One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium

TL;DR

This paper develops a comprehensive Born-Oppenheimer effective field theory from QCD to describe and predict the properties of various exotic hadrons, including hybrids, tetraquarks, pentaquarks, and doubly heavy baryons, unifying different models.

Contribution

It derives a universal Schrödinger framework from QCD for all exotic states, incorporating nonadiabatic effects, and connects molecular and tetraquark pictures within a single theoretical approach.

Findings

Derived coupled Schrödinger equations for all exotic states.

Identified static potentials and nonperturbative correlators needed for lattice calculations.

Explained the mixing and avoided level crossing phenomena leading to molecular exotics.

Abstract

The discovery of XYZ exotic states in the hadronic sector with two heavy quarks, represents a significant challenge in particle theory. Understanding and predicting their nature remains an open problem. In this work, we demonstrate how the Born$-$Oppenheimer (BO) effective field theory (BOEFT), derived from Quantum Chromodynamics (QCD) on the basis of scale separation and symmetries, can address XYZ exotics of any composition. We derive the Schr\"odinger coupled equations that describe hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia at leading order, incorporating nonadiabatic terms, and present the predicted multiples. We define the static potentials in terms of the QCD static energies for all relevant cases. We provide the precise form of the nonperturbative low-energy gauge-invariant correlators required for the BOEFT: static energies, generalized Wilson loops, gluelumps, and adjoint mesons. These are to be calculated on the lattice and we calculate here their short-distance behavior. Furthermore, we outline how spin-dependent corrections and mixing terms can be incorporated using matching computations. Lastly, we discuss how static energies with the same BO quantum numbers mix at large distances leading to the phenomenon of avoided level crossing. This effect is crucial to understand the emergence of exotics with molecular characteristics, such as the $\chi_{c1}(3872)$. With BOEFT both the tetraquark and the molecular picture appear as part of the same description.