Abstract
The three-particle K-matrix, \( \mathcal{K} \)df,3, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions in all isospin channels through next-to-leading order in Chiral Perturbation Theory, generalizing previous work done at maximum isospin. We obtain analytic expressions through quadratic order (or cubic order, in the case of zero isospin) in the expansion about the three-pion threshold.
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Acknowledgments
The work of JBB was supported by the Spanish MU grant FPU19/04326. Additionally, JBB received support from the European project H2020-MSCA-ITN-2019//860881-HIDDeN and the staff exchange grant 101086085-ASYMMETRY, and from the Spanish Ministerio de Ciencia e Innovación project PID2020-113644GB-I00. The work of JB and MS was supported by the Swedish Research Council grants contract numbers 2016-05996 and 2019-03779; MS also received support from the French government under the France 2030 investment plan, as part of the “Initiative d’Excellence d’Aix-Marseille Université — A*MIDEX” under grant AMX-22-RE-AB-052. The work of FRL was supported in part by the U.S. Department of Energy (USDOE), Office of Science, Office of Nuclear Physics, under grant Contract Numbers DE-SC0011090 and DE-SC0021006. FRL also acknowledges financial support by the Mauricio and Carlota Botton Fellowship. TH was supported by the Czech Science Foundation grant 23-06770S, by the Charles University grant PRIMUS 23/SCI/025, and by the MSCA Fellowships CZ — UK2 project No. CZ.02.01.01/00/22_010/0008115 financed by Programme Johannes Amos Comenius (OP JAK). The work of SRS was supported in part by the USDOE grant No. DE-SC0011637.
JBB and FRL would like to thank the Physics Department at the University of Washington for its hospitality during a visit in which this work was initiated.
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Baeza-Ballesteros, J., Bijnens, J., Husek, T. et al. The three-pion K-matrix at NLO in ChPT. J. High Energ. Phys. 2024, 48 (2024). https://doi.org/10.1007/JHEP03(2024)048
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DOI: https://doi.org/10.1007/JHEP03(2024)048