetry

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References (13)

Low-Energy Axial-Vector Form Factors for $K_{e 4}$ Decay Based on Broken Chiral Symmetry