# Atlas Jet Calibration CSC note

## Editors

S.Menke, I.Vivarelli

## Authors

V. Giangiobbe, P. Giovannini, A. Gupta, A. Jantsch, D. Lopez Mateos, P. Loch, K. Lohwasser, Z. Marshall, S. Menke, F. Merrit, F. Paige, G. Pospelov, J. Proudfoot, C. Roda, A. Schwartzman, I. Vivarelli

## Note draft

• This is now the same (final) text as in the CSC book ...

## Abstract

The jet energy scale is proven to be an important issue for many different physics analyses. It is the largest systematic uncertainty for the top mass measurement at Tevatron, it is one of the largest uncertainties in the inclusive jet cross section measurement, whose understanding is the first step towards new physics searches. Finally, it is an important ingredient of many standard model analyses. This note discusses different strategies to correct the jet energy for detector level effects

## 1 Introduction

The jet calibration process can be seen as a two-step procedure. In the first step, the jet reconstructed from the calorimeters is corrected to remove all the effects due to the detector itself (nonlinearities due to the non-compensating ATLAS calorimeters, the presence of dead material, cracks in the calorimeters and tracks bending in/out the jet cone due to the solenoidal magnetic field). This calibrates the jet to the particle level, i.e. to the corresponding jet obtained running the same reconstruction algorithm directly on the final state Monte Carlo particles. The second step, is the correction of the jet energy back to the parton level, which will not be discussed in this section.

There are currently several calibration approaches studied in the ATLAS collaboration based on the calorimeter response on the cell level or layer level and either in the context of jets or of clusters.

The first part of the section describes a possible approach for the calibration to the particle jet. The energy of the jet is corrected using cell weights. The weights are computed by minimizing the resolution of the energy measurement with respect to the particle jet. The performance of the calibration in terms of jet linearity and resolution is assessed in a variety of events (QCD dijets, top-pairs and SUSY events). The different structure of these events (different color structure, different underlying event) will manifest itself as a variation in the quality of the calibration. This method has been the most widely used so far in the ATLAS collaboration.

Other methods have also been studied. Here we discuss one alternative global calibration approach, which makes use of the longitudinal development of the shower to correct for calorimeter non-compensation. The jet energy is corrected weighting its energy deposits in the longitudinal calorimeter samples. Although the resolution improvement is smaller with respect to other methods, this method is simple and less demanding in terms of agreement between the detector simulation predictions and real data.

The second part of this section describes the concept of local hadronic calibration. First clusters are reconstructed in the calorimeters with an algorithm to optimize noise suppression and particle separation. Shower shapes and other cluster characteristics are then used to classify the clusters as hadronic or electromagnetic in nature. The hadronic clusters are subject to a cell weighting procedure to compensate for the different response to hadrons compared to electrons and for energy deposits outside the calorimeter. In contrast to the cell weights mentioned above no minimization is performed and the actual visible and invisible energy deposits in active and inactive calorimeter material as predicted by Monte Carlo simulations are used to derive the weights. One of the advantages of this method is that the jet reconstruction runs over objects which have the proper scale (in contrast to the global approach, where the scale corrections are applied after the jet is reconstructed from uncorrected objects).

The third part of the note describes refinements of the jet calibration that can be done using the tracker information: the residual dependence of the jet scale on the jet charged fraction can be accounted for improving the jet resolution. An algorithm to correct the b-jet scale in case of semileptonic decays will also be discussed.

## Conclusion

In the first part of the article, we discussed two different ways of using the full ATLAS simulation to calibrate jets. The global method is proven to recover the linearity of the energy measurement while improving the resolution in a wide energy range on Monte Carlo samples. We proved its robustness over different quark content, shower model, and event complexity. The local hadron calibration has been shown to almost fully recover the linearity with respect to the jet calorimeter energy deposits. Even though a correction step to go back to the truth jet scale is missing, the method is promising. In the last part of the article, we discussed the possible use of the tracker information of the jet to improve the jet resolution. After the application of the global calibration, the method is able to further improve the jet energy resolution especially at low ET . Finally we discussed a possible way of recovering the neutrino energy in semileptonic b-quark decays.

The calibration methods discussed in this note will be used to provide jet corrections for the ATLAS detector. We stress that the validation of the corrections heavily relies on in­situ measurements as discussed in [20].

## Acknowledgments

This work was supported in part by the EC, through the ARTEMIS Research Training Network (contract number MRTN-CT-2006-035657), and for one of the authors (K. Lohwasser) by the DAAD Doktorandenstipendium.

## References

[1] M.P. Casado and M. Cavalli Sforza, ATLAS note (1996), ATL-TILECAL-96-075.

