Event Generation from Effective Field Theory

TL;DR

The paper introduces Soft Collinear Effective Theory (SCET) as a principled framework to generate fully exclusive collider events, unifying QCD hard emissions with parton showers through renormalization-group resummation of large logarithms. By performing QCD-to-SCET matching, RG running, and threshold matching, it reproduces Sudakov factors and QCD-like splitting functions within a systematically improvable effective theory, and demonstrates agreement with full QCD at NLO for key observables. It also shows how SCET naturally interpolates between the regimes where QCD is dominant and where parton showers excel, enabling an event-generator paradigm with controllable errors and clear avenues for higher-order improvements. The results include explicit LL/RG structures, short-distance coefficient running, and concrete steps toward an SCET-based event generator that merges matrix elements with resummed parton-branching in a consistent, improvable way.

Abstract

A procedure is developed for using Soft Collinear Effective Theory (SCET) to generate fully exclusive events, which can then be compared to data from collider experiments. We show that SCET smoothly interpolates between QCD for hard emissions, and the parton shower for soft emissions, while resumming all large logarithms. In SCET, logarithms are resummed using the renormalization group, instead of classical Sudakov factors, so subleading logarithms can be resummed as well. In addition, all loop effects of QCD can be reproduced in SCET, which allows the effective theory to incorporate next-to-leading and higher-order effects. We also show through SCET that in the soft/collinear limit, successive branchings factorize, a fact which is essential to parton showers, and that the splitting functions of QCD are reproduced. Finally, combining these results, we present a example of an algorithm that incorporates the SCET results into an event generator which is systematically improvable.

Figures (3)

• Figure 1: Errors on the RG kernel (Sudakov factor) $\Pi_2$ from next-to-leading log uncertainties. The light band comes from one NLL effect, varying the $B^1_2 \alpha_s$ term in the anomalous dimension, from $0<B^1_2<3$. The dark band is from another NLL effect, the $\Gamma^2_2 \alpha_s^2 \log$ term in $\gamma_2$, varying $\Gamma^2_2$ between $-2$ and $2$. We normalize so that $\mu=1$ corresponds to 1 TeV. The LO RG kernel is the lowermost curve in the figure.
• Figure 2: Thrust distribution from 3-parton states, at $E_{\mathrm{CM}}=1$ TeV. QCD (dashed red line), parton-shower approximation (dotted blue line), and SCET (solid black line) are shown. The grey band is a representation of NLL uncertainties, by varying the $B_2^1$ and $B_3^1$ terms in $\gamma_2$ and $\gamma_3$, between 0 and their true values.
• Figure 3: Percentage of events which have 2-jets, as a function of cutoff, using the $k_T$ algorithm. Shown is QCD (dashed red line), the parton-shower approximation (dotted blue line), and SCET (solid black line). The grey band is the NLL uncertainty, as in Figure \ref{['fig:thrust']}.