Abstract
We derive an explicit expression for the Lellouch-Lüscher (LL) factor in the K → 3π decays at leading order (without derivative couplings). Several important technical details are addressed, like a proper decomposition into the isospin amplitudes, the choice of a minimal set of effective couplings and the renormalization, as well as the algorithm for the solution of the pertinent Faddeev equations in the infinite volume which is based on the contour deformation method. Most importantly, our numerical results demonstrate that the three-body force contributes very little to the LL factor. This result paves the way for the study of the K → 3π decays on the lattice.
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Acknowledgments
The authors would like to thank J. Bijnens, S. Dawid, H.-W. Hammer, B. Kubis and F. Romero-Lopez for interesting discussions. The work of R.B., F.M. and A.R. was funded in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — Project-ID 196253076 — TRR 110 and by the Ministry of Culture and Science of North Rhine-Westphalia through the NRW-FAIR project. A.R., in addition, thanks Volkswagenstiftung (grant no. 93562) and the Chinese Academy of Sciences (CAS) President’s International Fellowship Initiative (PIFI) (grant no. 2024VMB0001) for the partial financial support. The work of J.-Y.P. and J.-J.W. was supported by the National Natural Science Foundation of China (NSFC) under Grants No. 12135011, 12175239, 12221005. The work of J.-J.W. was also supported by the National Key R&D Program of China under Contract No. 2020YFA0406400, and by Chinese Academy of Sciences under Grant No. YSBR-101.
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Pang, JY., Bubna, R., Müller, F. et al. Lellouch-Lüscher factor for the K → 3π decays. J. High Energ. Phys. 2024, 269 (2024). https://doi.org/10.1007/JHEP05(2024)269
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DOI: https://doi.org/10.1007/JHEP05(2024)269