Some dynamical properties of the pion in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math>→<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math>νγ and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math>→<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mi mathvariant="normal">−</mi></mrow></msup></mrow></math>ν decays

Ching-Yieh Lee

doi:10.1103/PhysRevD.32.658

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Some dynamical properties of the pion in $π^{+}$ → $e^{+}$ νγ and $π^{+}$ → $e^{+}$ $e^{+}$ $e^{-}$ ν decays

Ching-Yieh Lee

Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan 115, Republic of China

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Phys. Rev. D 32, 658 – Published 1 August, 1985

DOI: https://doi.org/10.1103/PhysRevD.32.658

Abstract

We investigate some of the dynamical properties of the pion by explicitly calculating the γ and ξ parameters in $π^{+}$ → $e^{+}$ νγ and $π^{+}$ → $e^{+}$ $e^{+}$ $e^{-}$ ν decays within the relativistic quark model, nucleon-loop approximation, and the σ model. One of the purposes in this study is to clarify a sign ambiguity raised recently in the prediction of γ within the quark model. The second purpose is to give some precise predictions for ξ, which has not yet been discussed extensively. The last purpose in this analysis involves a possible connection between ξ and chiral-symmetry breaking. Within the σ model, this parameter is found to depend logarithmically upon $m_{π}$ , the explicit-breaking parameter of the symmetry.

References (24)

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This was already pointed out by the authors in Ref. 14.
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[c1] S. Adler, Phys. Rev. 177, 2426 (1969); J. S. Bell and R. Jackiw, Nuovo Cimento 60 A, 47 (1969).

[c2] J. Kogut et al., Phys. Rev. Lett. 48, 1140 (1982); , ibid. 50, 393 (1983); H. Hamber and G. Parisi, ibid. 47, 1792 (1981); J. Kogut, Rev. Mod. Phys. 55, 775 (1983).

[c3] D. A. Bryman, P. Depommier and C. Leroy, Phys. Rep. 88, 151 (1982) and references therein.

[c4] P. Depommier, J. Heintze, C. Rubbia and V. Soergel, Phys. Lett. 7, 285 (1963).

[c5] A. Stetz, J. Carroll, D. Ortendahl, V. Perez-Mendez, G. Igo, N. Chirapatpimol and M. A. Nasser, Phys. Rev. Lett. 33, 1455 (1974).

[c6] T. Das, V. S. Mathur and S. Okubo, Phys. Rev. Lett. 19, 859 (1967).

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

[c8] F. Scheck and A. Wullschleger, Nucl. Phys. B 67, 504 (1973).

[c9] S. F. Berezhnev et al., Yad. Fiz. 16, 185 (1972) [Sov. J. Nucl. Phys. 16, 99 (1973)]; G. Bardin et al., Nucl. Phys. B 120, 45 (1977); G. T. Adylov et al., ibid. B 128, 461 (1977); E. B. Dally et al., Phys. Rev. Lett. 39, 1176 (1977); A. Quenzer et al., Phys. Lett. 76 B, 512 (1978).

[c10] H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967).

[c11] W. Kummer and J. Kuti, Nuovo Cimento 45, 242 (1966).

[c12] M. Moreno, Phys. Rev. D 16, 720 (1977).

[c13] M. Moreno and J. Pestieau, Phys. Rev. D 13, 175 (1976).

[c14] R. Montemayor and M. Moreno, Phys. Rev. D 20, 250 (1979).

[c15] N. Paver and M. D. Scadron, Nuovo Cimento 78 A, 159 (1983).

[c16] M. Gell-Mann and M. Levy, Nuovo Cimento 16, 53 (1960).

[c17] This was already pointed out by the authors in Ref. 14.

[c18] K. Lane, Phys. Rev. D 10, 2605 (1974); P. Langacker, Phys. Rev. Lett. 34, 1592 (1975); M. A. B. Beg and S. S. Shei, Phys. Rev. D 12, 3092 (1975); H. Pagels, ibid. 19, 3080 (1979); R. Haymaker and J. Perez-Mercader, Phys. Lett. 106 B, 201 (1981); Phys. Rev. D 27, 1353 (1983).

[c19] L. N. Chang and N. P. Chang, Phys. Rev. D 29, 312 (1984).

[c20] S. Weinberg, Phys. Rev. Lett. 18, 188 (1967).

[c21] See also J. Kripfganz and C. Leroy, Phys. Rev. D 21, 1327 (1980).

[c22] V. N. Pervushin and M. K. Volkov, Phys. Lett. 58 B, 74 (1975).

[c23] T. Goldman and W. J. Wilson, Phys. Rev. D 15, 709 (1977).

[c24] L. F. Li and H. Pagels, Phys. Rev. Lett. 26, 1204 (1971).

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Some dynamical properties of the pion in $π^{+}$ → $e^{+}$ νγ and $π^{+}$ → $e^{+}$ $e^{+}$ $e^{-}$ ν decays

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Some dynamical properties of the pion in π+→e+νγ and π+→e+e+e−ν decays

Abstract

References (24)

Some dynamical properties of the pion in $π^{+}$ → $e^{+}$ νγ and $π^{+}$ → $e^{+}$ $e^{+}$ $e^{-}$ ν decays