<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math></span> Invariance and the Unitarity Limit in <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow><mo>→</mo><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math></span>

H. H. Chen; S. Y. Lee

doi:10.1103/PhysRevD.4.903

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$T$ Invariance and the Unitarity Limit in $K_{L}^{0} \to μ^{+} μ^{-}$

H. H. Chen^*

S. Y. Lee^†

Department of Physics, University of California, Irvine, California 92664

Department of Physics, University of California, Los Angeles, California 90024

^*Work supported by the U. S. Atomic Energy Commission.
^†Supported in part by the National Science Foundation.

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Phys. Rev. D 4, 903 – Published 1 August, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.903

Abstract

The role of $T$ invariance in the unitarity (lower) limit of the decay $K_{L}^{0} \to μ^{+} μ^{-}$ is examined. We note that the assumption of $T$ invariance is necessary only insofar as $ε$ , the $CP$ -violating parameter in the neutral $K$ system, is nonzero. Because of the smallness of this parameter, a chance cancellation appears unlikely. Therefore, the unitarity (lower) limit for $K_{L}^{0} \to μ^{+} μ^{-}$ can be decreased only (with the above exception) by including in the unitarity sum intermediate states other than the two-photon state (e.g., three-pion states).

References (15)

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([4])
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[c1] B. L. Ioffe and E. P. Shabalin, Yadern. Fiz. 6, 828 (1967) [Sov. J. Nucl. Phys. 6, 603 (1968)] R. N. Mohapatra, J. S. Rao, and R. E. Marshak, Phys. Rev. Letters 20, 1081 (1968) Phys. Rev. 171, 1502 (1968) M. Gell-Mann, M. L. Goldberger, N. M. Kroll, and F. E. Low, ibid. 179, 1518 (1969)

[c2] M. L. Good, L. Michel, and E. de Rafael, Phys. Rev. 151, 1194 (1966)

[c3] M. A. Baqi Bég, Phys. Rev. 132, 426 (1963) L. M. Sehgal, Nuovo Cimento 45, 785 (1966) Phys. Rev. 183, 1511 (1969) C. Quigg and J. D. Jackson, Lawrence Radiation Laboratory Report No. UCRL-18487 (unpublished)

[c4] B. R. Martin, E. de Rafael, and J. Smith, Phys. Rev. D 2, 179 (1970)

[c5] A. Pais and S. B. Treiman, Phys. Rev. 176, 1974 (1968)

[c6] M. Banner, J. W. Cronin, J. K. Liu, and J. E. Pilcher, Phys. Rev. Letters 21, 1103 (1968) R. Arnold, I. A. Budagov, D. C. Cundy, G. Myatt, F. Nezrick, G. H. Trilling, W. Venus, H. Yoshiki, B. Aubert, P. Heusse, E. Nagy, and C. Pascaud, Phys. Letters 28B, 56 (1968)

[c7] [4]

[c8] A. R. Clark, T. Elioff, R. C. Field, H. J. Frisch, R. P. Johnson, L. T. Kerth, and W. A. Wenzel, Bull. Am. Phys. Soc. 15, 1633 (1970) Phys. Rev. Letters 26, 1667 (1971) P. Darriulat, M. I. Ferrero, C. Grosso, M. Holder, J. Pilcher, E. Radermacher, C. Rubbia, M. Scire, A. Stande, and K. Tittel, Phys. Letters 33B, 249 (1970)

[c9] J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Phys. Rev. Letters 13, 138 (1964)

[c10] T. T. Wu and C. N. Yang, Phys. Rev. Letters 13, 380 (1964) S. B. Treiman, in Proceedings of the Fourteenth International Conference on High-Energy Physics, Vienna, 1968, edited by J. Prentki and J. Steinberger (CERN, Geneva, Switzerland, 1968), p. 305 T. D. Lee and L. Wolfenstein, Phys. Rev. 138, B1490 (1965) V. V. Barmin et al., Phys. Letters 33B, 377 (1970)

[c11] [4] C. G. Callan and S. B. Treiman [Phys. Rev. Letters 18, 1083 (1967) ibid.19, 57(E) (1967)]

[c12] ([4])

[c13] B. D. Hyams, N. Koch, D. C. Potter, L. Von Lindern, E. Lorenz, G. Lütjens, U. Stierlin, and P. Weilhammer, Phys. Letters 29B, 521 (1969) R. D. Stutzke, A. Abashian, L. H. Jones, P. M. Mantsch, J. R. Orr, and J. H. Smith, Phys. Rev. 177, 2009 (1969)

[c14] G. R. Farrar and S. B. Treiman, Phys. Rev. D 4, 257 (1971)

[c15] N. H. Christ and T. D. Lee, Phys. Rev. D 4, 209 (1971)

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$T$ Invariance and the Unitarity Limit in $K_{L}^{0} \to μ^{+} μ^{-}$

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T Invariance and the Unitarity Limit in KL0→μ+μ−

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References (15)

$T$ Invariance and the Unitarity Limit in $K_{L}^{0} \to μ^{+} μ^{-}$