Tetraquark resonances computed with static lattice QCD potentials and scattering theory

We study tetraquark resonances with lattice QCD potentials computed for two static quarks and two dynamical quarks, the Born-Oppenheimer approximation and the emergent wave method of scattering theory. As a proof of concept we focus on systems with isospin $I = 0$, but consider different relative angular momenta $l$ of the heavy $b$ quarks. We compute the phase shifts and search for \mbox{S} and \mbox{T} matrix poles in the second Riemann sheet. We predict a new tetraquark resonance for $l = 1$, decaying into two $B$ mesons, with quantum numbers $I(J^P) = 0(1^-)$, mass $m = 10576_{-4}^{+4} \, \textrm{MeV}$ and decay width $\Gamma = 112_{-103}^{+90} \, \textrm{MeV}$.Comment: 7 pages, 6 figures, 1 table, Proceedings of the 35th International Symposium on Lattice Field Theory, Granada, Spai

ΛMSˉ(nf=2)\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)} from a momentum space analysis of the quark-antiquark static potential

We determine $\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ by fitting perturbative expressions for the quark-antiquark static potential to lattice results for QCD with $n_f=2$ dynamical quark flavors. To this end we use the perturbative static potential at the presently best known accuracy, i.e. up to ${\cal O}(\alpha_s^4)$, in momentum space. The lattice potential is computed on a fine lattice with $a \approx 0.042 \, \textrm{fm}$ in position space. To allow for a comparison and matching of both results, the lattice potential is transformed into momentum space by means of a discrete Fourier transform. The value of $\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ is extracted in momentum space. All sources of statistical and systematic errors are discussed. The uncertainty in the value of $\Lambda_{\bar{\textrm{MS}}}^{(n_f=2)}$ is found to be smaller than that obtained in a recent position space analysis of the static potential based on the same lattice data.Comment: 30 pages, 6 figures; some clarifications added, matches journal versio