Elusive ‘‘penguin’’ mechanism for <i>K</i> decay

Ling-Lie Chau; Hai-Yang Cheng; Wai-Yee Keung

doi:10.1103/PhysRevD.32.1837

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Elusive ‘‘penguin’’ mechanism for K decay

Ling-Lie Chau

Hai-Yang Cheng

Wai-Yee Keung

Department of Physics, Brookhaven National Laboratory, Upton, New York 11973

Department of Physics, Brandeis University, Waltham, Massachusetts 02254

Department of Physics, Brookhaven National Laboratory, Upton, New York 11973

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Phys. Rev. D 32, 1837 – Published 1 October, 1985

DOI: https://doi.org/10.1103/PhysRevD.32.1837

Abstract

We observe that the uncertainty in estimating the ‘‘penguin’’ diagram is so large that its contribution to A(K→2π) can range from 30% to negligible, and thus no meaningful lower bound can be set for ε’/ε. We then map out the relations between the experimental measurements of ε’/ε and $m_{t}$ and the hadronic dynamical parameters for use in the search for the ‘‘penguin.’’

References (21)

M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B 120, 316 (1977); Zh. Eksp. Teor. Fiz. 72, 1245 (1977) [Sov. Phys. JETP 45, 670 (1977)].
F. J. Gilman and M. B. Wise, Phys. Lett. 83 B, 83 (1979); B. Gubernia and R. D. Peccei, Nucl. Phys. B 163, 1289 (1980).
P. Ginsparg and M. B. Wise, Phys. Lett. 127 B, 265 (1983).
F. J. Gilman and J. S. Hagelin, Phys. Lett. 126 B, 111 (1983); ibid. 133 B, 443 (1984).
See reports at the Twenty-second International Conference on High Energy Physics, Leipzig, 1984 (unpublished) of the experiments the Chicago-Stanford-Saclay collaboration, Fermilab experiment No. 617, and the BNL-Yale collaboration, BNL experiment No. 749.
This inconsistency was shown in the talk by B. Winstein at the APS Meeting, Washington, 1984 (unpublished).
J. F. Donoghue, E. Golowich, B. R. Holstein and W. A. Ponce, Phys. Rev. D 21, 186 (1980); ibid. 23, 1213 (1981).
J. F. Donoghue, Phys. Rev. D 30, 1499 (1984).
Notice the ironic reversal of the values of $B_{K}^{sprime}$ to those of $B_{K}$ from the bag and from the other estimates. Actually the vacuum-insertion value of $B_{K}^{sprime}$ is somewhat less than 0.33, which we use just to emphasize the irony of the situation.
P. Colic, B. Guberina, D. Tadic and J. Trampetic, Nucl. Phys. B 221, 141 (1983).
J. Donoghue, E. Golowich and B. Holstein, Phys. Lett. 119 B, 412 (1982).
J. Bijnens, H. Sonoda and M. B. Wise, Phys. Rev. Lett. 53, 2367 (1984).
L. L. Chau, in Proceedings of the 1980 Guangzhou Conference on Theoretical Particle Physics, Guangzhou, China, 1980 (Science Press/Van Nostrand, New York, 1981).
L.-L. Chau, Phys. Rep. 95 C, 1 (1983).
This point had been stressed on many previous occasions, e.g., L.-L. Chau, in Proceedings of the 8th International Workshop on Weak Interactions and Neutrinos, 1982, Javea, Spain (unpublished); see p. 38 of Ref. 14.
P. Ginsparg, S. Glashow and M. Wise, Phys. Rev. Lett. 50, 1415 (1983); E. A. Paschos, B. Stech and U. Türke, Phys. Lett. 128 B, 240 (1983); K. Kleinknecht and B. Renk, Z. Phys. C 20, 67 (1983); L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1984).
L.-L. Chau and W.-Y. Keung, Phys. Rev. D 29, 592 (1984); Phys. Rev. Lett. 53, 1802 (1984).
C. T. Hill, Phys. Lett. 97 B, 275 (1980).
If the pole contributions from π , ~ $η_{8}$ , and especially $η_{0}$ are important, another parameter needs to be added to Eq. (6). Here we use Eq. (6) without this additional parameter based upon one of the solutions obtained in a recent analysis on K -> 2 gamma by L.-L. Chau and H. Y. Cheng (unpublished).
T. Inami and C. S. Lim, Prog. Theor. Phys. 65, 297 (1981); ibid. 65, 1772(E) (1981).
The importance of this simultaneous analysis of epsilon and $ε^{sprime}$ / epsilon had been emphasized by K.-C. Chou, talk at Erice, Italy, 1984 (unpublished); see, also, K. C. Chou, Y. L. Wu, and Y. B. Xie, Academica Sinica, Institute fur Theoretical Physics, Beijing Report No. ASITP-84-005 (unpublished).

