We perform a systematic and comprehensive analysis of sub-leading colour corrections in perturbative QCD processes involving multiple soft gluon emissions. This necessitates going beyond the standard parton shower paradigm in order to incorporate interference effects and is accomplished using the CVolver program, which simulates parton showers at the amplitude level. We can compute cross-sections with full-colour precision and also broken down explicitly in terms of their Nc dependence. In this paper, we focus on the jet cross-section with a veto of additional jets in some fixed region of phase-space, since this is sensitive to wide-angle, soft gluon radiation. We consider <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi>Z</mi> <mo>→</mo> <mi>q</mi> <mover accent="true"> <mi>q</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ Z\to q\overline{q} $</EquationSource> </InlineEquation>, H → gg, <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi>q</mi> <mover accent="true"> <mi>q</mi> <mo stretchy="true">¯</mo> </mover> <mo>→</mo> <mi>q</mi> <mover accent="true"> <mi>q</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ q\overline{q}\to q\overline{q} $</EquationSource> </InlineEquation>, qg → qg, gg → gg and colour-singlet → <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi>q</mi> <mover accent="true"> <mi>q</mi> <mo stretchy="true">¯</mo> </mover> <mi>q</mi> <mover accent="true"> <mi>q</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ q\overline{q}q\overline{q} $</EquationSource> </InlineEquation>. We find that non-trivial sub-leading colour effects are generally important at the 5–30% level and much more than this for certain interference contributions. Remarkably, for this observable, we find that for all of the t-channel gluon exchange processes that we consider, the strictly leading colour approximation, which includes the replacement CF → CA/2, is an excellent approximation to the full colour result (up to an overall colour factor).

Exact colour evolution for jet observables

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2026年2月17日

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Jeffrey R. Forshaw,
Simon Plätzer,
Fernando Torre González

摘要

We perform a systematic and comprehensive analysis of sub-leading colour corrections in perturbative QCD processes involving multiple soft gluon emissions. This necessitates going beyond the standard parton shower paradigm in order to incorporate interference effects and is accomplished using the CVolver program, which simulates parton showers at the amplitude level. We can compute cross-sections with full-colour precision and also broken down explicitly in terms of their N_c dependence. In this paper, we focus on the jet cross-section with a veto of additional jets in some fixed region of phase-space, since this is sensitive to wide-angle, soft gluon radiation. We consider $Z \to q \bar{q}$ $ Z\to q\overline{q} $ , H → gg, $q \bar{q} \to q \bar{q}$ $ q\overline{q}\to q\overline{q} $ , qg → qg, gg → gg and colour-singlet → $q \bar{q} q \bar{q}$ $ q\overline{q}q\overline{q} $ . We find that non-trivial sub-leading colour effects are generally important at the 5–30% level and much more than this for certain interference contributions. Remarkably, for this observable, we find that for all of the t-channel gluon exchange processes that we consider, the strictly leading colour approximation, which includes the replacement C_F → C_A/2, is an excellent approximation to the full colour result (up to an overall colour factor).