Are There Tetraquarks at Large $N_c$ in QCD(F)?

Understand

Weinberg recently pointed out a flaw in the standard argument that large $N_c$ QCD with color-fundamental quarks [QCD(F)] cannot yield narrow tetraquark states.

• In particular, he observed that the argument does not rule out narrow tetraquarks associated with the leading-order connected diagrams; such tetraquarks would have a width scaling as $N_c^{-1}$.
• It is shown here, however, that while the standard analysis of tetraquarks does not rule them out, a more thorough analysis rules out quantum-number exotic tetraquarks associated with the leading-order connected diagrams.
• This analysis is based entirely on conventional assumptions used in large $N_c$ physics applied to the analytic properties of meson-meson scattering.