Abstract
By studying the color structure of multiparticle production processes in $\mathrm{p}+\mathrm{A}$-type (dilute-dense) collisions, we find that higher-point functions beyond typical dipoles and quadrupoles, e.g., sextupoles, octupoles, etc., naturally appear in the cross sections, but are explicitly suppressed in the large-${N}_{c}$ limit. We evaluate the sextupole in the McLerran-Venugopalan model and find that, in general, its analytical form cannot be written as combination of dipoles and quadrupoles. Within the color glass condensate framework, we present a proof that in the large-${N}_{c}$ limit, all multiparticle production processes in the collision of a dilute system off a dense system can, up to all orders in ${\ensuremath{\alpha}}_{s}$, be described in terms of only dipoles and quadrupoles.
Highlights
Calculating cross sections for multi-particle production processes can be theoretically challenging when a resummation of multiple interactions is needed, as is the case in large parton density environments such as the small-x regime accesible in high energy nuclear collisions
The sum over color indices in the final state guaranties that if a final state particle participates in the multiple scattering both in the amplitude and the conjugate amplitude, both Wilson lines appear next to each other in the contribution to the cross section, and if they are placed at the same transverse coordinate they exactly cancel out
Most of these studies are based on the dipole model approach [11], which shows directly a clear relation between the total cross section and the forward amplitude of a color dipole going through a background color field, but the same conclusions can be found from the setup explained in the previous sections after one integrates out all the particles in the final state
Summary
Calculating cross sections for multi-particle (multi-jet) production processes can be theoretically challenging when a resummation of multiple interactions is needed, as is the case in large parton density environments such as the small-x regime accesible in high energy nuclear collisions. Each parton traversing the field contributes to the scattering amplitude with a Wilson line in the appropriate representation (fundamental for quarks, adjoint for gluons) at a fixed transverse coordinate Provided they are put together in the correct order, the Wilson lines account for the color flow of the process under consideration. One could suggest that this Nc power counting implies that the leading Nc contribution always comes from a term which only includes color dipole amplitudes (traces of two Wilson lines) and has a maximal number of color traces This guess has been proven wrong since thorough studies of two-particle production processes [3,4,5] have shown that some processes do not admit a description in terms of only color dipoles, but that in addition color quadrupoles (traces of four Wilson lines) are involved as well in the large-Nc limit. The inductive step is greatly simplified by the observation that it is not necessary to consider all the diagrams contributing to a given process but to find at least one diagram with a term given only by dipoles and quadrupoles which dominates in the large-Nc limit
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