Born-Oppenheimer potentials for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> gauge th

We develop parametrizations of eight of the lowest Born-Oppenheimer potentials for quarkonium hybrid mesons as functions of the separation <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>r</a:mi></a:math> of the static quark and antiquark sources. The parameters are determined by fitting results calculated using pure <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>S</c:mi><c:mi>U</c:mi><c:mo stretchy="false">(</c:mo><c:mn>3</c:mn><c:mo stretchy="false">)</c:mo></c:math> lattice gauge theory. The parametrizations have the correct limiting behavior at small <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>r</g:mi></g:math>, where the potentials form multiplets associated with gluelumps. They have the correct limiting behavior at large <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>r</i:mi></i:math>, where the potentials form multiplets associated with excitations of a relativistic string. There is a narrow avoided crossing in the small-<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>r</k:mi></k:math> region between two potentials with the same Born-Oppenheimer quantum numbers. Published by the American Physical Society 2024