DK/Dπ scattering and an exotic virtual bound state at the SU(3) flavour symmetric point from lattice QCD
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Abstract
Elastic $S-$wave scattering of a charm meson with a light pseudoscalar meson in $J^P =0^+$ is investigated in the flavour $\bar{\mathbf{3}}$, $\mathbf{6}$ and $\overline{\mathbf{15}}$ sectors at the $SU(3)f$ flavour point using lattice QCD, working on three volumes with $m{\pi} \approx 700$ MeV. Large bases of interpolating operators are employed to extract finite-volume spectra, which are subsequently used with the L"uscher method to provide constraints on infinite-volume scattering amplitudes. Examining the singularities of the amplitudes, the $S-$wave amplitude in the flavour $\bar{\mathbf{3}}$ sector is found to contain a deeply bound state, strongly coupled to elastic threshold, corresponding to the $J^P = 0^+$ $D_{s0}^*(2317)$. In the exotic flavour $\mathbf{6}$ sector a virtual bound state is found at $\sqrt{s_{\rm{pole}}} = 2510 - 2610$ MeV, roughly $40-140$ MeV below threshold, whereas the $\overline{\mathbf{15}}$ channel shows weak repulsion.
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Acknowledgements: We thank our colleagues within the Hadron Spectrum Collaboration (www.hadspec.org), in particular Jozef Dudek, and also thank Christoph Hanhart and Feng-Kun Guo for useful discussions. JDEY, CET and DJW acknowledge support from the U.K. Science and Technology Facilities Council (STFC) [grant numbers ST/T000694/1, ST/X000664/1]. DJW acknowledges support from a Royal Society University Research Fellowship. The software codes Chroma [77], QUDA [78, 79] and Redstar [80] were used. Some software codes used in this project were developed with support from the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Nuclear Physics, Scientific Discovery through Advanced Computing (SciDAC) program; also acknowledged is support from the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. This work used the Cambridge Service for Data Driven Discovery (CSD3), part of which is operated by the University of Cambridge Research Computing Service (www.csd3.cam.ac.uk) on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The DiRAC component of CSD3 was funded by BEIS capital funding via STFC capital grants ST/P002307/1 and ST/R002452/1 and STFC operations grant ST/R00689X/1. Other components were provided by Dell EMC and Intel using Tier-2 funding from the Engineering and Physical Sciences Research Council (capital grant EP/P020259/1). This work also used the earlier DiRAC Data Analytic system at the University of Cambridge. This equipment was funded by BIS National E-infrastructure capital grant (ST/K001590/1), STFC capital grants ST/H008861/1 and ST/H00887X/1, and STFC DiRAC Operations grant ST/K00333X/1. DiRAC is part of the National E-Infrastructure. Propagators used in this project were generated using DiRAC facilities, at Jefferson Lab under the USQCD Collaboration and the LQCD ARRA Project, under an ALCC award, using resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. and using resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources. Gauge configurations were generated using resources awarded from the U.S. Department of Energy INCITE program at the Oak Ridge Leadership Computing Facility, the NERSC, the NSF Teragrid at the TACC and the Pittsburgh Supercomputer Center, using DiRAC facilities and at Jefferson Lab. Data Access Statement. The numerical values of the finite-volume energies along with statistical uncertainties and correlations, as well as full results of the fits, can be found in supplementary material. Reasonable requests for other data can be directed to the authors and will be considered in accordance with the Hadron Spectrum Collaboration’s policies on sharing data.
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1029-8479
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STFC (ST/T000694/1)
Science and Technology Facilities Council (ST/X000664/1)
Science and Technology Facilities Council (ST/H008861/1)
Science and Technology Facilities Council (ST/K001590/1)
Science and Technology Facilities Council (ST/K00333X/1)
Engineering and Physical Sciences Research Council (EP/P020259/1)
Science and Technology Facilities Council (ST/R002452/1)
Science and Technology Facilities Council (ST/R00689X/1)