Track-Based Jet Corrections in ATLAS

Introduction

The understanding of the jet energy response and resolution will play a decisive role in many physics analysis and searches. Jet reconstruction in ATLAS has traditionally relied on calorimeter information only. In order to correct for the non-compensating nature of the calorimeter, the Jet Calibration Task Force has planed to factorize the jet energy scale into several corrections, such that on average jets have a uniform response centered at 1. However a deeper insight might be achieved by looking at the tracking information. On a jet-by-jet basis, jets may be over(under)-corrected depending on their topologies, particle content, out-of-clustering energy, among others. Therefore, tracking properties will be explore to extract jet-by-jet information and correct the response of each jet individualy by applying track-based corrections, without changing the overall jet energy scale.

This technique can be applied to different JES scenarios, like jets calibrated using the H1-style, the layer-weighting calibrations or over jets calibrated with a simple calibration, like the Numerical Inversion Technique (which can also be implemented over H1-style scales) in order to make the response of jets as a function of flat and centered at 1 for all regions (within a few percent). Currently, the track corrections are only available for Cone 0.4 topo jets with ||<0.7 and it has been derived for both Numerical Inversion and H1-style calibrated jets. This page will be updated as the corrections are extended in eta and calculated for other jets. Here we describe a technique that can be used to improve the resolution of these jets, which were already calibrated.

Baseline Track Selection

Selecting genuine tracks is crucial to calculate candidate track variables. Different track quality cuts have been analysed and the final set is summarized below. Only tracks within a cone of radius 0.4 in around a jet's axis were included in the calculation of track variables.

Baseline Track Selection Cuts

Track > 1 GeV

< 3.0

Precision hits (pixel or micro-strip hits) > 6

< 0.2cm

< 0.45cm

It is worth mentioning that a variation of the previous cut was also studied, including the extra requirement for b-tagging, ie. at least two hits in the pixel detector, where one must be in the b-layer. Nevertheless, it was found that the sensitivity of the response to the track variables remains the same within errors. On the other hand, although cutting on IP might be useful for Jx samples, it is not optimum for b-jets (e.g. ttbar events) since b-decays may have bigger IP values. Therefore, during data-taking, a specific flavoured track-based correction will be derived, in which the latter cuts would not be applied (although it has the caveat it can not be derived using using a data-driven approach, but using true Monte Carlo information)

Response Sensitivity To Track Variables over H1 calibrated jets

The sensitivity of the response to a wide set of track variables (table below) has been analyzed, aiming at understanding which track variable might contain the most useful information about jet-by-jet fluctuations, as topology, fragmentation, out-of-clustering energy among others. Local Hadron calibration has suggested that about 80 % of the corrections applied to jets at the EM scale account for dead material effects. The track multiplicity in the jet, , may provide a handle on how much energy jets have lost when going through the cryostat, main source of dead material losses. The distribution of the track multiplicity along with the sensitivity of the response to for different bins are attached below. The transverse jet momentum resolution, defined as , is proportional to the width of the jet momentum response in bins of transverse momentum normalized to the average true jet momentum in a bin. If the response of the jets varied significantly with , the transverse jet momentum resolution would be artificially broadened. A variation of 11% at the lowest bin (30-40 GeV) has been observed. By correcting for this effect, it would be possible to reduce the overall broadening of the momentum distribution and hence improve the jet transverse momentum resolution (the same argument holds for other track variables).

Track Variable	Definition	Potencial for improvement at 35 GeV
	Track multiplicity	11%
	Fraction of pT carried by the leading track	8%
	Maximum opening angle btw any two tracks in the jet	10 %
	Average DeltaR of tracks to the jet	10%
	Track pT weighted average DeltaR of tracks to the jet axis	9 %
	Track InvpT weighted average Delta R of tracks to the jet axis	7 %
	Asymmetry between the two leading tracks in the jet	4%
	Total pT carried by charged tracks in the jet	2%

Correction Strategy and Resolution Improvement

Track-based jet corrections to the jet response are applied after the standard ATLAS calorimeter jet energy scale. The track multiplicity () has been chosen to derive the correction since it was found to be the most promising variable among the set of track variables analyzed. The jet resolution before the correction can be thought of as several offset gaussians with different , therefore by re-centering the underlying distributions an improvement in the resolution is expected. Directly from the distributions, the improvement after applying correction is around 10 % at 35 GeV.

