Abstract
We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically π+K+, π+π+K+ and K+K+π+. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS Nf = 2 + 1 ensembles with pion masses of 200 MeV and 340 MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to p waves. This requires also results for the π+π+ and K+K+ spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit two-particle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in π+π+K+ and K+K+π+ systems, finding statistically significant nonzero results in most cases. We include s and p waves in the K matrix for π+K+ scattering, finding evidence for an attractive p-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory.
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Acknowledgments
We thank A. Rodas for useful discussions.
The work of ZTD and SRS is supported in part by the U.S. Department of Energy (USDOE) grant No. DE-SC0011637. The work of ADH is supported by The U.S. Department of Energy, Office of Science, Office of Nuclear Physics through Contract No. DE-SC0012704, and within the framework of Scientific Discovery through Advanced Computing (SciDAC) award Fundamental Nuclear Physics at the Exascale and Beyond. CJM acknowledges support from the U.S. NSF under award PHY-2209167. FRL has been supported in part by the USDOE, Office of Science, Office of Nuclear Physics, under grant Contract Numbers DE-SC0011090 and DE-SC0021006. FRL acknowledges financial support by the Mauricio and Carlota Botton Fellowship.
Calculations for this project were performed on the HPC clusters “HIMster II” at the Helmholtz-Institut Mainz and “Mogon II” at JGU Mainz. We are grateful to our colleagues in the CLS consortium for sharing ensembles.
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Draper, Z.T., Hanlon, A.D., Hörz, B. et al. Interactions of πK, ππK and KKπ systems at maximal isospin from lattice QCD. J. High Energ. Phys. 2023, 137 (2023). https://doi.org/10.1007/JHEP05(2023)137
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DOI: https://doi.org/10.1007/JHEP05(2023)137