QCD corrections of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mi>

In this paper, we compute the total and differential cross sections for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>e</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>e</a:mi><a:mo>−</a:mo></a:msup><a:mo stretchy="false">→</a:mo><a:mi>J</a:mi><a:mo>/</a:mo><a:mi>ψ</a:mi><a:mo>+</a:mo><a:mi>c</a:mi><a:mo>+</a:mo><a:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> at the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>B</f:mi></f:math> factories up to next-to-leading order (NLO) corrections within the framework of nonrelativistic quantum chromodynamics (QCD) factorization theory. We then obtain improved perturbative QCD (pQCD) series of those cross sections by using the principle of maximum conformality (PMC). We show that the PMC can be applied for any pQCD calculable observable at the total and differential levels via a self-consistent way in perturbation theory. We observe that a more precise prompt total cross section at the NLO level can be achieved after applying the PMC, e.g., <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>σ</h:mi><h:msubsup><h:mo stretchy="false">|</h:mo><h:mtext>prompt</h:mtext><h:mrow><h:mi>PMC</h:mi></h:mrow></h:msubsup><h:mo>=</h:mo><h:mn>0.56</h:mn><h:msubsup><h:mn>5</h:mn><h:mrow><h:mo>−</h:mo><h:mn>0.125</h:mn></h:mrow><h:mrow><h:mo>+</h:mo><h:mn>0.144</h:mn></h:mrow></h:msubsup><h:mtext> </h:mtext><h:mtext> </h:mtext><h:mi>pb</h:mi></h:math>. Here the uncertainty is the squared average of those from the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>α</k:mi><k:mi>s</k:mi></k:msub></k:math> fixed-point uncertainty <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi mathvariant="normal">Δ</m:mi><m:msub><m:mi>α</m:mi><m:mi>s</m:mi></m:msub><m:mo stretchy="false">(</m:mo><m:msub><m:mi>M</m:mi><m:mi>Z</m:mi></m:msub><m:mo stretchy="false">)</m:mo></m:math>, the uncertainty of charm quark mass <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi mathvariant="normal">Δ</r:mi><r:msub><r:mi>m</r:mi><r:mi>c</r:mi></r:msub></r:math>, and an estimated contribution of the uncalculated NNLO-terms as predicted by the Padé approximation approach. The differential cross sections <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>d</u:mi><u:mi>σ</u:mi><u:mo>/</u:mo><u:mi>d</u:mi><u:msub><u:mi>P</u:mi><u:mrow><u:mi>J</u:mi><u:mo>/</u:mo><u:mi>ψ</u:mi></u:mrow></u:msub></u:math>, <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>d</w:mi><w:mi>σ</w:mi><w:mo>/</w:mo><w:mi>d</w:mi><w:mo stretchy="false">|</w:mo><w:mi>cos</w:mi><w:mi>θ</w:mi><w:mo stretchy="false">|</w:mo></w:math>, and <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>d</ab:mi><ab:mi>σ</ab:mi><ab:mo>/</ab:mo><ab:mi>d</ab:mi><ab:mi>z</ab:mi></ab:math> for <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msup><cb:mi>e</cb:mi><cb:mo>+</cb:mo></cb:msup><cb:msup><cb:mi>e</cb:mi><cb:mo>−</cb:mo></cb:msup><cb:mo stretchy="false">→</cb:mo><cb:mi>J</cb:mi><cb:mo>/</cb:mo><cb:mi>ψ</cb:mi><cb:mo>+</cb:mo><cb:mi>c</cb:mi><cb:mo>+</cb:mo><cb:mover accent="true"><cb:mi>c</cb:mi><cb:mo stretchy="false">¯</cb:mo></cb:mover></cb:math> are further examined. Those results show that by further considering the feed-down contributions, the PMC predictions show better agreement with the Belle measurements. Published by the American Physical Society 2024