Incorporating next-to-leading order matrix elements for hadronic diboson production in showering event generators

TL;DR

The paper presents a framework to merge NLO QCD corrections with parton-shower event generators for hadronic diboson production by splitting phase space into a Dead Zone for hard emissions and a parton-shower region. It introduces a two-stage approach: matrix element corrections in the Dead Zone and a second-stage integration that folds the full NLO matrix element into the shower region, yielding events with NLO normalization and positive weights. Applications to $pp\rightarrow W^+Z$ at the LHC demonstrate good agreement with NLO distributions across a broad transverse-momentum range, while maintaining an exclusive, all-orders description of emissions and addressing normalization issues. The method is generalizable to any color-singlet process and can be implemented straightforwardly given access to NLO matrix elements, with considerations for potential negative weights and phase-space boundary effects.

Abstract

A method for incorporating information from next-to-leading order QCD matrix elements for hadronic diboson production into showering event generators is presented. In the hard central region (high jet transverse momentum) where perturbative QCD is reliable, events are sampled according to the first order tree level matrix element. In the soft and collinear regions next-to-leading order corrections are approximated by calculating the differential cross section across the phase space accessible to the parton shower using the first order (virtual graphs included) matrix element. The parton shower then provides an all-orders exclusive description of parton emissions. Events generated in this way provide a physical result across the entire jet transverse momentum spectrum, have next-to-leading order normalization everywhere, and have positive definite event weights. The method is generalizable without modification to any color singlet production process.

Figures (9)

• Figure 1: Example of a first order $WZ$ production graph with a gluon anchored to an internal line.
• Figure 2: The $\hat{s}/M^2$ vs. $\cos\hat{\theta}_j$ plane is shown with the boundary between the complimentary parton shower and Dead Zone regions denoted with a solid line. The phase space slicing region is a subset of the parton shower region and is denoted with a dashed line (for the specific phase space slicing parameters $\delta_{\mathrm s}=0.05,~\delta_{\mathrm c}=0.01$).
• Figure 3: The transverse momentum distribution of the $W^+Z$ system (inclusive recoil against emissions) $P^T_{\mathrm WZ}$ is compared at NLO, LO with parton shower, first order tree level in the Dead Zone, and at LO with soft and hard matrix element corrections. An enhanced view of the first low $P^T_{\mathrm WZ}$ bin is shown in the inset and the ratio of the NLO distribution to the LO and matrix element corrected distributions is shown at bottom.
• Figure 4: The transverse momentum distribution of the $Z$-boson $P^T_{\mathrm Z}$ is compared at NLO, LO with parton shower, first order tree level in the Dead Zone, and at LO with soft and hard matrix element corrections. An enhanced view of the first low $P^T_{\mathrm Z}$ bin is shown in the inset and the ratio of the NLO distribution to the LO and matrix element corrected distributions is shown at bottom.
• Figure 5: The rapidity separation distribution of the $W^+$ and $Z$-bosons is compared at NLO, LO with parton shower, first order tree level in the Dead Zone, and at LO with soft and hard matrix element corrections. The dip in the zero separation region is the approximate radiation zero. The ratio of the NLO distribution to the LO and matrix element corrected distributions is shown at bottom.