[2] ATLAS Collaboration, ATLAS Tile Calorimeter Technical Design Report, (CERN/LHCC/199642, Dec 1996).

[3] T. Sjöstrand, hep-ph/0108264 (2002).

[4] A.Moraes and others, Eur. Phys. J. C 50 (2007) 435­466.

[5] S.D.Ellis and D.E.Soper, Phys. Rev. D48 (1993).

[6] C.Roda and I.Vivarelli, ATLAS note (2005), ATL-PHYS-PUB-2005-019.

[7] S.Frixione and B.R.Webber, JHEP 0206 (2002) 029 (2002).

[8] Butterworth, J. M. and Forshaw, Jeffrey R. and Seymour, M. H., Z. Phys. C72 (1996) 637­646.

[9] The ATLAS Collaboration, Jet Reconstruction Performance, this volume.

[10] The ATLAS Collaboration, Supersymmetry Searches, this volume.

[11] V.Giangiobbe, Etude en Faisceau-Test de la Reponse des Calorimetres de l'experience ATLAS du LHC a des Pions Charges, d'Energie Comprise entre 3 et 350 GeV, Ph.D. thesis, Clermont Ferrand, 2006.

[12] P.Amaral, Nucl. Inst. and Meth. A443 (2000) 51­70.

[13] Abmowicz and Others, Nucl. Inst and Meth. 180 (1980) 429.

[14] E.Hughes, SLAC-PUB-5404 (1990).

[15] W. Lampl, S. Laplace, D. Lelas, P. Loch, H. Ma, S. Menke, S. Rajagopolan, D. Rousseau, S. Snyder, G. Unal, (2008), ATL-LARG-PUB-2008-002.

[16] E. Bergeaas, T. Carli, K.-J. Grahn, C. Issever, K. Lohwasser, S. Menke, G. Pospelov, P. Schacht, F. Spano, P. Speckmayer, P. Stavina, P. Strizenec, (2008), ATL-COM-LARG-2008-006.

[17] Agostinelli, S. and others, Nucl. Instrum. Meth. A506 (2003) 250­303.

[18] Allison, John and others, IEEE Trans. Nucl. Sci. 53 (2006) 270.

[19] E.Bergeaas and others, ATLAS note (2007), ATL-CAL-PUB-2007-001.

[20] The ATLAS Collaboration, Jet Energy Scale: In-situ Calibration Strategies, this volume.

[21] The ATLAS Collaboration, Soft Muon b-Tagging, this volume.

# Figures

Figure 1: Left: fractional energy carried by different particle types as a function of the jet energy. Right: fraction of true energy deposited in the different calorimeter samplings for a jet in the central (|η| < 0.7) calorimeter region as a function of its true energy.

Figure 2: Two example histograms of E_rec/E_truth. On the left, the histogram is done for 88 GeV < E_truth < 107 GeV and |η| < 0.5, on the right for 158 GeV < E_truth < 191 GeV and 1.0<|η|<1.5.

Figure 3: Dependence of the ratio E_rec/E_truth on E_truth for jets reconstructed with a cone algorithm with R_cone = 0.7 and with a Kt algorithm with R=0.6. The black (white) dots refer to jet with |η| < 0.5 (1.5 << |η| &lt 2). An ideal detector geometry has been used to simulate the events.

Figure 4: Dependence of the ratio Et^rec/Et^truth on the pseudorapidity for the cone algorithm with R_cone=0.7 (on the left) and for the Kt algorithm with R=0.6 (on the right). An ideal detector geometry has been used to simulate the events.

Figure 5: Energy resolution as a function of the jet energy for the cone algorithm with R_cone=0.7 (on the left) and for the Kt algorithm with R=0.6 (on the right). The black (white) dots refer to jets with |η| < 0.5 (1.5 < |η| < 2). The smooth curves correspond to a fit done using the parametrization of Eq. 9. An ideal detector geometry has been used to simulate the events.

Figure 6: Energy resolution as a function of the pseudorapidity for the cone algorithm with R_cone=0.7 (on the left) and for the Kt algorithm with R=0.6. An ideal detector geometry has been used to simulate the events.

Figure 7: Linearity as a function of energy for three pseudorapidity regions (on the left) and of the pseudorapidity for three transverse energy bins (on the right) for cone 0.4 tower jets in tt-bar events.

Figure 8: Linearity as a function of energy for three pseudorapidity regions (on the left) and of the pseudorapidity for three transverse energy bins (on the right) for cone 0.4 tower jets in SUSY events.

Figure 9: On the left: <E>/E_beam for simulated (black points) and real (gray points) data at the EM (dots) and calibrated (squares) scales. On the right: Double ratio R_HAD/R_EM.

