Baryon-baryon, meson-meson, and meson-baryon interactions in nonrelativistic QCD

Abstract: Van der Waals potentials describing interactions between color-singlet mesons and/or baryons vanish at leading order in potential nonrelativistic quantum chromodynamics (pNRQCD). This result and constraints from Gauss's law are used to prove that weakly-coupled pNRQCD van der Waals potentials in generic non-Abelian gauge theories with only heavy quarks are too weak to form bound states whose color state is a product of color-singlets. Quantum Monte Carlo calculations of four, five, and six quarks with equal masses provide numerical evidence that exotic color configurations are higher energy than products of color-singlet hadrons, suggesting that equal-mass fully-heavy tetraquark, pentaquark, and hexaquark bound states do not exist at next-to-leading order in pNRQCD and at all orders in QCD-like theories in which all quark masses are asymptotically large. Mechanisms for generating hadron-hadron bound states are identified, which necessarily involve large quark-mass hierarchies, relativistic effects arising from the presence of sufficiently light quarks, or nonperturbative effects outside the scope of weakly-coupled pNRQCD.