Combining QCD Matrix Elements at Next-to-Leading Order with Parton Showers in Electroproduction

TL;DR

This work addresses the challenge of merging next-to-leading order QCD matrix elements with parton showers in electroproduction by introducing a scale-dependent phase-space-slicing cut-off $\delta^{nlo}$ that cancels the Born, virtual, and soft/collinear pieces in the $n$-jet region. The remaining NLO corrections are carried by positive-weight hard $(n+1)$-parton matrix elements, which can be redistributed by the parton shower, enabling practical event generation without negative weights. The method is demonstrated for inclusive single-jet production in DIS at $O(alpha_s)$, where a dynamical cut-off is computed for each phase-space point and validated against standard phase-space slicing, showing percent-level agreement and stability under scale variations. Implemented in RAPGAP/MEPJET, the approach provides a viable path toward more complete NLO-PS matching and sets the stage for extensions to dijet production and other observables.

Abstract

We present a method to combine next-to-leading order (NLO) matrix elements in QCD with leading logarithmic parton showers by applying a suitably modified version of the phase-space-slicing method. The method consists of subsuming the NLO corrections into a scale-dependent phase-space-slicing parameter, which is then automatically adjusted to cut out the leading order, virtual, soft and collinear contributions in the matrix element calculation. In this way a positive NLO weight is obtained, which can be redistributed by a parton shower algortihm. As an example, we display the method for single-jet inclusive cross sections at O(alpha_s) in electroproduction. We numerically compare the modified version of the phase-space-slicing method with the standard approach and find very good agreement on the percent level.

Figures (2)

• Figure 1: The function $s_{\hbox{\scriptsize min}}$ versus $Q^2$ for the scales $\mu_R=\mu_F=\hbox{$\frac{1}{4}$}Q^2,Q^2,4Q^2$ for the four values $x=10^{-4},10^{-3},10^{-2}$ and $10^{-1}$.
• Figure 2: Inclusive single-jet cross section for $E_T^{\hbox{\scriptsize lab}}>5$ GeV, $|\eta^{\hbox{\scriptsize lab}}|<2$ and $Q^2>10$ GeV$^2$ as a function of $s_{\hbox{\scriptsize min}}$. The $s_{\hbox{\scriptsize min}}$ values at which the one-parton contributions vanish lie well within the $s_{\hbox{\scriptsize min}}$ independent region for all $Q^2$.