The Compact Solenoid CMS Jet energy correction with charged particle tracks in CMS

The performance of a jet–energy–correction algorithm using reconstructed charged particle tracks is presented. The jet energy correction allows the jet energy scale to be restored and improves the energy resolution for jets with energies up to 120 GeV. For low energy jets (20 GeV) it improves the resolution by a factor 1.7 with respect to uncorrected jets. For 100 GeV jets the resolution improves by 15%. The deviation from unity of the ratio of the reconstructed to the generated jet transverse energies decreases by a factor two for low– (cid:4)(cid:6)(cid:5) jets ( (cid:4)(cid:7)(cid:5)(cid:9)(cid:8)(cid:11)(cid:10)(cid:13)(cid:12) GeV). For high– (cid:4)(cid:6)(cid:5) jets, this ratio amounts to (cid:14)(cid:16)(cid:15) (cid:12)(cid:16)(cid:12)(cid:18)(cid:17)(cid:19)(cid:12)(cid:20)(cid:15) (cid:12)(cid:22)(cid:21) .


Introduction
or the ECAL and HCAL contributions can have different weights: . Earlier studies have shown that this method gives an improvement in linearity but the resolution is unchanged [3], and that the two styles of weighting give approximately the same results.

Cluster-based corrections
Calibration coefficients are applied separately to electromagnetic and hadronic clusters. The clusters found in ECAL and HCAL are separated according to the cluster origin (electron, 8 , hadron). Correction coefficients are different for the clusters initiated by electrons and photons, and by hadrons. For electromagnetic clusters, the corrected response is and for hadronic clusters, it is

Track based corrections
The main idea is to replace the energy from identified calorimeter clusters arising from charged particles by the track momenta measured in the inner tracking detector. A considerable improvement of the calorimeter jet energy resolution with the use of the reconstructed tracks (energy flow algorithm) has been already demonstrated in a number of HEP experiments at LEP [4], Tevatron [5] and HERA [6]. The use of the tracker information as developed for CMS [7,8] is described in this note and is found to be promising.
The "jet-based" method is very useful in the Level-1 trigger, where there is no possibility to use tracker information.
In the High-Level trigger, however, some information from the measured tracks is available. Full use of the tracker information for energy corrections is possible only in off-line analysis. and tabulated either with a sample of isolated tracks simulated at different energies or with test beam data (Section 3.1.2). This subtraction procedure does not require cluster separation and is therefore well suited to the case of high occupancy or coarse granularity. The momenta of the tracks that reach the calorimeter surface out of the reconstruction cone are simply added to the calorimeter jet energy.
In addition to the response subtraction procedure, the charged particle momenta could also be used to replace the energies of the calorimeter clusters compatible with the track extrapolation [7,8]. This possibility is not included in the current algorithm design and is not considered in the present study.

Response subtraction procedure and out-of-cone tracks
The following corrections are made for each jet found in the calorimeter.
The event vertex is found with the use of pixel track segments [2]. The pixel track segments originating from the event vertex and within the jet reconstruction cone are used as seeds for the Combinatorial Track Finder [16]. Tracks are required to have Out-of-cone tracks satisfy the following criteria ) plane between the calorimeter jet axis and the track direction at the production vertex, and ¥ is the distance between the jet axis and the expected impact point of the track on the calorimeter surface. The momenta of these tracks, reconstructed in the tracker, The momentum of each reconstructed track with an ECAL impact point inside the cone (Fig. 1) is measured in the tracker. The expected response in the calorimeters is obtained from a parametrization and then subtracted from the jet energy [8]. The track momentum is instead added to the jet energy. Before the subtraction, the reconstructed jet energy is are the responses of the electromagnetic and the hadron calorimeters to neutral and charged hadrons, and ¤ $ # £ © is the response of the electromagnetic calorimeter to electrons and photons, respectively.
Assuming that all tracks are recontructed, the reconstructed jet energy becomes, after subtraction After the addition of out-of-cone tracks, the final expression is The track reconstruction inefficiency leads to the appearence of an additional term in the expression for the corrected jet energy The systematic shift contribution results from the uncertainty on the expected response parametrization. The ¤ ) shift arises from neutral hadrons (and, equivalently, from charged hadrons with no associated track), the response of which is not corrected a posteriori.

Determination of the calorimeter expected response to charged particles
Two different methods were tested to determine the calorimeter expected response to charged particles. Both are based on measurements made with single isolated particles.
H & technique The expected response can be calculated from the e/ ratio measured for different energies with sets of isolated particles [14,17]. Isolated particles can be identified during the data taking. The ratio of the amounts of energies deposited in ECAL and HCAL has to be evaluated. The response in ECAL is different if the particles interact in the ECAL hadronically or not. The interacting and non-interacting particles are disentangled by measuring the energy deposited in a 3 3 array of crystals (7 .5 GeV, the particle is called a non-interacting particle, and the measured ¤ ¨ ¦ ¢ § energy is taken as the "expected" response in the ECAL. The expressions for the expected response to charged particles are given in Table 1 as functions of the particle momentum Table 1: Expected response for charged particles.
The particle interacts in ECAL The particle does not interact in ECAL are obtained from test beam data analysises (300 GeV pion beam [15]). The quantities are the expected ECAL and HCAL deposited energy fraction for the hadronic showers and are evaluated as: was used to account for the fraction of charged particle energy deposited in the ECAL as determined from the same test beam data [14].

