A positive-weight next-to-leading order simulation of weak boson pair production

TL;DR

The paper develops a positive-weight next-to-leading order (NLO) simulation for weak boson pair production (ZZ, WZ, WW) using the Powheg method within the Herwig++ framework, augmented by truncated showers and spin-correlated vector-boson decays. It organizes the NLO cross section into $ar{B}(oldsymbol{ ext{Φ}}_B)$, $B(oldsymbol{ ext{Φ}}_B)$, $V$, and $R$, with a Sudakov form factor governing the hardest emission and a detailed phase-space parameterization via Born and radiative variables. The authors exploit relations among WW, WZ, and ZZ matrix elements to reuse existing calculations, and perform extensive validation against MCFM and MC@NLO, both for inclusive and exclusive observables at Tevatron and LHC energies. The results show good agreement with independent NLO predictions and reveal the characteristic Powheg behavior of enhanced high-$p_T$ radiation, while also addressing dead zones and shower effects. The work delivers a validated, production-ready tool for high-precision diboson simulations in a fully exclusive, showered environment, to be included in the next public release of Herwig++.

Abstract

In this article we describe simulations of ZZ, WZ and WW production based on the positive weight next-to-leading-order matching scheme, Powheg, in the Herwig++ event generator. Building on earlier efforts within the Herwig++ framework, the simulation includes a full description of truncated showering effects, required to correctly model soft, wide angle, emissions in angular-ordered parton showers. We utilize simple relations among each of the diboson cross sections, holding to order alpha_S, in constructing the simulation. Spin correlation effects are also included in the decays of the vector bosons at the tree order. A large part of this work is concerned with a full and thorough validation of the simulations through comparisons with alternative methods and calculations.

Figures (9)

• Figure 1: In this figure we show predictions for the invariant mass $\left(p^{2}\right)$ and rapidity $\left(\mathrm{y}\right)$ of the vector boson pair system, in the left- and right-hand columns respectively; the results obtained using the Powheg simulation are shown in red while the blue dotted line and the black points represent the leading and next-to-leading order predictions from Mcfm. Since $p^{2}$ and $\mathrm{y}$ are Born variables in the Powheg simulation, they are distributed purely according to the $\overline{B}\left(\Phi_{B}\right)$ function, hence they must follow exactly the corresponding NLO prediction (Sect. \ref{['sub:Kinematics-and-phase']}).
• Figure 2: The polar angle between the incident parton traveling in the $+z$ direction and the first of the produced vector bosons in their rest frame; in $W^{\pm}Z$ and $W^{+}W^{-}$ production these are taken to be the $W^{\pm}$ and $W^{+}$ bosons respectively. Since this variable is fully inclusive and a close relative of the Born variable, $\theta$, the level of agreement shown here between the Powheg and Mcfm predictions provides strong confirmation as to the correctness of our implementation.
• Figure 3: On the left we show the distribution of the polar angle of one of the leptons emitted by one of the decaying weak bosons, in the rest frame of the decay, while on the right hand-side we show the corresponding transverse momentum spectrum. The colouring of the different predictions is as in the previous figures. Note that in plotting these quantities the branching fractions of the vector boson decays have been divided out.
• Figure 4: The transverse momentum spectrum of the produced weak boson pair system at Tevatron (left) and LHC (right) energies. Predictions from the Mc @nlo and Herwig++ Powheg simulations are present as black and red dashed lines respectively. Results from the leading order Herwig++ parton shower simulation are also shown as blue dotted lines. For the case of a single emission this quantity is equivalent to the radiative variable $p_{T}$ introduced in Section \ref{['sub:Kinematics-and-phase']}.
• Figure 5: The transverse momentum of the hardest jet in weak boson pair production at the LHC (left) and Tevatron (right), assuming a nominal LHC centre-of-mass energy, $\sqrt{s}=14\,\mathrm{TeV}$. The colouring of the histograms is the same as in figure \ref{['fig:VV_system_pT_spectra']}. As for the case of weak boson pair system, for a single emission this quantity is equal to the radiative variable $p_{T}$ in Section \ref{['sub:Kinematics-and-phase']}.