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Jet Energy Resolution in ATLAS

Introduction

The precise determination of the jet energy resolution is of key importance for electroweak precision measurements (top mass), discoveries of new high mass states (di-jet resonances) and QCD measurements (jet cross-section). This page presents the strategy to measure the jet energy resolution in-situ with the ATLAS detector in proton-proton collision at the LHC.

The measurement of the jet energy resolution is done using two different methods: the di-jet balance and the bi-sector techniques. These methods involve different assumptions that can be validated in data, and are sensitive to different sources of systematic uncertainties. The use of two independent measurements of the jet energy resolution is important in the initial phase of the in-situ performance measurements because it allow us to cross check results and test to what extent the simulation describes the data.

Documentation: ATLAS Notes and Select Presentations

The Di-jet Balance Method

The di-jet balance method for the determination of the jet $p_{T}$ resolution is based on momentum conservation in the transverse plane. It works properly in the ideal case of two jets only in the event that have the same particle level transverse momentum (jets composed by stable interacting particles with a lifetime longer than 10ps but excluding muons and neutrinos, that have not yet been passed through the simulation of the ATLAS detector).

Measurement of Resolution From Asymmetry

The asymmetry between the transverse momenta of the two leading jets $A(p_{T,1},p_{T,2})$ is defined as $A(p_{T,1},p_{T,2}) \equiv \frac{p_{T,1} - p_{T,2} }{p_{T,1} + p_{T,2}}$. The fitted Gaussian $\sigma$ is used to characterize the asymmetry distribution and determine the jet $p_{T}$ resolutions. Assuming transverse momentum balance and requiring the jets to be in the same rapidity $\eta$ region, the relation between $\sigma_{A}$ and the relative jet resolution is given by: $\sqrt{2}\sigma_{A} = \frac{\sigma_{p_{T}}}{p_{T}}$.

Soft Radiation Correction

In order for the di-jet balance method to strictly apply, events have to be selected with exactly two particle jets that satisfy the hypothesis of exact momentum balance in the transverse plane. Although requirements on $\Delta\phi$ and on the third jet transverse momentum, $p_{T,3}$, are designed to enrich the purity of the back-to-back jet sample, it is important to account for the effects due to the presence of additional soft particle jets not detected in the calorimeter.If the soft jets are produced roughly parallel to one of the leading jets in $\phi$, they will not appreciably affect the $\Delta\phi$ cut between the leading jets, but can significantly impact the $p_{T}$ balance between the leading jets due to momentum conservation. To estimate the asymmetry for a pure particle di-jet event, $\sigma_{A}$ is recomputed allowing the presence of additional jets in the sample for a series of $p_{T,3}$ cut-off threshold values. For each $p_T$ bin, the jet energy resolutions obtained with the different $p_{T,3}$ cuts are fitted with a straight line and extrapolated to zero: $\left(\frac{\sigma_{p_T}}{p_T}\right)_{p_{T,3}\ \rightarrow \ 0}$. A soft radiation correction factor is obtained as $K_{soft}(p_{T}) = \frac{\left(\frac{\sigma_{p_{T}}}{p_{T}}\right)_{p_{T,3}\; \longrightarrow\; 0}}{\left(\frac{\sigma_{p_{T}}}{p_{T}}\right)_{p_{T,3} < 10{\rm ~GeV}}} \ .$

Particle Imbalance Correction

Some transverse momentum often goes to the beam pipe along with the proton remnants, gets scattered around in the form of underlying event energy or ends up in particles slightly outside the fixed cone radius. The latter effect increase the average $p_{T}$ imbalance between the leading jets and they are unrelated to the detector resolution. The average smearing not related to detector effects is referred to as the particle level imbalance.

The Bi-sector Technique

The bi-sector method is based on the definition of an imbalance(transverse) vector, $\vec{P}_T$, which is defined as the vector sum of the two leading jets in the di-jet event. This vector is projected along an orthogonal coordinate system in the transverse plane, ($\psi,\, \eta$), where $\eta$ is chosen in the direction that bisects $\Delta\phi_{12} = \phi_{1} - \phi_{2}$, the angle formed by $\vec{P}_{T}^{\mathrm{jet,1}}$ and $\vec{P}_{T}^{\mathrm{jet,2}}$. This is illustrated in the sketch below:

BisectorSketch.png
A Sketch of the Bisector method

For a perfectly balanced di-jet event, $\vec{P}_{T}=0$. There are a number of sources that give rise to fluctuations and thus to a non-zero variance of its $\psi$ and $\eta$ components, which is denoted $\sigma_{\psi}^2 \equiv \mathrm{Var}(P_{T,\psi})$ and $\sigma_{\eta}^2 \equiv \mathrm{Var}(P_{T,\eta})$ respectively. At particle level (denoted with a superscript part), $\vec{P}^{part}_{T}$ receives contributions from initial state radiation mostly. This effect is expected to be isotropic in the ($\psi,\eta$) plane, leading to similar fluctuations in both components. It can be shown that:

$ \frac{\sigma(P_{T})}{\langle P_{T} \rangle} \,=\, \frac{\sqrt{\sigma^{2\ \ calo}_\psi -\sigma^{2\ \ calo}_\eta}} {\sqrt{2}\,\langle P_{T} \rangle \, |\cos\Delta\phi_{12}|} $.

