Shallow Bound States and Hints for Broad Resonances with Quark Content $\overline{b}\overline{c}ud$ in $B\text{−}\overline{D}$ and $B^{*}\text{−}\overline{D}$ Scattering from Lattice QCD

Journal Article · 08 April 2024 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.132.151902 · OSTI ID:2335827

Alexandrou, Constantia; Finkenrath, Jacob ; Leontiou, Theodoros ; Meinel, Stefan ; Pflaumer, Martin; Wagner, Marc

We present the first determination of the energy dependence of the $B\text{−}\overline{D}$ and $B^{*}\text{−}\overline{D}$ isospin-0, $S$ -wave scattering amplitudes both below and above the thresholds using lattice QCD, which allows us to investigate rigorously whether mixed bottom-charm $\overline{b}\overline{c}ud$ tetraquarks exist as bound states or resonances. The scattering phase shifts are obtained using Lüscher’s method from the energy spectra in two different volumes. To ensure that no relevant energy level is missed, we use large, symmetric $7\times 7$ and $8\times 8$ correlation matrices that include, at both source and sink, $B^{(*)}\text{−}\overline{D}$ scattering operators with the lowest three or four possible back-to-back momenta in addition to local $\overline{b}\overline{c}ud$ operators. We fit the energy dependence of the extracted scattering phase shifts using effective-range expansions. We observe sharp peaks in the $B^{(*)}\text{−}\overline{D}$ scattering rates close to the thresholds, which are associated with shallow bound states, either genuine or virtual, a few MeV or less below the $B^{(*)}\text{−}\overline{D}$ thresholds. In addition, we find hints for resonances with masses of order 100 MeV above the thresholds and decay widths of order 200 MeV. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• OSTI ID: 2335827
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 15 Vol. 132; ISSN 0031-9007; ISSN PRLTAO
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English