Transverse-momentum resummation at mixed QCD$\otimes$QED NNLL accuracy for Z boson production at hadron colliders

TL;DR

This work delivers the first NNLL mixed QCD⊗QED transverse-momentum resummation for neutral-current Drell–Yan processes, extending the standard QCD $q_T$-resummation formalism to include simultaneous QED ISR. The authors derive and implement the mixed resummation in $b$-space with double perturbative expansions in $\alpha_S$ and $\alpha$, introducing new contributions $g'^{(2,1)}$, $g'^{(1,2)}$, and $g'^{(3)}$, along with the mixed running via $\beta_{n,m}$ and $\beta'_{n,m}$. Their numerical study with the DYTURBO code and NNPDF40.QEDNNPDF shows percent-level mixed QCD⊗QED effects on the $q_T$ spectrum, with QED and mixed terms shifting the peak and shaping the low-$q_T$ region, while pure QCD uncertainties remain dominant and are stabilized by higher-order corrections. The results enhance the precision of the DY $q_T$ predictions at hadron colliders, with implications for EW fits, PDF determinations, and collider phenomenology. The work also provides a framework for extending mixed resummation to other processes and higher orders.

Abstract

We consider the transverse momentum ($q_T$) distribution of neutral charged bosons at hadron colliders. We perform the resummation of the logarithmically-enhanced effects due to simultaneous QCD and QED initial-state radiation, up to mixed next-to-next-to-leading logarithmic (NNLL) accuracy. We study the impact of such mixed QCD$\otimes$QED resummed contributions on top of pure QCD corrections, finding percent-level effects.

Figures (5)

• Figure 1: $Z$/$\gamma^*$ production at LHC, $\sqrt{s} = 13 \, \text{TeV}$ at NNLL (left plot) and N$^3$LL (right plot) in QCD with the inclusion of mixed QCD$\otimes$QED effects up to NNLL. In the upper plot the differential distributions are showed, while in the lower one we show the ratios with respect to the QCD prediction at the central scale.
• Figure 2: $Z$/$\gamma^*$ production at Tevatron, $\sqrt{s} = 1.96 \, \text{TeV}$ at NNLL (left plot) and N$^3$LL (right plot) in QCD with the inclusion of mixed QCD$\otimes$QED effects up to NNLL. In the upper plot the differential distributions are showed, while in the lower one we show the ratios with respect to the QCD prediction at the central scale.
• Figure 3: $Z$/$\gamma^*$ production at the LHC with $\sqrt{s} = 13 \, \text{TeV}$ (left) and Tevatron with $\sqrt{s} = 1.96 \, \text{TeV}$ (right) at $\text{N}^3\text{LL}$ in QCD with the inclusion of mixed effects up to NNLL. In the upper plot the differential distributions in the invariant mass are showed, while in the lower one the ratios with respect to the QCD prediction.
• Figure 4: $Z$/$\gamma^*$ production at the LHC with $\sqrt{s} = 13 \, \text{TeV}$ (left) and Tevatron with $\sqrt{s} = 1.96 \, \text{TeV}$ (right) at $\text{N}^3\text{LL}$ in QCD with the inclusion of mixed effects up to NNLL. In the upper plot the differential distributions in the rapidity $y$ are showed, while in the lower one the ratios with respect to the QCD prediction.
• Figure 5: $Z/\gamma^*$ production at the Tevatron ($\sqrt{s} = 1.96 \,\text{TeV}$) at NNLL (left) and N$^3$LL (right) in QCD, including mixed QCD$\otimes$QED effects up to NNLL accuracy with $\alpha$ fixed. The lower panels show the ratio with respect to the pure QCD prediction, highlighting the impact of QED and mixed corrections. The uncertainty bands are obtained via scale variation, following the constraints indicated in the upper panels.