Coupled-channel Dπ, Dη and D<inf>s</inf>K¯ scattering from lattice QCD

Abstract

We present the first lattice QCD study of coupled-channel $D\pi$, $D\eta$ and $D_{s}\bar{K}$ scattering in isospin-1/2 in three partial waves. Using distillation, we compute matrices of correlation functions with bases of operators capable of resolving both meson and meson-meson contributions to the spectrum. These correlation matrices are analysed using a variational approach to extract the finite-volume energy eigenstates. Utilising L\"uscher's method and its extensions, we constrain scattering amplitudes in $S$, $P$ and $D$-wave as a function of energy. By analytically continuing the scattering amplitudes to complex energies, we investigate the $S$-matrix singularities. Working at $m_\pi \approx 391$ MeV, we find a pole corresponding to a $J^{P} = 0^{+}$ near-threshold bound state with a large coupling to $D\pi$. We also find a deeply bound $J^{P} = 1^{-}$ state, and evidence for a $J^{P} = 2^{+}$ narrow resonance coupled predominantly to $D\pi$. Elastic $D\pi$ scattering in the isospin-$3/2$ channel is studied and we find a weakly repulsive interaction in $S$-wave.GM acknowledges support from the Herchel Smith Fund at the University of Cambridge and the Deutsche Forschungsgemeinschaft (DFG) under contract KN 947/1-2. SMR acknowledges support from Science Foundation Ireland [RFP-PHY-3201]. CET acknowledges support from the U.K. Science and Technology Facilities Council (STFC) [grant ST/L000385/1] and the Isaac Newton Trust/University of Cambridge Early Career Support Scheme [RG74916]. The software codes Chroma [58] and QUDA [59, 60] were used to perform this work at Jeerson Laboratory under the USQCD Initiative and the LQCD ARRA project, and on the Lonsdale cluster maintained by the Trinity Centre for High Performance Computing funded through grants from Science Foundation Ireland (SFI). This work also used the DiRAC Data Analytic system at the University of Cambridge, operated by the University of Cambridge High Performance Computing Service on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). 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. This research also used the Wilkes GPU cluster at the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc., NVIDIA and Mellanox, and part funded by STFC with industrial sponsorship from Rolls Royce and Mitsubishi Heavy Industries. Gauge con gurations were generated using resources awarded from the U.S. Department of Energy INCITE program at Oak Ridge National Laboratory, the NSF Teragrid at the Texas Advanced Computer Center and the Pittsburgh Supercomputer Center, as well as at Jeerson Lab.This is the final version of the article. It first appeared from Springer via https://doi.org/10.1007/JHEP10(2016)01