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From papers on the concept of quark/gluon jet tagging, I've seen that gluon jets have more particles and a broader radiation pattern. Why does carrying more color charge allow them to produce more particles? Is the broader radiation pattern a consequence of the production of more particles?

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You'll get better answers by QCD experts, most likely, but, crudely, leading logarithmic QCD predicts that the multiplicity of hadrons in a gluon jet should be larger than that in a quark jet by the ratio of their color SU(3) charges,$C_A/C_F =9/4$, the ratio of the Adjoint (3) to Fundamental (4/3) color representation Casimir invariants, cf Seymour, 1996.

So, typically, the likelihood of a gluon going to two gluons is larger than that for a quark to quark-gluon ( inspect the Feynman diagrams). Higher probabilities translate to more interactions. With more particles in your cone, it is likely to be broader, and have the momentum of the original hard particle coming out of the hard scattering be spread around more by the more numerous daughter particles more dispersed around the jet axis.

The original paper discussing this is Konishi, Ukawa, & Veneziano, (1978). "A simple algorithm for QCD jets", Physics Letters B78 (2-3), 243-248.

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