Mass spectrum of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mn>1</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:math> heavy quarkonium

Abstract

We calculate the masses and leptonic decay widths of the bottomonium <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>b</a:mi><a:mover accent="true"><a:mi>b</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> and charmonium <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>c</e:mi><e:mover accent="true"><e:mi>c</e:mi><e:mo stretchy="false">¯</e:mo></e:mover></e:math> states in a constituent quark model where the Cornell-like potential and spin-dependent interaction are employed, with all model parameters predetermined by studying ground and first radial excited states of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>S</i:mi></i:math>- and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>P</k:mi></k:math>-wave heavy quarkonium mesons. By comparing the theoretical predictions for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>J</m:mi><m:mrow><m:mi>P</m:mi><m:mi>C</m:mi></m:mrow></m:msup><m:mo>=</m:mo><m:msup><m:mn>1</m:mn><m:mrow><m:mo>−</m:mo><m:mo>−</m:mo></m:mrow></m:msup></m:math> quarkonium states with experimental data and considering possible mixtures of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>n</o:mi><o:mi>S</o:mi></o:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mo stretchy="false">(</q:mo><q:mi>n</q:mi><q:mo>−</q:mo><q:mn>1</q:mn><q:mo stretchy="false">)</q:mo><q:mi>D</q:mi></q:math> states, we provide tentative assignments for all observed <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msup><u:mi>J</u:mi><u:mrow><u:mi>P</u:mi><u:mi>C</u:mi></u:mrow></u:msup><u:mo>=</u:mo><u:msup><u:mn>1</u:mn><u:mrow><u:mo>−</u:mo><u:mo>−</u:mo></u:mrow></u:msup></u:math> heavy quarkonia. The work suggests that the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi mathvariant="normal">ϒ</w:mi><w:mo stretchy="false">(</w:mo><w:mn>10860</w:mn><w:mo stretchy="false">)</w:mo></w:math> and <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mi mathvariant="normal">ϒ</bb:mi><bb:mo stretchy="false">(</bb:mo><bb:mn>11020</bb:mn><bb:mo stretchy="false">)</bb:mo></bb:math> are <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>b</gb:mi><gb:mover accent="true"><gb:mi>b</gb:mi><gb:mo stretchy="false">¯</gb:mo></gb:mover></gb:math> <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mn>5</kb:mn><kb:mi>S</kb:mi><kb:mo>−</kb:mo><kb:mn>4</kb:mn><kb:mi>D</kb:mi></kb:math> mixture states, and the <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>ψ</mb:mi><mb:mo stretchy="false">(</mb:mo><mb:mn>4360</mb:mn><mb:mo stretchy="false">)</mb:mo></mb:math> and <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi>ψ</qb:mi><qb:mo stretchy="false">(</qb:mo><qb:mn>4415</qb:mn><qb:mo stretchy="false">)</qb:mo></qb:math> are largely <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mn>4</ub:mn><ub:mi>S</ub:mi></ub:math> and <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:mn>3</wb:mn><wb:mi>D</wb:mi></wb:math> <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mi>c</yb:mi><yb:mover accent="true"><yb:mi>c</yb:mi><yb:mo stretchy="false">¯</yb:mo></yb:mover></yb:math> states, respectively. The <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:mi>ψ</cc:mi><cc:mo stretchy="false">(</cc:mo><cc:mn>4230</cc:mn><cc:mo stretchy="false">)</cc:mo></cc:math> may not be accommodated with the conventional meson picture in the present work. Published by the American Physical Society 2024

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