Measurement of Event Shapes in Proton-Antiproton Collisions at Center-of-Mass Energy 1.96 TeV

TL;DR

This work measures event-shape observables in proton-antiproton collisions at 1.96 TeV using unclustered calorimeter energies to study transverse thrust and thrust minor. It shows that underlying-event effects significantly distort standard distributions, motivates a UE-insensitive thrust differential, and compares data to PYTHIA Tune A and NLO+NLL predictions. The thrust differential agrees with both theory and Tune A within ~20%, validating perturbative QCD for hadronic final-state shapes while highlighting the UE modeling needs. Overall, the results demonstrate that properly constructed observables can enable meaningful tests of QCD in hadron-hadron collisions and improve UE modeling.

Abstract

A study of event shape observables in proton-antiproton collisions at 1.96 TeV is presented. The data for this analysis were recorded by the CDF II detector at the Tevatron collider. The variables studied are the transverse thrust and thrust minor, both defined in the plane perpendicular to the beam direction. The observables are measured using energies from unclustered calorimeter cells. In addition to studies of the differential distributions, we present the dependence of event shape mean values on the leading jet transverse energy. Data are compared with pythia Tune A and to resummed parton level predictions that were matched to fixed order results at NLO accuracy (NLO+NLL). Predictions from pythia Tune A agree fairly well with the data. However, the underlying event contributes significantly to these observables, making it difficult to make direct comparisons to the NLO+NLL predictions, which do not account for the underlying event. To overcome this difficulty, we introduce a new observable, a weighted difference of the mean values of the thrust and thrust minor, which is less sensitive to the underlying event, allowing for a comparison with NLO+NLL. Both pythia Tune A and the NLO+NLL calculations agree well within the 20% theoretical uncertainty with the data for this observable, indicating that perturbative QCD successfully describes shapes of the hadronic final states.

Figures (10)

• Figure 1: Predictions of the transverse thrust and thrust minor distributions for $E_{T}^{lead.jet}$ greater than 200 GeV from a parton level NLO+NLL calculation and from pythia without an underlying event at the parton level and without an underlying event at the hadron level (i.e. after hadronization).
• Figure 2: Predictions of the transverse thrust and thrust minor distributions for $E_{T}^{lead.jet}$ greater than 200 GeV from a parton-level NLO+NLL calculation and from pythia at the parton level without an underlying event and at the parton level with an underlying event (Tune A).
• Figure 3: Predictions of the mean values of the transverse thrust and thrust minor as a function of the leading jet transverse energy from a parton level NLO+NLL calculation and from pythia at the parton level without an UE ( pythia Parton), at the parton level with an underlying event (Tune A Parton), and at the hadron level with an underlying event (Tune A Hadron).
• Figure 4: Mean value of $\gamma_{MC}$, from Eq. (6), as obtained from pythia at the parton level with and without multiple parton interactions.
• Figure 5: Predictions of the mean values of the thrust differential as a function of the leading jet transverse energy from a parton level NLO+NLL calculation and from pythia at the parton level with (Tune A) and without an underlying event (Parton). The plot indicates that the underlying event has only a small effect on the mean value of the thrust differential.