Figure 10: The longitudinal weights as a function of jet energy for four layers in three f_em bins and for central jet η

Figure 11: Jet energy linearity as a function of jet energy (left), and as a function of jet pseudorapidity (right). The points are for jets reconstructed at the electromagnetic scale (EM), for the global weighting scheme described here (Samp) and for the H1-style calibration described in the previous Section. The jets have a cone radius of R_cone=0.7.

Figure 12: Jet energy resolution for jets with a cone radius of 0.7 for two regions in pseudorapidity. The three sets of point show the resolution at the detector (EM) scale, after H1-style and longitudinal weighting.

Figure 13: Noise contents (left) and number of cells per jet (right) of Cone jets with R_cone = 0.7 for different energies for towers as input (open symbols) and topological clusters as input (filled symbols).

Figure 14: Number of topo clusters with Et > 1 GeV vs. number of stable truth particles with Et > 1 GeV from a QCD dijet simulation.

Figure 15: Linearity for Cone jets with R_cone = 0.7 (left) and Kt jets with R = 0.6 (right), both calibrated with the local hadron calibration method (LC), using truth particle jets (MC) as reference. The linearity is shown as a function of the matched truth jet energy.

Figure 16: Linearity for Cone jets with R_cone = 0.7 (left) and Kt jets with R = 0.6 (right), both calibrated with the local hadron calibration method, using truth particle jets as reference. The linearity is shown as a function of the matched truth jet |η|.

Figure 17: Resolution for Cone jets normalized to the reconstructed jet energy with R_cone = 0.7 (left) and Kt jets with R = 0.6 (right), both calibrated with the local hadron calibration method, using truth particle jets as reference. The resolution is shown as a function of the matched truth jet energy.

Figure 18: E_(weighted + DM corrected)/E_(in cluster truth + DM truth), the reconstructed weighted and dead-material corrected energy over the the predicted true energy inside clusters and associated dead material regions (left) and E_(in cluster truth + DM truth)/E_truth, the ratio of the predicted true energy inside clusters and associated dead material regions (the denominator in the left plot) over the energy of the matched truth particle jet (right) as function of the matched truth jet energy for cone jets with R_cone = 0.7.

Figure 19: Black: difference between reconstructed and truth jet transverse energy for jets with 0<|η|<0.7 and 40 GeV < pt < 200 GeV. The mean (width) of this distribution is proportional to the jet energy response (resolution). Since jets with different f_trk have different responses, the transverse energy resolution is artificially broadened because of the offset of the distributions for each f_trk bin. The normalization is arbitrary.

Figure 20: On the left, fits as a function of reconstructed jet pt for central (|η|<0.7) jets in bins of f_trk. On the right, straight line fit of one of the parameters determined by pt fits, as a function of f_trk.

Figure 21: On the left: absolute jet energy response as a function of f_trk, before and after applying the track-jet response correction. The distribution of f_trk has been overlaid to show the jet distribution. All jets used in the fits are included. On the right: jet transverse energy response after the track-jet response correction for jets with 0<|η|<0.7 and 40 GeV < pt < 200 GeV. The underlying Gaussian distributions are now overlapping, and the measured jet transverse energy resolution has been reduced.

Figure 22: Jet transverse momentum resolution as a function of jet pt before and after correcting for f_trk.

Figure 23: Average missing transverse energy as a function of the f_trk difference between the two leading jets in a dijet sample before (left) and after (right) track-based jet energy corrections. The width and tails are improved.

Figure 24: Fraction of pt carried by the neutrino in b jets decaying semileptonically (b -> μX or b -> c -> μX). The abscissa corresponds to the total transverse component for the jet (all interacting particles except muons), muon and neutrino momenta. We use b jets from QCD dijet samples as described in Section 7.1.

Figure 25: Left: Jet response as a function of jet pt for semileptonic b jets containing one muon for different values of x (equation 15). Here pt_true^(jet+μ+ν) refers to the transverse component of the vector addition of the true jet momentum (all interacting particles except muons included), the true muon momentum and the neutrino momentum. Right: Value of the results from straight line fits to the points in the left plot as a function of x. The fit function C(x)=a + b e^(-c x) is also shown.

Figure 26: Response of semileptonic b jets before and after applying the neutrino correction to jets from a tt-bar sample (left) and a bb-bar sample (right).

-- Main.ivivarel - 26 Oct 2006 -- SvenMenke - 21 Dec 2008 -- SvenMenke - 02 Feb 2009

Responsible: IacopoVivarelli
Last reviewed by:

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Topic revision: r9 - 2010-12-06 - PatrickJussel

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