Matching NNLO to parton shower using N$^3$LL colour-singlet transverse momentum resummation in GENEVA

TL;DR

This work extends the Geneva NNLO+PS framework by using the colour-singlet transverse momentum $q_ op$ as the 0-jet resolution variable, enabling $N^3LL$ resummation via the RadISH formalism and fully exclusive Drell–Yan predictions matched to a Pythia8 shower. It validates the approach by comparing to Matrix+RadISH for resummation accuracy and NNLO fixed-order results, then demonstrates good agreement with 13 TeV ATLAS and CMS data across $q_ op$ and $box{$oldsymbol{ extphi^*}$}$ observables. A key finding is that a more local recoil scheme in the shower can align showered results with analytic $N^3LL$ predictions, while the dual-resolution-variable setup allows robust assessment of systematic effects. The framework provides a versatile, high-precision tool for colour-singlet production, with potential extensions to other processes and further refinements in nonperturbative tuning and joint-resummation strategies.

Abstract

We extend the GENEVA Monte Carlo framework using the transverse momentum of a colour-singlet system as the resolution variable. This allows us to use next-to-next-to-next-to leading logarithm (N$^3$LL) resummation via the \radish formalism to obtain precise predictions for any colour-singlet production process at the fully exclusive level. Thanks to the implementation of two different resolution variables within the GENEVA framework, we are able to assess the impact of such a choice on differential observables for the first time. As a first application we present predictions for Drell-Yan lepton pair production at next-to-next-to-leading order (NNLO) in QCD interfaced to a parton shower simulation that includes additional all-order radiative corrections. We provide fully showered and hadronised events using PYTHIA8, while retaining the NNLO QCD accuracy for observables which are inclusive over the additional radiation. We also show that it is possible to obtain a numerically good agreement between showered GENEVA predictions and the N$^3$LL resummation for the transverse momentum spectrum by choosing a more local recoil scheme. We compare our final predictions to LHC data at 13 TeV, finding good agreement across several distributions.

Figures (14)

• Figure 1: Damping function used to further suppress the resummation at large values of $q_\perp$, see text for details.
• Figure 2: Nonsingular cumulant at order $\alpha_{\mathrm{S}}^2$ as a function of $q_\perp^{\rm cut}$.
• Figure 3: Comparison between the resummed N$^3$LL (left panel) and matched N$^3$LL+NLO$_1$ (right panel) results obtained with Matrix+RadISH and with Geneva+RadISH.
• Figure 4: Comparison between the NNLO results obtained with Matrix and the results obtained with Geneva+RadISH. Upper panel: invariant mass (left) and rapidity (right) of the lepton pair. Lower panel: rapidity (left) and transverse momentum (right) of the hardest lepton.
• Figure 5: Comparison between the parton level and the showered results with and without the Pythia8dipoleRecoil option for the rapidity distribution (left) and for the transverse momentum distribution (right) of the lepton pair.