Lepton pair decays of the <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></math></span> meson in the light-front model

C. Q. Geng; C. W. Hwang

doi:10.1103/PhysRevD.66.034005

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Lepton pair decays of the $K_{L}$ meson in the light-front model

C. Q. Geng^1,2 and C. W. Hwang¹

¹Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China
²Theory Group, TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, Canada V6T 2A3

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Phys. Rev. D 66, 034005 – Published 9 August, 2002

DOI: https://doi.org/10.1103/PhysRevD.66.034005

Abstract

We analyze $K_{L}$ lepton pair decays of $K_{L} \to l^{+} l^{-} γ$ and $K_{L} \to l^{+} l^{-} l^{' +} l^{' -} (l, l^{'} = e, μ)$ within the framework of the light-front QCD approach (LFQA). With the $K_{L} \to γ^{*} γ^{*}$ form factors evaluated in a model with the LFQA, we calculate the decay branching ratios and find that our results are all consistent with the experimental data. In addition, we study $K_{L} \to l^{+} l^{-}$ decays. We point out that our prediction for $K_{L} \to e^{+} e^{-}$ is about $20 %$ smaller than that in chiral perturbation theory. We also discuss whether one could extract the short-distance physics from $K_{L} \to μ^{+} μ^{-} .$

References (43)

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S.L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1585 (1973); ibid.M.K. Gaillard and B.W. Lee, 10, 897 (1974); ibid.M.K. Gaillard, B.W. Lee, and R.E. Shrock, 13, 2674 (1976); R.E. Shrock and M.B. Voloshin, Phys. Lett. 87B, 375 (1979).
A.J. Buras, Phys. Rev. Lett. 46, 1354 (1981); L. Bergstrom, E. Masso, P. Singer, and D. Wyler, Phys. Lett. 134B, 373 (1984); C.Q. Geng and J.N. Ng, Phys. Rev. D 41, 2351 (1990).
L. Bergstrom, E. Masso, and P. Singer, Phys. Lett. B 249, 141 (1990); G. Bélanger and C.Q. Geng, Phys. Rev. D 43, 140 (1991); L. Ritchie and S.G. Wojcicki, Rev. Mod. Phys. 65, 1149 (1993); L. Littenberg and G. Valencia, Annu. Rev. Nucl. Part. Sci. 43, 729 (1993).
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C.W. Hwang, Phys. Rev. D 64, 034011 (2001).
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E799 Collaboration, N.B. Spencer et al., Phys. Rev. Lett. 74, 3323 (1995).
E845 Collaboration, K.E. Ohl et al., Phys. Rev. Lett. 65, 1407 (1990).
NA31 Collaboration, C.D. Barr et al., Phys. Lett. B 240, 283 (1990).
H. Wahl (private communication).
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Ll. Ametller, A. Bramon, and E. Massó, Phys. Rev. D 48, 3388 (1993).
L. Bergström et al., Phys. Lett. 126B, 117 (1983).
E871 Collaboration, D. Ambrose et al., Phys. Rev. Lett. 81, 4309 (1998).
E871 Collaboration, D. Ambrose et al., Phys. Rev. Lett. 84, 1389 (2000).
G. Buchalla and A.J. Buras, Nucl. Phys. B412, 106 (1996); A.J. Buras and R. Fleischer, hep-ph/9704376.
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[c1] For a review, see L. Littenberg and G. Valencia, Annu. Rev. Nucl. Part. Sci. 43, 729 (1993).

[c2] S.L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1585 (1973); ibid.M.K. Gaillard and B.W. Lee, 10, 897 (1974); ibid.M.K. Gaillard, B.W. Lee, and R.E. Shrock, 13, 2674 (1976); R.E. Shrock and M.B. Voloshin, Phys. Lett. 87B, 375 (1979).

[c3] A.J. Buras, Phys. Rev. Lett. 46, 1354 (1981); L. Bergstrom, E. Masso, P. Singer, and D. Wyler, Phys. Lett. 134B, 373 (1984); C.Q. Geng and J.N. Ng, Phys. Rev. D 41, 2351 (1990).

[c4] L. Bergstrom, E. Masso, and P. Singer, Phys. Lett. B 249, 141 (1990); G. Bélanger and C.Q. Geng, Phys. Rev. D 43, 140 (1991); L. Ritchie and S.G. Wojcicki, Rev. Mod. Phys. 65, 1149 (1993); L. Littenberg and G. Valencia, Annu. Rev. Nucl. Part. Sci. 43, 729 (1993).

[c5] G. Valencia, Nucl. Phys. B517, 339 (1998).

