Weak-Interaction Effects in <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>→</mo><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow><mi>γ</mi></math></span>

Peter Herczeg; Paul Singer

doi:10.1103/PhysRevD.8.4107

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Weak-Interaction Effects in $η \to π^{+} π^{-} γ$

Peter Herczeg^* and Paul Singer^†

Department of Physics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213

^*Address from September 1, 1973: Los Alamos Scientific Laboratory, University of California, Los Alamos, New Mexico 87544.
^†Permanent address: Technion-Israel Institute of Technology, Haifa, Israel.

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Phys. Rev. D 8, 4107 – Published 1 December, 1973

DOI: https://doi.org/10.1103/PhysRevD.8.4107

Abstract

Parity-violating effects due to the strangeness-conserving nonleptonic weak interaction are studied in the process $η (X^{0}) \to π^{+} π^{-} γ$ . The circular polarization and the parity-violating linear polarization are calculated in the framework of the Cabibbo theory by using a pole model for the strong and electromagnetic interactions. The isoscalar ( $\sim {cos}^{2} θ$ ) and isovector ( $\sim {sin}^{2} θ$ ) components of the weak Hamiltonian are found to give comparable contributions. The magnitude of the circular polarization is obtained to be (1-5) × $10^{- 9}$ and the linear polarization, being dependent on final-state interactions, is smaller by nearly two orders of magnitude. In theories with a large isovector component in the weak nonleptonic Hamiltonian (theories involving neutral currents or second-class currents) the circular polarization can be larger, an estimate giving (1-3) × $10^{- 8}$ .

References (37)

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V. M. Lobashov et al., Zh. Eksp. Teor. Fiz. Pis'ma Red. 11, 124 (1970) [JETP Lett. 11, 76 (1970)] V. M. Lobashov et al.Nucl. Phys. A197, 241 (1972)
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P. Herczeg and P. Singer, Bull. Am. Phys. Soc. 18, 25 (1973)
Omitted endnote
B. H. J. McKellar and P. Pick, Phys. Rev. D 6, 2184 (1972)
Omitted endnote
B. Barrett and T. Truong, Phys. Rev. 147, 1161 (1966)
J. Bernstein, G. Feinberg, and T. D. Lee, Phys. Rev. 139, B1650 (1965) S. Barshay, Phys. Lett. 17, 78 (1965)
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Omitted endnote
Omitted endnote
Omitted endnote
Omitted endnote
B. W. Lee and H. T. Nieh, Phys. Rev. 166, 1507 (1968)
N. M. Kroll, T. D. Lee, and B. Zumino, Phys. Rev. 157, 1376 (1967)
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R. Gatto and L. Maiani, Phys. Lett. 26B, 95 (1967)
[25]
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([27])
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R. J. Blin-Stoyle and P. Herczeg, Phys. Lett. 23, 376 (1966)

[c1] E. M. Henley, in Proceedings of the International Conference on Few-Particle Problems in the Nuclear Interaction, Los Angeles, 1972, edited by I. Šlaus (North-Holland, Amsterdam, 1972) D. H. WilkinsonProceedings of the International Conference on Few-Particle Problems in the Nuclear Interaction, Los Angeles, 1972North-Holland, Amsterdam1972

[c2] E. Fischbach and D. Tadić, Phys. Rep. 6C, 123 (1973) M. Gari, ibid. 6C, 317 (1973) R. J. Blin-Stoyle, in Proceedings of the Topical Conference on Weak Interactions, CERN, 1969 (CERN, Geneva, 1969) E. M. Henley, Ann. Rev. Nucl. Sci. 19, 367 (1969)

[c3] V. M. Lobashov et al., Zh. Eksp. Teor. Fiz. Pis'ma Red. 11, 124 (1970) [JETP Lett. 11, 76 (1970)] V. M. Lobashov et al.Nucl. Phys. A197, 241 (1972)

[c4] B. H. J. McKellar and P. Pick, Nucl. Phys. B22, 625 (1970)

[c5] D. U. L. Yu, E. M. Henley, T. Keliher, and W. J. Pardee, Bull. Am. Phys. Soc. 17, 493 (1972)

[c6] E. M. Henley, A. H. Huffman, and D. U. L. Yu, Phys. Rev. D 7, 943 (1973)

[c7] M. Simonius, Phys. Lett. 41B, 415 (1972) V. R. Brown, E. M. Henley, and F. R. Krejs, Phys. Rev. Lett. 30, 770 (1973)

