Forward <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:mo>+</mml:mo><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:mo>+</mml:mo><mml:msup><mml:mi>ψ</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math> production with high-energy factorization

We calculate the cross sections of associated <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:mo>+</a:mo><a:msup><a:mi>ψ</a:mi><a:mo>′</a:mo></a:msup></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>J</c:mi><c:mo>/</c:mo><c:mi>ψ</c:mi><c:mo>+</c:mo><c:mi>J</c:mi><c:mo>/</c:mo><c:mi>ψ</c:mi></c:math> production in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>p</e:mi><e:mi>p</e:mi></e:math> collisions at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msqrt><g:mi>s</g:mi></g:msqrt><g:mo>=</g:mo><g:mn>13</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>TeV</g:mi></g:math> in the forward kinematic region. The high-energy factorization (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>k</i:mi><i:mi>T</i:mi></i:msub></i:math>-factorization) framework supplemented with the Catani-Ciafaloni-Fiorani-Marchesini evolution of gluon densities in a proton is applied. We demonstrate that the latest data on <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>J</k:mi><k:mo>/</k:mo><k:mi>ψ</k:mi><k:mo>+</k:mo><k:mi>J</k:mi><k:mo>/</k:mo><k:mi>ψ</k:mi></k:math> production and first experimental data on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>J</m:mi><m:mo>/</m:mo><m:mi>ψ</m:mi><m:mo>+</m:mo><m:msup><m:mi>ψ</m:mi><m:mo>′</m:mo></m:msup></m:math> events taken very recently by the LHCb Collaboration can be described well by the color singlet terms and contributions from double parton scattering (DPS) with the standard choice for <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>σ</o:mi><o:mi>eff</o:mi></o:msub></o:math> parameter. The relative production rate <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>σ</q:mi><q:mo stretchy="false">(</q:mo><q:mi>J</q:mi><q:mo>/</q:mo><q:mi>ψ</q:mi><q:mo>+</q:mo><q:msup><q:mi>ψ</q:mi><q:mo>′</q:mo></q:msup><q:mo stretchy="false">)</q:mo><q:mo>/</q:mo><q:mi>σ</q:mi><q:mo stretchy="false">(</q:mo><q:mi>J</q:mi><q:mo>/</q:mo><q:mi>ψ</q:mi><q:mo>+</q:mo><q:mi>J</q:mi><q:mo>/</q:mo><q:mi>ψ</q:mi><q:mo stretchy="false">)</q:mo></q:math> is found to be sensitive to the DPS terms as well as to feeddown contributions. Published by the American Physical Society 2024

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