Standard dipole parton showers are known to yield incorrect subleading-colour contributions to the leading (double) logarithmic terms for a variety of observables. In this work, concentrating on final-state showers, we present two simple, computationally efficient prescriptions to correct this problem, exploiting a Lund-diagram type classification of emission regions. We study the resulting effective multiple-emission matrix elements generated by the shower, and discuss their impact on subleading colour contributions to leading and next-to-leading logarithms (NLL) for a range of observables. In particular we show that the new schemes give the correct full colour NLL terms for global observables and multiplicities. Subleading colour issues remain at NLL (single logarithms) for non-global observables, though one of our two schemes reproduces the correct full-colour matrix-element for any number of energy-ordered commensurate-angle pairs of emissions. While we carry out our tests within the PanScales shower framework, the schemes are sufficiently simple that it should be straightforward to implement them also in other shower frameworks.

We revisit the calculation of the average jet multiplicity in high-energy collisions. First, we introduce a new definition of (sub)jet multiplicity based on Lund declusterings obtained using the Cambridge jet algorithm. We develop a new systematic resummation approach. This allows us to compute both the Lund and the Cambridge average multiplicities to next-to-next-to-double (NNDL) logarithmic accuracy in electron-positron annihilation, an order higher in accuracy than previous works in the literature. We match our resummed calculation to the exact NLO ($$ \mathcal{O} $$ O ($$ {\alpha}_s^2 $$ α s 2 )) result, showing predictions for the Lund multiplicity at LEP energies with theoretical uncertainties up to 50% smaller than the previous state-of-the-art. Adding hadronisation corrections obtained by Monte Carlo simulations, we also show a good agreement with existing Cambridge multiplicity data. Finally, to highlight the flexibility of our method, we extend the Lund multiplicity calculation to hadronic collisions where we reach next-to-double logarithmic accuracy for colour singlet production.

We compute the average Lund multiplicity of high-energy QCD jets. This extends an earlier calculation, done for event-wide multiplicity in e+e− collisions [1], to the large energy range available at the LHC. Our calculation achieves next-to-next-to-double logarithmic (NNDL) accuracy. Our results are split into a universal collinear piece, common to the e+e− calculation, and a non-universal large-angle contribution. The latter amounts to 10–15% of the total multiplicity. We provide accurate LHC predictions by matching our resummed calculation to fixed-order NLO results and by incorporating non-perturbative corrections via Monte Carlo simulations. Including NNDL terms leads to a 50% reduction of the theoretical uncertainty, with non-perturbative corrections remaining below 5% down to transverse momentum scales of a few GeV. This proves the suitability of Lund multiplicities for robust theory-to-data comparisons at the LHC.

We revisit the calculation of the average jet multiplicity in high-energy collisions. First, we introduce a new definition of (sub)jet multiplicity based on Lund declusterings obtained using the Cambridge jet algorithm. We develop a new systematic resummation approach. This allows us to compute both the Lund and the Cambridge average multiplicities to next-to-nextto-double (NNDL) logarithmic accuracy in electron-positron annihilation, an order higher in accuracy than previous works in the literature. We match our resummed calculation to the exact NLO (O α 2 s ) result, showing predictions for the Lund multiplicity at LEP energies with theoretical uncertainties up to 50% smaller than the previous state-of-the-art. Adding hadronisation corrections obtained by Monte Carlo simulations, we also show a good agreement with existing Cambridge multiplicity data. Finally, to highlight the flexibility of our method, we extend the Lund multiplicity calculation to hadronic collisions where we reach next-to-double logarithmic accuracy for colour singlet production.

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