Algorithm performance
The algorithm performance is evaluated with the library of responses constructed with generated single particle samples. The

H &
technique requires test beam data with different beam energies to estimate

Reconstruction of single jet
Samples of QCD di-jet events in different intervals of the initial parton transverse momentum, @ © ¥ , were simulated with Pythia 6.158 [18]. At the generator level, jets are found with a simple cone algorithm ( A ¥ ¢ ) around the leading particle in the jet. Particles belonging to the jet are passed through the complete detector simulation; other particles in the event are ignored. The calorimeter digitization is done in the no pile-up scenario.
Calorimeter jets and jets at particle level (generated jets) are reconstructed within a cone of radius A ¢ with the iterative cone algorithm [2]. The generated jets do not include muons and neutrinos. Reconstructed jets are compared with generated jets. The comparison is focused on the detector effects and is somewhat insensitive to effects of initial and final state radiation as well as of underlying and pile-up events.
The quality of the track reconstruction plays an important r@ 4 le. The mean number of generated and reconstructed tracks in a cone The energy resolution and the reconstructed energy dependence on the generated transverse energy are shown in Figs. 8 and 9 for jets generated with ¡ ¦ . When the jet energy corrections are applied, the reconstructed jet energy fraction for 20 GeV generated jets increases from 0.5 to 0.85 and the same fraction for 120 GeV jets increases from 0.87 to 1.03. For jet energies from 50 to 120 GeV, the non-linearity is within 8%. The variation of the resolution and linearity arising from the inclusion of out-of-cone tracks is presented in the same figures. The resolution improves by about 30% as a result of adding the out-of-cone tracks.
In the endcap region (Figs. 10 and 11), jets with the same ¤ ¥ as in the barrel are more energetic. The energy of jets with ¤ ¦ ¥ =30 GeV in the endcap corresponds to that of jets with ¤ ¥ =90 GeV in barrel. In addition, the tracking efficiency is smaller in the endcap than in the barrel. Therefore, the tracker information is not relevant in the endcap above 80-90 GeV and is less rewarding for lower ¤ ¥ jets than in the barrel.

Reconstruction of dijet events
Di-jet events with  (Fig. 17). A ratio of the X mass reconstructed to the X mass generated for calorimetry jets and calorimeter-plus-tracker jets is shown in Fig. 18.
The di-jet mass is restored with a systematic shift of about 1% and the resolution is improved by 10%. The ratio of the reconstructed to the generated X mass is 0.88 before corrections with tracks and 1.01 after corrections. The calculation of the pile-up events contribution to the mass spectrum is done with a simple estimate. Taking into account that pile-up events add on average ¤ ! 2.5 GeV [19] in a cone with A ¢ to the jet energy, the contribution of the pile-up energy to the mean reconstructed mass is estimated to be assuming no correlations between the jet energies. After subtraction of the additional pile-up energy (! § ¥ ¢ GeV) from the reconstructed jet energy, the ratio of the reconstructed to the generated masses is 0.84 and 0.97 before and after applying corrections, respectively.

Reconstruction of h(125 GeV) mass
One channel investigated at CMS is the gluon fusion into radion, , where one of the Higgs bosons decays into " . The mass of the latter can be determined from the corresponding reconstructed di-jet invariant mass. This channel was generated and digitized with low luminosity pile-up. The distribution of the di-jet mass reconstructed with the calorimeters only is shown in Fig. 19. Only jets with § and with good matching to the quarks are considered. The mass of the Higgs boson is underestimated by about 20 The jet energy correction (Fig. 20) restores the mass scale and the resolution is improved from 13.2% to 11%.

Conclusion
Track information allows the jet energy resolution and linearity to be improved. For low energy jets (20 GeV), the resolution improves by a factor 1.7. For 100 GeV jets, the resolution improves by 15%. The non-linearity decreases by a factor two for low  and HCAL to the initial pion energy (p) from test beam data [15]. Pions interacting only in HCAL (close circle); pions interacting in ECAL or HCAL; without readout weighting (close squares); with passive weighting, i.e., constant coefficient to the first HCAL readout (empty circles); dynamic weighting, i.e. event-by-event correction (empty squares). Response HCAL (cone 0.5) / P tracker P T (GeV) Figure 3: Ratio of the mean response in ECAL to the original particle energy for isolated pions interacting in the ECAL as a function of the particle transverse energy for

Particles interacting in ECAL
. The hatched area corresponds to the RMS of the ratio distribution at that energy. Generated All Generated with P T >1 GeV/c Reconstructed |η| jet ≤ 0.3

Number of charged particle tracks
Jet E T (GeV) Figure 5: Ratio of the mean response in HCAL to the original particle energy for isolated pions notinteracting in the ECAL as a function of the particle transverse energy for ¡ ¨ . The hatched area corresponds to the RMS of the ratio distribution at that energy.  ) as a function of jet energy. Circles -the generated charged particles with no 1 GeV/c. Squares -the reconstructed tracks.