One Born Oppenheimer Effective Theory to rule all Exotics

Abstract

The discovery of XYZ exotic states in the hadronic sector with two heavy quarks constitute one of the most important open problems in particle theory. In this work, we demonstrate that the QCD derived Born-Oppenheimer effective field theory (BOEFT) framework, provides a systematic framework to describe exotic states of arbitrary composition. The BOEFT construction is based on QCD taking into consideration the scale separation and symmetry of systems containing two heavy quarks. We show the results for the coupled channel Schr\"odinger equations incorporating nonadiabatic mixing terms that describes exotic states for arbitrary quantum number of the light degrees of freedom: hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia at leading order. Additionally, we present the results of the predicted spin-symmetry multiplets, and the expression of the nonperturbative gauge-invariant correlators to be computed on lattice that are required for BOEFT: static energies, generalized Wilson loops, gluelumps, adjoint mesons or baryons, and triplet or sextext mesons or baryons. Moreover, for the static energies, we describe the short-distance behavior based on multipole expansion and the mixing with heavy-light thresholds at long distances based on the conserved quantum numbers.