Kaon Partial-Conservation-of-Axial-Vector-Current Anomaly and <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>L</mi></mrow></msub></mrow><mo>→</mo><mi>γ</mi><mi>γ</mi></math></span> Decay

Douglas W. McKay

doi:10.1103/PhysRevD.8.4182

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Kaon Partial-Conservation-of-Axial-Vector-Current Anomaly and $K_{L} \to γ γ$ Decay

Douglas W. McKay

University of Kansas, Lawrence, Kansas 66044

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Phys. Rev. D 8, 4182 – Published 1 December, 1973

DOI: https://doi.org/10.1103/PhysRevD.8.4182

Abstract

The low-energy theorem is derived which relates the invariant vertex function of $K_{L} \to γ γ$ to the corresponding function of $〈 2 γ | [Q_{5}^{6}, L_{w}] | 0 〉$ , where it is assumed that Schwinger and seagull terms, if present, cancel against each other. A chiral Lagrangian model is studied which satisfies PCAC and which has an octet weak Lagrangian with $[Q_{5}^{6}, L_{w}] = 0$ . In this model, the effective $K_{L} \to γ γ$ coupling constant produced by certain baryon loop graphs is found to remain finite as the momentum of the kaon goes to zero. This contradicts the low-energy theorem and indicates the failure of seagull and Schwinger terms to cancel. The effective coupling produced by this anomaly is estimated to give a rate roughly comparable to the experimental one. Implications for mesonic effective-Lagrangian studies of $K$ decays are discussed.

References (24)

J. S. Bell and R. Jackiw, Nuovo Cimento 60, 47 (1969)
S. L. Adler, Phys. Rev. 177, 2426 (1969)
S. L. Adler, in Lectures on Elementary Particles and Quantum Field Theory—1970 (MIT Press, Cambridge, Mass., 1970) R. Jackiw, in Lectures on Current Algebra and its Applications (Princeton Univ. Press, Princeton, New Jersey, 1972)
R. Jackiw and K. Johnson, Phys. Rev. 182, 1459 (1969) C. R. Hagen, ibid. 188, 2416 (1969) J. Schwinger, 82, 664 (1951)
S. L. Adler, [2] S. L. Adler and W. A. Bardeen, Phys. Rev. 182, 1517 (1969) A. Zee, Phys. Rev. Lett. 29, 1198 (1972) J. H. Lowenstein and B. Schroer, Phys. Rev. D 7, 1929 (1973) C. Becchi, CERN Report No. 1611, 1973 (unpublished)
W. A. Bardeen, Phys. Rev. 184, 1848 (1969) R. W. Brown, C.-C. Shih, and B.-L. Young, 186, 1491 (1969) J. Wess and B. Zumino, Phys. Lett. 37B, 95 (1971)
D. J. Gross and R. Jackiw, Phys. Rev. D 6, 477 (1972) C. Bouchiat, J. Iliopoulos, and Ph. Meyer, Phys. Lett. 38B, 519 (1972)
K. G. Wilson, Phys. Rev. 179, 1499 (1969) R. J. Crewther, Phys. Rev. Lett. 28, 1421 (1972)
M. V. Terentiev, Zh. Eksp. Teor. Fiz. Pis'ma Red. 14, 140 (1971) [JETP Lett. 14, 94 (1971)] S. L. Adler, B. W. Lee, S. B. Treiman, and A. Zee, Phys. Rev. D 4, 3497 (1971) R. Aviv and A. Zee, ibid. 5, 2372 (1972) M. S. Chanowitz, M.-S. Chen, and L.-F. Li, ibid. 7, 3104 (1973)
J. Wess and B. Zumino, [6]
D. Sutherland and M. Veltman, Nucl. Phys. B2, 433 (1967)
D. McKay and H. Munczek [Phys. Rev. D 6, 2040 (1972)] R. Rockmore and T. F. Wong [Phys. Rev. Lett. 28, 1736 (1972) Phys. Rev. D 7, 3425 (1973)] [M. Gronau, 5, 118 (1972)]
Jackiw and Johnson ([4])
J. J. Sakurai, Phys. Rev. 156, 1508 (1967) Y. Hara and Y. Nambu, Phys. Rev. Lett. 16, 875 (1966)
Omitted endnote
Omitted endnote
B. W. Lee, Phys. Rev. 170, 1359 (1968)
J. Schechter, Phys. Rev. 174, 1829 (1968)
Omitted endnote
Omitted endnote
R. F. Sarraga and H. J. Munczek, Phys. Rev. D 4, 2884 (1971) M. Moshe and P. Singer, Phys. Rev. Lett. 27, 1685 (1971)
B. R. Holstein, Nuovo Cimento 2A, 561 (1971)
I. Bars, M. B. Halpern, and M. Yoshimura, Phys. Rev. D 7, 1233 (1973) H. J. Munczek, University of Kansas report (unpublished)
[R. J. Abrams et al., Phys. Rev. Lett. 29, 1118 (1972)]