The resolution is thus expressed in terms of calorimeter observables only. Soft radiation effects are removed by subtracting in quadrature $\sigma_{\eta}$ from $\sigma_{\psi}$ at calorimeter level.

Validation of the Soft Radiation Isotropy with Data

The bi-sector method is used for an in-situ validation of the soft radiation isotropy assumption. In addition, to become independent of the jet energy scale uncertainties, the cut on the third jet has been studied as a function of $p_{T,3}^{em-scale}$. The two leading jets are required to be in the same rapidity region, and there is no rapidity restriction for the third jet. The presence of a flat region indicates that the bi-sector method isotropy assumption holds in such $p_{T}$ range.

Results

The fractional jet transverse momentum resolution, $\sigma_{p_T}/{p_T}$ is parametrized as: $\frac{\sigma_{p_{T}}}{p_{T}} = \frac{N}{p_{T}} \oplus \frac{S}{\sqrt{p_{T}}}\oplus C \, ,$ where N, S and C are the noise, stochastic and constant terms. N parametrizes fluctuations due to noise and offset energy from multiple interactions, S parametrizes the stochastic fluctuations in the amount of energy sampled from the jet hadron shower and C encompasses the fluctuations that are a constant fraction of energy, respectively. In order to get the final jet $p_{T}$ resolution for both methods, the result is fitted using the previous equation.

Monte Carlo Truth Jet Energy Resolution:

The jet energy resolution derived from simulation based on MC truth serves as a benchmark for measurements of the jet resolution derived directly from collision data sample, using in-situ techniques introduced in the previous sections.

RMS vs Gaussian fits

The Monte Carlo truth jet resolution is described by the $\sigma$ of the gaussian fit to the core of the jet response distribution and it should be enough for many applications in physics analysis. However, e.g. searches for physics beyond the standard model require an accurate description of the non-gaussian tails.

Closure

Tails and Gaussianity Studies

Pile-up

Systematic Uncertanties

The systematic uncertainties on the jet energy resolution have been determined from the simulation. The single largest contribution comes from the statistical uncertainties of the fits. The uncertainties are broken into statistical and systematic component.

Di-jet Balance Method

Different $\Delta\phi$ cuts (from 2.75 up to 3.0)

Soft radiation correction Modeling

Bi-sector Method

The precision with which we can ascertain that $\sigma^{part}_\psi=\sigma^{part}_\eta$ using an in-situ technique

Forward Region

Datasets

The common SM QCD D3PDs and GRLs can be found on the SMJetAnalysis2010 twiki. Dedicated NTUP JET_MET slims have been done to include other JES schemes

Binning

All studies are done in the following rapidity regions (See JetCrossSectionExtended):

0.0, 0.8, 1.2, 2.1, 2.8, 3.6, 4.4

All studies are done the following average pT(1,2) binning (See JetCrossSectionExtended):

30, 35, 40, 60, 80, 110, 160, 210, 260, 310, 400, 500, 600, 800, 1000, 1200, 1500, 1800, 2500 GeV

Event Selection

  • GRL:
    • All events must pass the most recent SM Jet Good Run Lists, as listed on SMJetAnalysis2010.

  • Vertex Selection: require that the first vertex (PV0) have $N^{PV}_{trk} \geq 5$

Trigger Selection

Strategy for JER

Jet Selection

  • Jet Collections and Calibration:

    • Anti-kt, R = 0.4, topo-cluster, EM+JES scale
    • Anti-kt, R = 0.6, topo-cluster, EM+JES scale

    • Anti-kt, R = 0.4, topo-cluster, LCW scale
    • Anti-kt, R = 0.6, topo-cluster, LCW scale

    • Anti-kt, R = 0.4, topo-cluster, GSC scale
    • Anti-kt, R = 0.6, topo-cluster, GSC scale

    • Anti-kt, R = 0.4, topo-cluster, GCW scale
    • Anti-kt, R = 0.6, topo-cluster, GCW scale

Dead Tile Calorimeter Regions

**A snippet to remove bad JER calorimeter regions

JERProvider

Link to JERProvider

-- GastonRomeo - 11-Nov-2010

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