Weak Gauge Boson Radiation in Parton Showers

TL;DR

This work extends parton-shower algorithms to include weak gauge-boson emissions (W and Z) on equal footing with QCD and QED, linking real weak radiation to negative virtual corrections through unitarity. The authors develop a robust weak-shower framework, address mass, spin, and flavour-change effects, and implement matrix-element merging to improve accuracy near heavy-boson mass thresholds. They validate the approach against matrix-element calculations and use it to study jet observables at the LHC, including W/Z production inside jets and W/Z+jets, finding improved agreement with data. They also discuss limitations, such as Bloch-Nordsieck violations and incomplete electroweak interference, and outline prospects for future colliders and further enhancements to matching and merging strategies.

Abstract

The emission of W and Z gauge boson is included in a traditional QCD + QED shower. The unitarity of the shower algorithm links the real radiation of the weak gauge bosons to the negative weak virtual corrections. The shower evolution process leads to a competition between QCD, QED and weak radiation, and allows for W and Z boson production inside jets. Various effects on LHC physics are studied, both at low and high transverse momenta, and effects at higher-energy hadron colliders are outlined.

Figures (16)

• Figure 1: The differential cross section as a function of (a) ${\mathrm p}_{\perp\mathrm{evol}}$ and (b) $z$ for weak boson emission in $s$-channel processes. The differential cross sections are shown both with and without including the ME corrections and are separated into ISR and FSR. The center of mass energy was 7 TeV and the minimum ${\mathrm p}_{\perp\mathrm{hard}}$ was set to 50 GeV.
• Figure 2: Scatter plots showing the weight distributions as a function of $\Delta R$ between the final state quark and the final state gluon for the process ${\mathrm u} {\mathrm g} \to {\mathrm u} {\mathrm g} {\mathrm Z}$. In (a) all trial emissions are included, whereas the no-double-counting cuts have been imposed in (b). The ISR points masks part of the FSR ones. The starting minimum $p_{\perp}$ of the hard process was set to 50 GeV and only the weak shower was enabled. $R = 0.6$ was used in the clustering step for (b).
• Figure 3: Comparison between CalcHEP and Pythia 8 results for representative (a) $s$-channel ${\mathrm d} \bar{{\mathrm d}} \to {\mathrm u} \bar{{\mathrm u}} {\mathrm Z}$ and (b) $t$-channel processes. The center of mass energy was 8 TeV and the following phase-space cuts were applied to avoid divergent regions: $p_{\perp{\mathrm u}} > 100$ GeV, $p_{\perp{\mathrm g}} > 100$ GeV, and $M_{{\mathrm u}{\mathrm g}} > 150$ GeV.
• Figure 4: Angular distributions in the $2 \to 4$ process ${\mathrm u} {\mathrm g} \to {\mathrm u} {\mathrm g} {\mathrm e}^+ {\mathrm e}^-$ between (a) the ${\mathrm u}$ quark and the electron and (b) the gluon and the electron, defined in the ${\mathrm W}$ rest frame. To avoid divergent phase-space regions the same cuts are applied as in Fig. \ref{['fig:pTValidations']}.
• Figure 5: Comparison between the $2 \to 3$ ME calculation and the prediction from the PS for the ${\mathrm u} \bar{{\mathrm u}} \to {\mathrm u} \bar{{\mathrm d}} {\mathrm W}^-$ process, including only electroweak diagrams. Similar cuts as in Fig. \ref{['fig:pTValidations']} were applied.