Bound Isoscalar Axial-Vector <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mi>c</mml:mi><mml:mover accent="true"><mml:mi>u</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>d</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> Tetraquark <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math> from Lattice QCD Using Two-Meson and Diquark-Antidiquark Variational Basis
M. Padmanath, Archana Radhakrishnan, Nilmani Mathur
Abstract
We report a lattice QCD study of the heavy-light meson-meson interactions with an explicitly exotic flavor content bcu[over ¯]d[over ¯], isospin I=0, and axial-vector J^{P}=1^{+} quantum numbers in search of possible tetraquark bound states. The calculation is performed at four values of lattice spacing, ranging from ∼0.058 to ∼0.12 fm, and at five different values of valence light quark mass m_{u/d}, corresponding to pseudoscalar meson mass M_{ps} 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 DB[over ¯]^{*} elastic S-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 m_{u/d} dependence of the DB[over ¯]^{*} scattering length (a_{0}) suggests that at the physical pion mass a_{0}^{phys}=+0.57(_{-5}^{+4})(17) fm, which clearly points to an attractive interaction between the D and B[over ¯]^{*} mesons that is strong enough to host a real bound state T_{bc}, with a binding energy of -43(_{-7}^{+6})(_{-24}^{+14}) MeV with respect to the DB[over ¯]^{*} threshold. We also find that the strength of the binding decreases with increasing m_{u/d} and the system becomes unbound at a critical light quark mass m_{u/d}^{*} corresponding to M_{ps}^{*}=2.73(21)(19) GeV.