Inclusive hadroproduction of charmonia-bottomonia pairs in the CGC framework

In this paper, we analyze the inclusive hadroproduction of heavy charmonia-bottomonia pairs in the color glass condensate framework in the dilute-dense approximation. The production mechanisms can be classified by the number of gluons emitted from projectiles as single- and double-parton scattering. We analyzed separately both types of contributions and evaluated the corresponding impact factors in the leading order in strong coupling <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>α</a:mi><a:mi>s</a:mi></a:msub></a:math>. For the double-parton scattering, the impact factors factorize into a product of impact factors of single charmonia and bottomonia production cross sections, and the cross section in the large-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>N</c:mi><c:mi>c</c:mi></c:msub></c:math> limit reduces to the well-known pocket formula. For the single-parton scattering, we found that the cross section of the process is sensitive to dipole, quadrupole, sextupole, and octupole scattering amplitudes (correlators of Wilson lines), thus opening possibility to study phenomenologically these novel objects. We also made phenomenological estimates of the cross sections in the dilute approximation and found that the provided approach provides a fair qualitative description of the LHCb data for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>J</e:mi><e:mo>/</e:mo><e:mi>ψ</e:mi><e:mo>+</e:mo><e:mi mathvariant="normal">ϒ</e:mi><e:mo stretchy="false">(</e:mo><e:mn>1</e:mn><e:mi>S</e:mi><e:mo stretchy="false">)</e:mo></e:math> production.