Charged Kaon K \to 3 pi CP Violating Asymmetries at NLO in CHPT

Abstract

We give the first full next-to-leading order analytical results in Chiral Perturbation Theory for the charged Kaon K \to 3 pi slope g and decay rates CP-violating asymmetries. We have included the dominant Final State Interactions at NLO analytically and discussed the importance of the unknown counterterms. We find that the uncertainty due to them is reasonable just for Δg_C, i.e. the asymmetry in the K^+ \to pi^+ pi^+ pi^- slope g; we get Δg_C = -(2.4 +- 1.2) 10^{-5}. The rest of the asymmetries are very sensitive to the unknown counterterms. In particular, the decay rate asymmetries can change even sign. One can use this large sentivity to get valuable information on those counterterms and on Im(G_8) coupling --very important for the CP-violating parameter epsilon'_K-- from the eventual measurement of these asymmetries. We also provide the one-loop O(e^2 p^2) electroweak octet contributions for the neutral and charged Kaon K \to 3 pi decays.

arXiv comment43+2 pages, 2 figures. Version accepted in JHEP. Small changes in the final numerics of CP asymmetries due to change in input value

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• Search for direct CP violating charge asymmetries in $K^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ and $K^{\pm }\to {\pi }^{\pm }{\pi }^0{\pi }^0$ decays
• Probing the Majorana neutrinos and their CP violation in decays of charged scalar mesons $\pi ,K,D,D_s,B,B_c$
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• Search for direct CP violation in the decays K\pm \to 3π\pm
• Dispersive construction of two-loop $P\to \pi \pi \pi$ $(P=K,\eta )$ amplitudes
• Measurements of the Charge Asymmetry of the Dalitz Plot Parameters for $K^{\pm }\to {\pi }^{\pm }{\pi }^0{\pi }^0$ Decays
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• Measuring the a0-a2 pion scattering lengths through K to 3 pi decays
• Recent results from the NA48 experiment at CERN: CP violation and CKM parameter Vus