Implementing the three-particle quantization condition for π + π + K + and related systems
Abstract Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to che...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-02-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP02(2022)098 |
| _version_ | 1819277836680167424 |
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| author | Tyler D. Blanton Fernando Romero-López Stephen R. Sharpe |
| author_facet | Tyler D. Blanton Fernando Romero-López Stephen R. Sharpe |
| author_sort | Tyler D. Blanton |
| collection | DOAJ |
| description | Abstract Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K $$ \mathcal{K} $$ df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O $$ \mathcal{O} $$ (1/L 5); and we calculate the leading-order predictions in chiral perturbation theory for K $$ \mathcal{K} $$ df,3 in the π + π + K + and π + K + K + systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π + π + K + levels using the two- and three-particle interactions predicted by chiral perturbation theory. |
| first_indexed | 2024-12-24T00:02:27Z |
| format | Article |
| id | doaj.art-49563c198dbc4216b6e5bf5e1c153448 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-24T00:02:27Z |
| publishDate | 2022-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-49563c198dbc4216b6e5bf5e1c1534482022-12-21T17:25:05ZengSpringerOpenJournal of High Energy Physics1029-84792022-02-012022214910.1007/JHEP02(2022)098Implementing the three-particle quantization condition for π + π + K + and related systemsTyler D. Blanton0Fernando Romero-López1Stephen R. Sharpe2Department of Physics, University of MarylandCTP, Massachusetts Institute of TechnologyPhysics Department, University of WashingtonAbstract Recently, the formalism needed to relate the finite-volume spectrum of systems of nondegenerate spinless particles has been derived. In this work we discuss a range of issues that arise when implementing this formalism in practice, provide further theoretical results that can be used to check the implementation, and make available codes for implementing the three-particle quantization condition. Specifically, we discuss the need to modify the upper limit of the cutoff function due to the fact that the left-hand cut in the scattering amplitudes for two nondegenerate particles moves closer to threshold; we describe the decomposition of the three-particle amplitude K $$ \mathcal{K} $$ df,3 into the matrix basis used in the quantization condition, including both s and p waves, with the latter arising in the amplitude for two nondegenerate particles; we derive the threshold expansion for the lightest three-particle state in the rest frame up to O $$ \mathcal{O} $$ (1/L 5); and we calculate the leading-order predictions in chiral perturbation theory for K $$ \mathcal{K} $$ df,3 in the π + π + K + and π + K + K + systems. We focus mainly on systems with two identical particles plus a third that is different (“2+1” systems). We describe the formalism in full detail, and present numerical explorations in toy models, in particular checking that the results agree with the threshold expansion, and making a prediction for the spectrum of π + π + K + levels using the two- and three-particle interactions predicted by chiral perturbation theory.https://doi.org/10.1007/JHEP02(2022)098Lattice QCDLattice Quantum Field Theory |
| spellingShingle | Tyler D. Blanton Fernando Romero-López Stephen R. Sharpe Implementing the three-particle quantization condition for π + π + K + and related systems Journal of High Energy Physics Lattice QCD Lattice Quantum Field Theory |
| title | Implementing the three-particle quantization condition for π + π + K + and related systems |
| title_full | Implementing the three-particle quantization condition for π + π + K + and related systems |
| title_fullStr | Implementing the three-particle quantization condition for π + π + K + and related systems |
| title_full_unstemmed | Implementing the three-particle quantization condition for π + π + K + and related systems |
| title_short | Implementing the three-particle quantization condition for π + π + K + and related systems |
| title_sort | implementing the three particle quantization condition for π π k and related systems |
| topic | Lattice QCD Lattice Quantum Field Theory |
| url | https://doi.org/10.1007/JHEP02(2022)098 |
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