First lattice QCD calculation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:mrow></mml:math> semileptonic decay containing <mml:math xmlns:mml="http:

We perform the first lattice calculation on the semileptonic decay of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>J</a:mi><a:mo>/</a:mo><a:mi>ψ</a:mi></a:math> using the (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>2</c:mn><c:mo>+</c:mo><c:mn>1</c:mn></c:mrow></c:math>)-flavor Wilson-clover gauge ensembles generated by CLQCD collaboration. Three gauge ensembles with different lattice spacings, from 0.0519 to 0.1053 fm, and pion masses, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>m</e:mi><e:mi>π</e:mi></e:msub><e:mo>∼</e:mo><e:mn>300</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>MeV</e:mi></e:math>, are utilized. After a naive continuum extrapolation using three lattice spacings, we obtain <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>Br</g:mi><g:mo stretchy="false">(</g:mo><g:mi>J</g:mi><g:mo>/</g:mo><g:mi>ψ</g:mi><g:mo stretchy="false">→</g:mo><g:msub><g:mi>D</g:mi><g:mi>s</g:mi></g:msub><g:mi>e</g:mi><g:msub><g:mi>ν</g:mi><g:mi>e</g:mi></g:msub><g:mo stretchy="false">)</g:mo><g:mo>=</g:mo><g:mn>1.90</g:mn><g:mo stretchy="false">(</g:mo><g:mn>6</g:mn><g:mo stretchy="false">)</g:mo><g:mo stretchy="false">(</g:mo><g:mn>5</g:mn><g:msub><g:mo stretchy="false">)</g:mo><g:msub><g:mi>V</g:mi><g:mrow><g:mi>c</g:mi><g:mi>s</g:mi></g:mrow></g:msub></g:msub><g:mo>×</g:mo><g:msup><g:mn>10</g:mn><g:mrow><g:mo>−</g:mo><g:mn>10</g:mn></g:mrow></g:msup></g:math> and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>Br</p:mi><p:mo stretchy="false">(</p:mo><p:mi>J</p:mi><p:mo>/</p:mo><p:mi>ψ</p:mi><p:mo stretchy="false">→</p:mo><p:mi>D</p:mi><p:mi>e</p:mi><p:msub><p:mi>ν</p:mi><p:mi>e</p:mi></p:msub><p:mo stretchy="false">)</p:mo><p:mo>=</p:mo><p:mn>1.21</p:mn><p:mo stretchy="false">(</p:mo><p:mn>6</p:mn><p:mo stretchy="false">)</p:mo><p:mo stretchy="false">(</p:mo><p:mn>9</p:mn><p:msub><p:mo stretchy="false">)</p:mo><p:msub><p:mi>V</p:mi><p:mrow><p:mi>c</p:mi><p:mi>d</p:mi></p:mrow></p:msub></p:msub><p:mo>×</p:mo><p:msup><p:mn>10</p:mn><p:mrow><p:mo>−</p:mo><p:mn>11</p:mn></p:mrow></p:msup></p:math>, where the first errors are statistical, and the second come from the uncertainties of Cabibbo-Kobayashi-Maskawa matrix element <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>V</y:mi><y:mrow><y:mi>c</y:mi><y:mi>s</y:mi><y:mo stretchy="false">(</y:mo><y:mi>d</y:mi><y:mo stretchy="false">)</y:mo></y:mrow></y:msub></y:math>. The ratios of the branching fractions between lepton <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>μ</cb:mi></cb:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>e</eb:mi></eb:math> are also calculated as <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>R</gb:mi><gb:mrow><gb:mi>J</gb:mi><gb:mo>/</gb:mo><gb:mi>ψ</gb:mi></gb:mrow></gb:msub><gb:mo stretchy="false">(</gb:mo><gb:msub><gb:mi>D</gb:mi><gb:mi>s</gb:mi></gb:msub><gb:mo stretchy="false">)</gb:mo><gb:mo>=</gb:mo><gb:mn>0.97002</gb:mn><gb:mo stretchy="false">(</gb:mo><gb:mn>8</gb:mn><gb:mo stretchy="false">)</gb:mo></gb:math> and <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msub><mb:mi>R</mb:mi><mb:mrow><mb:mi>J</mb:mi><mb:mo>/</mb:mo><mb:mi>ψ</mb:mi></mb:mrow></mb:msub><mb:mo stretchy="false">(</mb:mo><mb:mi>D</mb:mi><mb:mo stretchy="false">)</mb:mo><mb:mo>=</mb:mo><mb:mn>0.97423</mb:mn><mb:mo stretchy="false">(</mb:mo><mb:mn>15</mb:mn><mb:mo stretchy="false">)</mb:mo></mb:math> after performing a continuum limit including only <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msup><sb:mi>a</sb:mi><sb:mn>2</sb:mn></sb:msup></sb:math> term. The ratios provide necessary theoretical support for the future experimental test of lepton flavor universality. Published by the American Physical Society 2024