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

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arxiv 2406.05123 v2 pith:HHMLBD54 submitted 2024-06-07 hep-ph hep-lat

classification hep-phhep-lat
keywords potentialsborn-oppenheimerassociatedbehaviorcorrectformgaugelimiting
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 1 Pith paper

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  1. Hybrid static potentials and gluelumps on $N_f=3+1$ ensembles

    hep-lat 2025-01 conditional novelty 6.0 of 10

    New lattice QCD measurements of hybrid static potentials, static-light thresholds, and gluelump masses on N_f=3+1 ensembles with pions near 420 MeV, using Laplace trial states.

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