[c6] J.O. Eeg, K. Kumericki, and I. Picek, Eur. Phys. J. C 1, 531 (1998); D. Gomez Dumm and A. Pich, Phys. Rev. Lett. 80, 4633 (1998); ibid.M. Knecht, S. Peris, M. Perrottet, and E. de Rafael, 83, 5230 (1999).

[c7] G. D’Ambrosio, G. Isidori, and J. Portoles, Phys. Lett. B 423, 385 (1998).

[c8] KTeV Collaboration, A. Alavi-Harati et al., Phys. Rev. Lett. 87, 071801 (2001).

[c9] KTeV Collaboration, A. Alavi-Harati et al., Phys. Rev. Lett. 86, 5425 (2001).

[c10] NA48 Collaboration, A. Lai et al., hep-ex/0006040.

[c11] KTeV Collaboration, A. Alavi-Harati et al., Phys. Rev. Lett. 87, 111802 (2001).

[c12] T. Miyazaki and E. Takasugi, Phys. Rev. D 8, 2051 (1973).

[c13] L. Zhang and J.L. Goity, Phys. Lett. B 398, 387 (1997); Phys. Rev. D 57, 7031 (1998).

[c14] For a review, see B.D. Ksister and W.N. Polyzou, Adv. Nucl. Phys. 20, 225 (1991); F. Coester, Prog. Part. Nucl. Phys. 29, 1 (1992).

[c15] F. Cardarelli et al., Phys. Rev. D 53, 6682 (1996); P.J. O’Donnell et al., Phys. Lett. B 325, 219 (1994).

[c16] N.B. Demchuk et al., Phys. At. Nucl. 59, 2152 (1996).

[c17] C.Y. Cheung, C.W. Hwang, and W.M. Zhang, Z. Phys. C 75, 657 (1997).

[c18] H.Y. Cheng, C.Y. Cheung, and C.W. Hwang, Phys. Rev. D 55, 1559 (1997).

[c19] W. Jaus, Phys. Rev. D 41, 3394 (1990); ibid.44, 2851 (1991); Z. Phys. C 54, 611 (1992).

[c20] F.J. Gilman and M.B. Wise, Phys. Rev. D 19, 976 (1979).

[c21] G. Eilam et al., Phys. Rev. D 53, 3629 (1996); ibid.X.G. He and G. Valencia, 61, 075003 (2000); ibid.J. Tandean, 61, 114022 (2000), and references therein.

[c22] C.W. Hwang, Phys. Lett. B 530, 93 (2002).

[c23] C.W. Hwang, Phys. Rev. D 64, 034011 (2001).

[c24] H.J. Melosh, Phys. Rev. D 9, 1095 (1974).

[c25] W.M. Zhang, Chin. J. Phys. (Taipei) 31, 717 (1994); hep-ph/9510428.

[c26] H.M. Choi and C.R. Ji, Phys. Rev. D 59, 074015 (1999).

[c27] W. Jaus, Phys. Rev. D 44, 2851 (1991).

[c28] Particle Data Group, D.E. Groom et al., Eur. Phys. J. C 15, 1 (2000).

[c29] S.R. Amendolia et al., Phys. Lett. B 178, 435 (1986).

[c30] E799 Collaboration, N.B. Spencer et al., Phys. Rev. Lett. 74, 3323 (1995).

[c31] E845 Collaboration, K.E. Ohl et al., Phys. Rev. Lett. 65, 1407 (1990).

[c32] NA31 Collaboration, C.D. Barr et al., Phys. Lett. B 240, 283 (1990).

[c33] H. Wahl (private communication).

[c34] H. Burkhardt et al., Phys. Lett. B 199, 139 (1987).

[c35] T. Inami and C.S. Lim, Prog. Theor. Phys. 65, 297 (1981).

[c36] For a recent review, see A.J. Buras, hep-ph/0101336.

[c37] Ll. Ametller, A. Bramon, and E. Massó, Phys. Rev. D 48, 3388 (1993).

[c38] L. Bergström et al., Phys. Lett. 126B, 117 (1983).

[c39] E871 Collaboration, D. Ambrose et al., Phys. Rev. Lett. 81, 4309 (1998).

[c40] E871 Collaboration, D. Ambrose et al., Phys. Rev. Lett. 84, 1389 (2000).

[c41] G. Buchalla and A.J. Buras, Nucl. Phys. B412, 106 (1996); A.J. Buras and R. Fleischer, hep-ph/9704376.

[c42] M. Ciuchini et al., J. High Energy Phys. 07, 013 (2001).

[c43] C. Q. Geng and C. W. Hwang (in progress).

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Lepton pair decays of the $K_{L}$ meson in the light-front model

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Lepton pair decays of the KL meson in the light-front model

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Lepton pair decays of the $K_{L}$ meson in the light-front model