Parton Showers beyond Leading Logarithmic Accuracy

Parton showers are among the most widely used tools in collider physics. Despite their key importance, none so far have been able to demonstrate accuracy beyond a basic level known as leading logarithmic order, with ensuing limitations across a broad spectrum of physics applications. In this Letter, we propose criteria for showers to be considered next-to-leading logarithmic accurate. We then introduce new classes of shower, for final-state radiation, that satisfy the main elements of these criteria in the widely used large-$N_C$ limit. As a proof of concept, we demonstrate these showers’ agreement with all-order analytical next-to-leading logarithmic calculations for a range of observables, something never so far achieved for any parton shower.

Figure 1

Left: distribution for the difference in azimuthal angle between the two highest-$k_t$ primary Lund declusterings in the pythia8 dipole shower algorithm, normalized to the NLL result [51, 66], Sec. 4 of the Supplemental Material; successively smaller ${\alpha }_s$ values keep fixed ${\alpha }_s\ln k_{t1}$. Middle: the same for the PanGlobal($\beta =0$) shower. Right: the ${\alpha }_s\to 0$ limit of the ratio for multiple showers. This observable directly tests part of our NLL (squared) matrix-element correctness condition. A unit value for the ratio signals success.

Figure 2

Left: ratio of the cumulative $y_{23}$ distribution from several showers divided by the NLL answer, as a function of ${\alpha }_s\ln y_{23}/2$, for ${\alpha }_s\to 0$. Right: summary of deviations from NLL for many shower and observable combinations [either ${\mathrm{\Sigma }}_{\text{shower}}({\alpha }_s\to 0,{\alpha }_{s}L=-0.5)/{\mathrm{\Sigma }}_{\mathrm{NLL}}-1$ or $[N_{\text{shower}}^{\text{subjet}}({\alpha }_s\to 0,{\alpha }_s{L}^2=5)/N_{\mathrm{NLL}}^{\text{subjet}}-1]/\sqrt{{\alpha }_s}$]. Red squares indicate clear NLL failure; amber triangles indicate NLL fixed-order failure that is masked at all orders; green circles indicate that all NLL tests passed.