Calculating Track-Based Observables for the LHC

TL;DR

A field-theoretic definition of the track function and its renormalization group evolution are given, in excellent agreement with the pythia parton shower, and a next-to-leading order calculation of the total energy fraction of charged particles in e+ e-→ hadrons is performed.

Abstract

By using observables that only depend on charged particles (tracks), one can efficiently suppress pile-up contamination at the LHC. Such measurements are not infrared safe in perturbation theory, so any calculation of track-based observables must account for hadronization effects. We develop a formalism to perform these calculations in QCD, by matching partonic cross sections onto new non-perturbative objects called track functions which absorb infrared divergences. The track function T_i(x) describes the energy fraction x of a hard parton i which is converted into charged hadrons. We give a field-theoretic definition of the track function and derive its renormalization group evolution, which is in excellent agreement with the Pythia parton shower. We then perform a next-to-leading order calculation of the total energy fraction of charged particles in e+ e- -> hadrons. To demonstrate the implications of our framework for the LHC, we match the Pythia parton shower onto a set of track functions to describe the track mass distribution in Higgs plus one jet events. We also show how to reduce smearing due to hadronization fluctuations by measuring dimensionless track-based ratios.

Figures (6)

• Figure 1: Schematic relationship between the partonic matrix element $\sigma_3$ and the matching coefficient $\overline{\sigma}_3$ for $e^+ e^- \to q \bar{q} g$. Here, black (blue) dots represents the tree-level ($\mathcal{O}(\alpha_s)$) track functions. Diagrams with emissions from the other quark leg are elided for simplicity. Note the trivial matching condition $\sigma_2 = \overline{\sigma}_2$.
• Figure 2: LO (dotted) and NLO (solid) track functions extracted in Pythia from the fraction of the jet energy carried by charged particles.
• Figure 3: The evolution of the NLO gluon (top) and $d$-quark (bottom) track functions compared to Pythia. Starting from $\mu=100$ GeV (shown in Fig. \ref{['fig:pythiatrack']}), we evolve using Eq. \ref{['eq:T_RGE']} down to $\mu=10$ GeV and up to $\mu=1000$ GeV. The bumps in the Pythia distributions near $x=0,1$ at $Q = 10$ GeV correspond to genuine non-perturbative effects at $\Lambda_{\rm QCD}$.
• Figure 4: Normalized distribution of the energy fraction $w$ of charged particles in $e^+ e^-$ at $Q=91$ GeV, calculated at LO (green) and NLO (orange), compared with Pythia (blue). The uncertainty bands are obtained by varying $\mu$ between $Q/2$ and $2 Q$, and do not include track function uncertainties.
• Figure 5: Track mass distribution in $pp \to H+$jet obtained from the Pythia parton shower matched onto either track functions or the Lund string model.