Abstract
We derive the modified Lüscher equation in the presence of the long-range force caused by the exchange of a light particle. It is shown that the use of this equation enables one to circumvent the problems related to the strong partial-wave mixing and the t-channel sub-threshold singularities. It is also demonstrated that the present method is intrinsically linked to the so-called modified effective-range expansion (MERE) in the infinite volume. A detailed comparison with the two recently proposed alternative approaches is provided.
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Acknowledgments
The authors thank Vadim Baru, Evgeny Epelbaum, Jambul Gegelia, Christoph Hanhart, Nils Hermanssohn-Truedsson, Bai-Long Hoid, Lu Meng and Fernando 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, and by the National Key R&D Program of China under Contract No. 2020YFA0406400, and by the Chinese Academy of Sciences under Grant No. YSBR-101, and by the Xiaomi Foundation / Xiaomi Young Talents Program. H.-W.H. was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundati on) — Project ID 279384907 — SFB 1245.
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Bubna, R., Hammer, HW., Müller, F. et al. Lüscher equation with long-range forces. J. High Energ. Phys. 2024, 168 (2024). https://doi.org/10.1007/JHEP05(2024)168
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DOI: https://doi.org/10.1007/JHEP05(2024)168