The impact of the nonlinear effects in the QCD on the observables is directly related to the magnitude of the saturation scale <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>Q</a:mi><a:mi>s</a:mi></a:msub></a:math>, which is predicted to increase with the energy, rapidity, and multiplicity. In this paper, we investigate the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>D</c:mi><c:mn>0</c:mn></c:msup></c:math> meson 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 forward rapidities and/or high multiplicities considering the color glass condensate (CGC) formalism and the solutions of the running coupling Balitsky-Kovchegov equation. The contributions of gluon- and charm-initiated processes are taken into account, and a comparison with the current LHCb data is performed. The impact of an intrinsic charm component in the proton’s wave function is also estimated. Predictions for the self-normalized yields of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>D</g:mi><g:mn>0</g:mn></g:msup></g:math> mesons as a function of the multiplicity of coproduced charged hadrons are presented, considering <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>p</i:mi><i:mi>p</i:mi></i:math> collisions at <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msqrt><k:mi>s</k:mi></k:msqrt><k:mo>=</k:mo><k:mn>13</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>TeV</k:mi></k:math> and different values of the meson rapidity. A comparison with the predictions for the kaon and isolated photon production is performed. Our results indicate that a future experimental analysis of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>D</m:mi><m:mn>0</m:mn></m:msup></m:math> meson production at forward rapidities and high multiplicities can be useful to probe the CGC formalism and to disentangle the contribution of initial—and final—state effects. Published by the American Physical Society 2024
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