[c1] J. S. Bell and R. Jackiw, Nuovo Cimento 60, 47 (1969)

[c2] S. L. Adler, Phys. Rev. 177, 2426 (1969)

[c3] S. L. Adler, in Lectures on Elementary Particles and Quantum Field Theory—1970 (MIT Press, Cambridge, Mass., 1970) R. Jackiw, in Lectures on Current Algebra and its Applications (Princeton Univ. Press, Princeton, New Jersey, 1972)

[c4] R. Jackiw and K. Johnson, Phys. Rev. 182, 1459 (1969) C. R. Hagen, ibid. 188, 2416 (1969) J. Schwinger, 82, 664 (1951)

[c5] S. L. Adler, [2] S. L. Adler and W. A. Bardeen, Phys. Rev. 182, 1517 (1969) A. Zee, Phys. Rev. Lett. 29, 1198 (1972) J. H. Lowenstein and B. Schroer, Phys. Rev. D 7, 1929 (1973) C. Becchi, CERN Report No. 1611, 1973 (unpublished)

[c6] W. A. Bardeen, Phys. Rev. 184, 1848 (1969) R. W. Brown, C.-C. Shih, and B.-L. Young, 186, 1491 (1969) J. Wess and B. Zumino, Phys. Lett. 37B, 95 (1971)

[c7] D. J. Gross and R. Jackiw, Phys. Rev. D 6, 477 (1972) C. Bouchiat, J. Iliopoulos, and Ph. Meyer, Phys. Lett. 38B, 519 (1972)

[c8] K. G. Wilson, Phys. Rev. 179, 1499 (1969) R. J. Crewther, Phys. Rev. Lett. 28, 1421 (1972)

[c9] M. V. Terentiev, Zh. Eksp. Teor. Fiz. Pis'ma Red. 14, 140 (1971) [JETP Lett. 14, 94 (1971)] S. L. Adler, B. W. Lee, S. B. Treiman, and A. Zee, Phys. Rev. D 4, 3497 (1971) R. Aviv and A. Zee, ibid. 5, 2372 (1972) M. S. Chanowitz, M.-S. Chen, and L.-F. Li, ibid. 7, 3104 (1973)

[c10] J. Wess and B. Zumino, [6]

[c11] D. Sutherland and M. Veltman, Nucl. Phys. B2, 433 (1967)

[c12] D. McKay and H. Munczek [Phys. Rev. D 6, 2040 (1972)] R. Rockmore and T. F. Wong [Phys. Rev. Lett. 28, 1736 (1972) Phys. Rev. D 7, 3425 (1973)] [M. Gronau, 5, 118 (1972)]

[c13] Jackiw and Johnson ([4])

[c14] J. J. Sakurai, Phys. Rev. 156, 1508 (1967) Y. Hara and Y. Nambu, Phys. Rev. Lett. 16, 875 (1966)

[c15] Omitted endnote

[c16] Omitted endnote

[c17] B. W. Lee, Phys. Rev. 170, 1359 (1968)

[c18] J. Schechter, Phys. Rev. 174, 1829 (1968)

[c19] Omitted endnote

[c20] Omitted endnote

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

[c22] B. R. Holstein, Nuovo Cimento 2A, 561 (1971)

[c23] I. Bars, M. B. Halpern, and M. Yoshimura, Phys. Rev. D 7, 1233 (1973) H. J. Munczek, University of Kansas report (unpublished)

[c24] [R. J. Abrams et al., Phys. Rev. Lett. 29, 1118 (1972)]

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Kaon Partial-Conservation-of-Axial-Vector-Current Anomaly and $K_{L} \to γ γ$ Decay

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Kaon Partial-Conservation-of-Axial-Vector-Current Anomaly and KL→γγ Decay

Abstract

References (24)

Kaon Partial-Conservation-of-Axial-Vector-Current Anomaly and $K_{L} \to γ γ$ Decay