Evidence for shallow $\bar{b}\bar{c}ud$ tetraquark bound states and broad $\bar{b}\bar{c}ud$ tetraquark resonances in $B$-$D$ and $B^*$-$D$ scattering from lattice QCD

Author:

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

Keyword:

High Energy Physics - Lattice, High Energy Physics - Lattice (hep-lat), High Energy Physics - Experiment (hep-ex), High Energy Physics - Phenomenology (hep-ph), Nuclear Theory (nucl-th)

journal:

date:

2023-12-05 00:00:00

Abstract

We present the first determination of the energy dependence of the $B$-$D$ and $B^*$-$D$ 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 $\bar{b}\bar{c}ud$ tetraquarks exist as bound states or resonances. The scattering phase shifts are obtained using L\"uscher'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, $B^{(*)}$-$D$ scattering operators with the lowest three or four possible back-to-back momenta in addition to local $\bar{b}\bar{c}ud$ operators. We fit the energy dependence of the extracted scattering phase shifts using effective-range expansions. We observe sharp peaks in the $B^{(*)}$-$D$ scattering rates close to the thresholds, which are associated with shallow bound states, either genuine or virtual, a few MeV or less below the $B^{(*)}$-$D$ thresholds. In addition, we find evidence for resonances with masses of order $100$ MeV above the thresholds and decay widths of order $200$ MeV.

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