[c8] P. Herczeg and P. Singer, Bull. Am. Phys. Soc. 18, 25 (1973)

[c9] Omitted endnote

[c10] B. H. J. McKellar and P. Pick, Phys. Rev. D 6, 2184 (1972)

[c11] Omitted endnote

[c12] B. Barrett and T. Truong, Phys. Rev. 147, 1161 (1966)

[c13] J. Bernstein, G. Feinberg, and T. D. Lee, Phys. Rev. 139, B1650 (1965) S. Barshay, Phys. Lett. 17, 78 (1965)

[c14] J. J. Thaler et al., Phys. Rev. Lett. 29, 313 (1972)

[c15] Omitted endnote

[c16] Omitted endnote

[c17] Omitted endnote

[c18] Omitted endnote

[c19] B. W. Lee and H. T. Nieh, Phys. Rev. 166, 1507 (1968)

[c20] N. M. Kroll, T. D. Lee, and B. Zumino, Phys. Rev. 157, 1376 (1967)

[c21] M. Moshe and P. Singer, Phys. Rev. Lett. 27, 1685 (1971) Phys. Rev. D 6, 1379 (1972) R. F. Sarraga and H. J. Munczek, ibid. 4, 2884 (1971)

[c22] L. M. Brown, H. Munczek, and P. Singer, Phys. Rev. Lett. 21, 707 (1968) P. Singer, Phys. Rev. D 1, 86 (1970)

[c23] R. Gatto and L. Maiani, Phys. Lett. 26B, 95 (1967)

[c24] [25]

[c25] Particle Data Group, Rev. Mod. Phys. 45, 51 (1973)

[c26] ([27])

[c27] H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967) S. G. Brown and G. B. West, ibid. 180, 1613 (1969)

[c28] M. Gell-Mann, D. Sharp, and W. G. Wagner, Phys. Rev. Lett. 8, 261 (1962) L. M. Brown and P. Singer, ibid. 8, 460 (1962) ibid.16, 424E (1966)

[c29] F. Crawford and L. Price, Phys. Rev. Lett. 16, 333 (1966) P. J. Litchfield et al., Phys. Lett. 24B, 486 (1967) A. M. Cnops et al., ibid. 26B, 398 (1968) J. J. Thaler, Columbia University Thesis, Nevis-194, 1972 (unpublished) J. G. Layter et al., Phys. Rev. D 7, 2565 (1973) ibid.7, 2569 (1973)

[c30] D. Benaksas et al., Phys. Lett. 39B, 289 (1972) ibid.42B, 507 (1972)

[c31] G. Ascoli et al., Phys. Rev. Lett. 20, 1411 (1968) A. Werbrouck et al., Nuovo Cimento Lett. 6, 1267 (1970) M. Afzal et al., DESY Report No. 72/63 (unpublished) R. L. Ott, Berkeley thesis, LBL-1547 (unpublished)

[c32] P. Shen and K. Kang, Phys. Rev. D 7, 269 (1973) F. J. Gilman and M. Kugler, Phys. Rev. Lett. 30, 518 (1973) G. Fourez, Phys. Rev. 178, 2454 (1969)

[c33] J. Crennell et al., Phys. Rev. Lett. 24, 781 (1970) G. Rinauds et al., Nuovo Cimento 5A, 239 (1971) J. W. Lamsa et al., Nucl. Phys. B41, 388 (1972)

[c34] J. Ballam et al., Phys. Rev. D 1, 94 (1970)

[c35] B. H. J. McKellar and P. Pick, Phys. Rev. D 7, 260 (1973)

[c36] B. d'Espagnat, Phys. Lett. 1, 209 (1963) R. F. Dashen, S. C. Frautschi, M. Gell-Mann, and Y. Hara, in The Eightfold Way, edited by M. Gell-Mann and Y. Ne'eman (Benjamin, New York, 1964), p. 254 G. Segrè, Phys. Rev. 173, 1730 (1968) T. D. Lee, ibid. 171, 1731 (1968) R. J. Oakes, Phys. Rev. Lett. 20, 1539 (1968) D. Bailin, A. Love, and D. V. Nanopoulos, Rutherford Laboratory report, 1973 (unpublished)

[c37] R. J. Blin-Stoyle and P. Herczeg, Phys. Lett. 23, 376 (1966)

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Weak-Interaction Effects in $η \to π^{+} π^{-} γ$

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Weak-Interaction Effects in η→π+π−γ

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Weak-Interaction Effects in $η \to π^{+} π^{-} γ$