[c1] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B 120, 316 (1977); Zh. Eksp. Teor. Fiz. 72, 1245 (1977) [Sov. Phys. JETP 45, 670 (1977)].

[c2] F. J. Gilman and M. B. Wise, Phys. Lett. 83 B, 83 (1979); B. Gubernia and R. D. Peccei, Nucl. Phys. B 163, 1289 (1980).

[c3] P. Ginsparg and M. B. Wise, Phys. Lett. 127 B, 265 (1983).

[c4] F. J. Gilman and J. S. Hagelin, Phys. Lett. 126 B, 111 (1983); ibid. 133 B, 443 (1984).

[c5] See reports at the Twenty-second International Conference on High Energy Physics, Leipzig, 1984 (unpublished) of the experiments the Chicago-Stanford-Saclay collaboration, Fermilab experiment No. 617, and the BNL-Yale collaboration, BNL experiment No. 749.

[c6] This inconsistency was shown in the talk by B. Winstein at the APS Meeting, Washington, 1984 (unpublished).

[c7] J. F. Donoghue, E. Golowich, B. R. Holstein and W. A. Ponce, Phys. Rev. D 21, 186 (1980); ibid. 23, 1213 (1981).

[c8] J. F. Donoghue, Phys. Rev. D 30, 1499 (1984).

[c9] Notice the ironic reversal of the values of $B_{K}^{sprime}$ to those of $B_{K}$ from the bag and from the other estimates. Actually the vacuum-insertion value of $B_{K}^{sprime}$ is somewhat less than 0.33, which we use just to emphasize the irony of the situation.

[c10] P. Colic, B. Guberina, D. Tadic and J. Trampetic, Nucl. Phys. B 221, 141 (1983).

[c11] J. Donoghue, E. Golowich and B. Holstein, Phys. Lett. 119 B, 412 (1982).

[c12] J. Bijnens, H. Sonoda and M. B. Wise, Phys. Rev. Lett. 53, 2367 (1984).

[c13] L. L. Chau, in Proceedings of the 1980 Guangzhou Conference on Theoretical Particle Physics, Guangzhou, China, 1980 (Science Press/Van Nostrand, New York, 1981).

[c14] L.-L. Chau, Phys. Rep. 95 C, 1 (1983).

[c15] This point had been stressed on many previous occasions, e.g., L.-L. Chau, in Proceedings of the 8th International Workshop on Weak Interactions and Neutrinos, 1982, Javea, Spain (unpublished); see p. 38 of Ref. 14.

[c16] P. Ginsparg, S. Glashow and M. Wise, Phys. Rev. Lett. 50, 1415 (1983); E. A. Paschos, B. Stech and U. Türke, Phys. Lett. 128 B, 240 (1983); K. Kleinknecht and B. Renk, Z. Phys. C 20, 67 (1983); L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1984).

[c17] L.-L. Chau and W.-Y. Keung, Phys. Rev. D 29, 592 (1984); Phys. Rev. Lett. 53, 1802 (1984).

[c18] C. T. Hill, Phys. Lett. 97 B, 275 (1980).

[c19] If the pole contributions from π , ~ $η_{8}$ , and especially $η_{0}$ are important, another parameter needs to be added to Eq. (6). Here we use Eq. (6) without this additional parameter based upon one of the solutions obtained in a recent analysis on K -> 2 gamma by L.-L. Chau and H. Y. Cheng (unpublished).

[c20] T. Inami and C. S. Lim, Prog. Theor. Phys. 65, 297 (1981); ibid. 65, 1772(E) (1981).

[c21] The importance of this simultaneous analysis of epsilon and $ε^{sprime}$ / epsilon had been emphasized by K.-C. Chou, talk at Erice, Italy, 1984 (unpublished); see, also, K. C. Chou, Y. L. Wu, and Y. B. Xie, Academica Sinica, Institute fur Theoretical Physics, Beijing Report No. ASITP-84-005 (unpublished).

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Elusive ‘‘penguin’’ mechanism for K decay

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