Bound Isoscalar Axial-Vector Tetraquark from Lattice QCD Using Two-Meson and Diquark-Antidiquark Variational Basis
M. Padmanath (The Institute of Mathematical Sciences, a CI of Homi Bhabha National Institute, Chennai, 600113, India); Archana Radhakrishnan (Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India); Nilmani Mathur (Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India)
We report a lattice QCD study of the heavy-light meson-meson interactions with an explicitly exotic flavor content , isospin , and axial-vector quantum numbers in search of possible tetraquark bound states. The calculation is performed at four values of lattice spacing, ranging from to , and at five different values of valence light quark mass , corresponding to pseudoscalar meson mass of about 0.5, 0.6, 0.7, 1.0, and 3.0 GeV. The energy eigenvalues in the finite volume are determined through a variational procedure applied to correlation matrices built out of two-meson interpolating operators as well as diquark-antidiquark operators. The continuum limit estimates for elastic -wave scattering amplitude are extracted from the lowest finite-volume eigenenergies, corresponding to the ground states, using amplitude parametrizations supplemented by a lattice spacing dependence. Light quark mass dependence of the scattering length () suggests that at the physical pion mass , which clearly points to an attractive interaction between the and mesons that is strong enough to host a real bound state , with a binding energy of with respect to the threshold. We also find that the strength of the binding decreases with increasing and the system becomes unbound at a critical light quark mass corresponding to .