Next-to-leading order QCD jet production with parton showers and hadronization

TL;DR

This work develops and tests a method to match next-to-leading order QCD calculations of $e^+e^-\to3$ jets with a Monte Carlo parton shower and hadronization (via Pythia), producing realistic final states while preserving NLO accuracy for infrared-safe observables. The algorithm introduces Sudakov-based primary showers and subtraction terms to avoid double counting, then merges with a partially developed shower that respects multiple scales through a synthetic $k_T$ history and vetoed Pythia showers. Results show that NLO+PS+Had reproduces NLO for the three-jet fraction within ~10% and yields physically sensible jet-mass distributions after hadronization, closely matching Pythia predictions and removing unphysical features of pure NLO. Sensitivity studies confirm robustness to reasonable variations in matching parameters, supporting the practical utility of NLO+PS+Had for realistic jet phenomenology. The approach paves the way for more flexible NLO-MC hybrids and improved multi-jet event modeling in collider analyses.

Abstract

We report on a method for matching the next-to-leading order calculation of QCD jet production in e+e- annihilation with a Monte Carlo parton shower event generator (MC) to produce realistic final states. The final result is accurate to next-to-leading order (NLO) for infrared-safe one-scale quantities, such as the Durham 3-jet fraction y_3, and agrees well with parton shower results for multi-scale quantities, such as the jet mass distribution in 3-jet events. For our numerical results, the NLO calculation is matched to the event generator Pythia, though the method is more general. We compare one scale and multi-scale quantities from pure NLO, pure MC, and matched NLO-MC calculations.

Figures (11)

• Figure 1: Jet mass distribution in three-jet events, $f_3^{-1}\,df_3/dM$, calculated at next-to-leading order for $\sqrt s = M_Z$. The three jets are identified using the $k_T$ algorithm with $y_{\rm cut} = 0.05$. Then $M$ is the invariant mass of one of the three jets, with each event making three contributions to $df_3/dM$. The renormalization scale is chosen as $\mu = \sqrt s / 6$ and $\alpha_s(M_Z)=0.118$. This is a pure NLO calculation using beowulf. There is a large negative contribution in the first bin.
• Figure 2: Jet mass distribution in three-jet events, $f_3^{-1}\,df_3/dM$, calculated according to PythiaPythia with default parameters for $\sqrt s = M_Z$. The cross section is defined as in Fig. \ref{['fig:df3dmNLO']}. The jet mass distribution from the perturbative NLO calculation in Fig. \ref{['fig:df3dmNLO']} is shown for comparison.
• Figure 3: Parton splitting in Refs. nloshowersInloshowersII. The filled circles represent graphs for the Born amplitude and complex conjugate amplitude. Each of the partons emerging from the Born amplitude splits into two partons with a vertex, represented by the squares, that includes a Sudakov suppression factor. The extra gluon coming from the circles on the right and left represents the soft gluon radiated from the three jets. Each of the seven daughter partons undergoes further, secondary, splittings according to Pythia and enters the final state as a complete shower with hadronization. The secondary splittings are represented by the diamonds.
• Figure 4: Treatment of order $\alpha_s^{B+1}$ graphs. One particular cut diagram is shown, in this case a cut diagram with a virtual loop. The second diagram illustrates a subtraction term, which corresponds to a contribution at order $\alpha_s^{B+1}$ from Fig. \ref{['bornshower']}. The partonic final state is generated with a weight proportional to the difference of matrix elements, then this final state is sent to Pythia, which is represented by the diamonds.
• Figure 5: Three-jet fraction, $f_3$, versus $y_{\rm cut}$. The top panel shows $f_3[{\tt NLO}]$. The bottom panel shows the ratios of $f_3[{\tt NLO+PS+Had}]$, $f_3[{\tt LO+PS+Had}]$, $f_3[{\tt LO}]$, and $f_3[{\tt Pythia}]$ to $f_3[{\tt NLO}]$. The parameters are as in Figs. \ref{['fig:df3dmNLO']} and \ref{['fig:df3dmPythia']}.