Finite- and infinite-volume study of $DDπ$ scattering
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| Format: | Preprint |
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2024
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| author | Dawid, Sebastian M. Romero-López, Fernando Sharpe, Stephen R. |
| author_facet | Dawid, Sebastian M. Romero-López, Fernando Sharpe, Stephen R. |
| contents | We develop a comprehensive framework for extracting the pole position and properties of the doubly-charmed tetraquark $T_{\rm cc}^+(3875)$ from lattice QCD data using the relativistic three-particle formalism. This approach incorporates the effect of the one-pion exchange diagram in $DDπ$ and $DD^*$ scattering, making it applicable at energies coinciding with the left-hand cut in the partial-wave projected $DD^*$ amplitude. We present an example application of this framework to existing lattice QCD data at $m_π= 280$ MeV. We solve the integral equations describing the $DDπ$ reaction, use LSZ reduction to determine the corresponding $DD^*$ amplitude, and find the values of the infinite-volume two- and three-body $K$ matrices that lead to agreement with lattice $DD^*$ phase shifts within their uncertainties. Using these $K$ matrices in the three-particle quantization condition, we describe the finite-volume $DD^*$ spectrum and find good agreement with the lattice QCD energies. Our results suggest that, at this pion mass, the tetraquark appears as a pair of subthreshold complex poles whose precise location strongly depends on the value of the $DDπ$ three-particle $K$ matrix. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_17059 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite- and infinite-volume study of $DDπ$ scattering Dawid, Sebastian M. Romero-López, Fernando Sharpe, Stephen R. High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory We develop a comprehensive framework for extracting the pole position and properties of the doubly-charmed tetraquark $T_{\rm cc}^+(3875)$ from lattice QCD data using the relativistic three-particle formalism. This approach incorporates the effect of the one-pion exchange diagram in $DDπ$ and $DD^*$ scattering, making it applicable at energies coinciding with the left-hand cut in the partial-wave projected $DD^*$ amplitude. We present an example application of this framework to existing lattice QCD data at $m_π= 280$ MeV. We solve the integral equations describing the $DDπ$ reaction, use LSZ reduction to determine the corresponding $DD^*$ amplitude, and find the values of the infinite-volume two- and three-body $K$ matrices that lead to agreement with lattice $DD^*$ phase shifts within their uncertainties. Using these $K$ matrices in the three-particle quantization condition, we describe the finite-volume $DD^*$ spectrum and find good agreement with the lattice QCD energies. Our results suggest that, at this pion mass, the tetraquark appears as a pair of subthreshold complex poles whose precise location strongly depends on the value of the $DDπ$ three-particle $K$ matrix. |
| title | Finite- and infinite-volume study of $DDπ$ scattering |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2409.17059 |