Abstract.
We present an updated analysis of the rare decay \(K_{\mathrm{L}} \rightarrow\pi^{0} \mu^{ + } \mu^{-}\) within the standard model. In particular, we present the first complete calculation of the two-photon CP-conserving amplitude within chiral perturbation theory, at the lowest non-trivial order. Our results confirm the previous findings that the CP-conserving contribution to the decay rate cannot be neglected. By means of an explicit two-loop calculation, we show that this contribution can be estimated with sufficient accuracy compared to the CP-violating terms. We predict \({\cal B}(K_{\mathrm{L}}\rightarrow\pi^{0}\mu^{ + } \mu^{-})_{\mathrm{SM}} = (1.5\pm0.3)\times10^{-11}\), with approximately equal contributions from the CP-conserving component, the indirect-CP-violating term, and the interesting direct-CP-violating amplitude. The error of this prediction is mainly of parametric nature and could be substantially reduced with better data on the \(K_{\mathrm{S}}\rightarrow\pi^{0}\ell^{ + }\ell^{-}\) modes. The standard model predictions for various differential distributions and the sensitivity to possible new-physics effects are also briefly discussed.
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References
F.J. Gilman, M.B. Wise, Phys. Rev. D 21, 3150 (1980); C. Dib, I. Dunietz, F.J. Gilman, Phys. Rev. D 39, 2639 (1989)
G. Buchalla, G. D’Ambrosio, G. Isidori, Nucl. Phys. B 672, 387 (2003) [hep-ph/0308008]
J.R. Batley et al. [NA48/1 Collaboration], Phys. Lett. B 576, 43 (2003) [hep-ex/0309075]
T. Fonseca Martin [NA48/1 Collaboration], talk presented at the 18th Rencontres de Physique de la Vallée d’Aoste, La Thuile, February 29-March 6, 2004 [www.pi.infn.itlathuilelathuile\_2004.html]
A. Lai et al. [NA48 Collaboration], Phys. Lett. B 536, 229 (2002) [hep-ex/0205010]
A. Alavi-Harati et al. [KTeV Collaboration], Phys. Rev. Lett. 83, 917 (1999) [hep-ex/9902029]
L.M. Sehgal, Phys. Rev. D 38, 808 (1988)
G. Ecker, A. Pich, E. de Rafael, Nucl. Phys. B 303, 665 (1988)
J. Flynn, L. Randall, Phys. Lett. B 216, 221 (1989)
P. Heiliger, L.M. Sehgal, Phys. Rev. D 47, 4920 (1993)
G. Ecker, A. Pich, Nucl. Phys. B 366, 189 (1991)
A.J. Buras, R. Fleischer, S. Recksiegel, F. Schwab, hep-ph/0402112
P. Agrawal, J.N. Ng, G. Belanger, C.Q. Geng, Phys. Rev. Lett. 67, 537 (1991)
G. Ecker, A. Pich, E. de Rafael, Nucl. Phys. B 291, 692 (1987)
G. D’Ambrosio, G. Ecker, G. Isidori, J. Portolés, JHEP 08, 004 (1998) [hep-ph/9808289]
A.J. Buras, M.E. Lautenbacher, M. Misiak, M. Münz, Nucl. Phys. B 423, 349 (1994) [hep-ph/9402347]; G. Buchalla, A.J. Buras, M.E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996) [hep-ph/9512380]
M. Battaglia et al. , hep-ph/0304132
S. Friot, D. Greynat, E. de Rafael, Rare Kaon Decays Revisited, CTP-2004/P.014; D. Greynat, talk presented at the 3rd EURIDICE Collaboration meeting, Vienna, 12-14 February 2004
G. Ecker, A. Pich, E. de Rafael, Phys. Lett. B 189, 363 (1987)
L. Cappiello, G. D’Ambrosio, Nuovo Cim. A 99, 155 (88)
G. D’Ambrosio, G. Ecker, G. Isidori, H. Neufeld, Phys. Lett. B 380, 165 (1996) [hep-ph/9603345]
G.P. Lepage, J. Comput. Phys. 27, 192 (1978)
S. Wolfram, Mathematica - a system for doing mathematics by computer (Addison-Wesley, New York 1988)
J. Kambor, J. Missimer, D. Wyler, Phys. Lett. B 261, 496 (1991)
A. Cohen, G. Ecker, A. Pich, Phys. Lett. B 304, 347 (1993)
F. Gabbiani, G. Valencia, Phys. Rev. D 64, 094008 (2001) [hep-ph/0105006]; D 66, 074006 (2002) [hep-ph/0207189]
M.V. Diwan, H. Ma, T.L. Trueman, Phys. Rev. D 65, 054020 (2002) [hep-ph/0112350]
A. Alavi-Harati et al. [KTeV Collaboration], hep-ex/0309072
A. Alavi-Harati et al. [KTeV Collaboration], Phys. Rev. Lett. 84, 5279 (2000) [hep-ex/0001006]
Y. Nir, M.P. Worah, Phys. Lett. B 423, 319 (1998) [hep-ph/9711215]; A.J. Buras, A. Romanino, L. Silvestrini, Nucl. Phys. B 520, 3 (1998) [hep-ph/9712398]; G. Colangelo, G. Isidori, JHEP 09, 009 (1998) [hep-ph/9808487]; A.J. Buras et al. , Nucl. Phys. B 566, 3 (2000) [hep-ph/9908371]; G. D’Ambrosio, G. Isidori, Phys. Lett. B 530, 108 (2002) [hep-ph/0112135]
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Received: 26 April 2004, Published online: 23 June 2004
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Isidori, G., Smith, C. & Unterdorfer, R. The rare decay \(K_{\mathrm{L}} \rightarrow\pi^{0} \mu^{ + } \mu^{-}\) within the SM. Eur. Phys. J. C 36, 57–66 (2004). https://doi.org/10.1140/epjc/s2004-01879-0
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DOI: https://doi.org/10.1140/epjc/s2004-01879-0