<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> polarization and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline

The quarkonium production in association with a heavy-quark pair of the same flavor was found to play an important role in various production schemes and provide a distinctive signature that could be studied in experiment. Within the nonrelativistic QCD framework, we perform the first complete calculation of the hadroproduction process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>g</a:mi><a:mi>g</a:mi><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:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> at the next-to-leading order (NLO) in the expansion of strong coupling constant <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>α</f:mi><f:mi>s</f:mi></f:msub></f:math>. The result tells us that the NLO corrections substantially enhance the color-singlet yield and alter the predicted polarization patterns and, hence, lead to a better agreement with experimental data across the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>p</h:mi><h:mi>T</h:mi></h:msub></h:math> spectrum. In contrast to charm-quark fragmentation, the fixed-order <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>J</j:mi><j:mo>/</j:mo><j:mi>ψ</j:mi></j:math> and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>c</l:mi><l:mover accent="true"><l:mi>c</l:mi><l:mo stretchy="false">¯</l:mo></l:mover></l:math> associated production channel displays a markedly different kinematic behavior. While the inclusion of this process greatly reduces the discrepancy between color-singlet theoretical prediction and experimental measurement, a residual gap of approximately 1 order of magnitude still remains.