Born-Oppenheimer Potentials for $SU(3)$ Gauge Theory

Abstract

We develop parameterizations of 8 of the lowest Born-Oppenheimer potentials for quarkonium hybrid mesons as functions of the separation $r$ of the static quark and antiquark sources. The parameters are determined by fitting results calculated using pure $SU(3)$ lattice gauge theory. The parameterizations have the correct limiting behavior at small $r$, where the potentials form multiplets associated with gluelumps. They have the correct limiting behavior at large $r$, where the potentials form multiplets associated with excitations of a relativistic string. There is a narrow avoided crossing in the small-$r$ region between two potentials with the same Born-Oppenheimer quantum numbers.

37 pages, 10 figures, 4 tables: v2: introduced additional references, modified figures; Journal version

References in corpus (25)

• The $XYZ$ states: experimental and theoretical status and perspectives
• Born-Oppenheimer Approximation for the XYZ Mesons
• Quarkonium Hybrids with Nonrelativistic Effective Field Theories
• How the Z_c(3900) Reveals the Spectra of Quarkonium Hybrid and Tetraquark Mesons
• String breaking by light and strange quarks in QCD
• Heavy Quarkonium Hybrids: Spectrum, Decay and Mixing
• Precision computation of hybrid static potentials in SU(3) lattice gauge theory
• The Born-Oppenheimer approximation in an effective field theory language
• On the effective theory of long open strings
• Spin structure of heavy-quark hybrids
• QCD spin effects in the heavy hybrid potentials and spectra
• Exotic to standard bottomonium transitions
• Nonrelativistic effective field theory for heavy exotic hadrons
• Hybrid static potentials in SU(3) lattice gauge theory at small quark-antiquark separations
• Determination of ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ and analytic parameterization of the static quark-antiquark potential
• Zb tetraquark channel from lattice QCD and Born-Oppenheimer approximation
• A lattice QCD study of generalized gluelumps
• Effective field theory for double heavy baryons at strong coupling
• Tetraquark systems $\bar{b}b\bar{d}u$ in the static limit and lattice QCD
• Heavy hybrid decays to quarkonia
• Novel implementation of the multipole expansion to quarkonium hadronic transitions
• Hyperfine splittings of heavy quarkonium hybrids
• Heavy meson thresholds in Born-Oppenheimer Effective field theory
• Eight very excited spectra and one possible axion in SU(3) lattice gauge theory
• Spectrum of very excited ${\Sigma }_g^{+}$ flux tubes in SU(3) gauge theory

Cited by in corpus (6)

• One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium
• The nature of ${\chi }_{c1}\left(3872\right)$ and $T_{cc}^{+}\left(3875\right)$
• Unravelling Pentaquarks with Born--Oppenheimer effective theory
• Investigating hybrid mesons with $0^{+-}$ and $2^{+-}$ exotic quantum numbers
• Hybrid to Quarkonia transitions
• Exotic hadrons associated with $b$-quark