Why quarkonium hybrid coupling to two <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi></mml:mrow></mml:math>-wave heavy-light mesons is not suppressed
R. Bruschini
Abstract
We examine the couplings of quarkonium hybrids to heavy-light meson pairs in the Born-Oppenheimer approximation for QCD. The lowest hybrid multiplets consist of bound states of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="normal">Π</a:mi><a:mi>u</a:mi></a:msub></a:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msubsup><d:mi mathvariant="normal">Σ</d:mi><d:mi>u</d:mi><d:mo>−</d:mo></d:msubsup></d:math> potentials. We find that the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msubsup><g:mi mathvariant="normal">Σ</g:mi><g:mi>u</g:mi><g:mo>−</g:mo></g:msubsup></g:math> potential can couple to pairs of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>S</j:mi></j:math>-wave mesons through string breaking, while the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mi mathvariant="normal">Π</l:mi><l:mi>u</l:mi></l:msub></l:math> potential cannot. From this observation, we derive model-independent selection rules that contradict previous expectations that quarkonium hybrids are forbidden to decay into pairs of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>S</o:mi></o:math>-wave mesons. These Born-Oppenheimer selection rules are consistent with the partial decay widths of the lowest charmonium hybrid with exotic quantum numbers <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mrow><q:msup><q:mrow><q:mi>J</q:mi></q:mrow><q:mrow><q:mi>P</q:mi><q:mi>C</q:mi></q:mrow></q:msup><q:mo>=</q:mo><q:msup><q:mrow><q:mn>1</q:mn></q:mrow><q:mrow><q:mo>−</q:mo><q:mo>+</q:mo></q:mrow></q:msup></q:mrow></q:math> recently calculated using lattice QCD. Published by the American Physical Society 2024