The jet momentum response is non-Gaussian when plotted in bins of , therefore the momentum response is initially calculated in bins of in order to get rid of spectrum effects. Since the correction has to be applied over the reconstructed jet , the numerical inversion method is implemented. By using the definition of jet response, , pairs are formed of jet momentum response and reconstructed jet transverse momentum: . The numerical inversion is derived and applied to these pairs giving .

In addition, it is important to point out that whatever the track-based variable is, there is no way to get rid of from the track-based jet correction strategy, since the correction must be applied as a function of . The jet momentum response, uniform and centered at 1 on average, is fitted as a function of and . Projections over two planes are done in order to easily inspect the shape of the response and decide initial parameters to be used as inputs for a global %R($n_{trk}$,$p^{reco}_{T}$)% fit. The response as a function of and has been parametrized as follow:

A grid is constructed with bins in and and fitted using the form addressed above. The surface defined by the fit function and the measured points and slices of the fit are presented.

Parameter	Fitted Value	Error
p0	1.024	0.004
p1	0.19	0.03
p2	0.013	0.002
p3	-0.0019	0.0001
p4	-0.021	0.003
p5	0.012	0.003
p6	4e-05	3e-05
p7	0.0008	0.0003
p8	0.015	0.007
p9	-0.28	0.04
p10	0.030	0.003

As closure test, the response and the fractional transverse jet momentum resolution are calculated before and after the correction. When adding track information, the response as a function of before and after applying the correction over H1 calibrated jets is found to remain centered at 1 within 1%. In addition, an improvement of 10.6% is observed at 35 GeV when comparing the fractional transverse jet momentum resolution as a function of before and after applying the correction over H1 calibrated jets.

Sequential Track-Based Jet Correction

After correcting for the most promising track variable, which has turned out to be , it might be possible that other jet-by-jet energy fluctuations, that were not taken into account for the track multiplicity, still remains. In consecuence, additional track-based jet correction have been considered in order to maximally improve the jet transverse momentum resolution. The sensitivity of the response to the rest of track variables after applying a correction has been studied. Although all these variables are each worth exploring, clearly the optimal set will not include all possibilities, since different ways of describing a jet might be highly correlated and therefore deriving only one correction might be proved sufficient. It is found that track variables that may account for out-of-clustering energy might be good candidates in order to derive a sequential correction. has been chosen, since it may distinguish different kinds of radiations and less sensitive to fakes that either or . Following the correction strategy already explained above, a sequential track-based jet correction has been derived. The Response as a function of and has been parametrized as follow:

A grid was constructed with bins in and and fitted whereas the surface defined by the fit function of the is shown below. A closure test has been performed after applying the sequential track-based jet correction (i.e. ). The response as a function of is found to be centered at one within 1% and an additional improvement of 1% at low (30-40 GeV) is achieved in the fractional jet transverse momentum resolution. Although the re-centering of several gaussians has been satisfactory done and the artificial broaden is removed, the spread of the distributions is much bigger that such shifting, which yields to an additional improvement of only 1%. Once the sequential track-based jet correction is applied, no further room for improvement has been observed. It is worth mentioning that all these corrections will need to be tested in both a pile-up and data scenarios, since it is likely that the optimal combination of variables differs from that in pure Monte Carlo.

Effect of track-based jet correction on jets calibrated at the EM scale

The Jet Calibration Task Force has planned to factorize the jet energy corrections in several components, where each component will be derived using either a data-driven method or a Monte Carlo based method as the simulation is being adjusted to the data. Having an insight into how the track-based jet corrections performs over different kinds of calibrated jets is crucial to further improve the jet transverse momentum resolution during early data. Moreover, understanding correlations between track corrections and cell weighting will be extremely important, contributing to the general understanding of the JES.

Calibration constants for the Numerical Inversion addressed in the Jet Calibration Task Force Twiki Page are applied to the uncalibrated EM signal, , such that (on average) jets have a uniform response in transverse momentum. Jet-by-jet fluctuations are corrected using the track multiplicity to study to what extend track-jet corrections can be applied to improve the resolution using both Numerical Inversion + track and H1 calibration + track corrections. The new correction derived using EM + NI calibrated jets and the fitted parameters' values are summarized below.

Parameter	Fitted Value	Error
p0	1.065	0.004
p1	0.30	0.01
p2	0.0110	0.0004
p3	0.0005	0.0018
p4	-0.029	0.002
p5	0.0045	0.0007
p6	-4.8e-05	0.0001
p7	0.00111	0.0001
p8	0.0082	0.003
p9	-0.35	0.01
p10	0.0184	0.0007

Figures above show the response as a function of before and after applying the correction over the two different JES scenarios (H1 and EM + NI calibrated jets). It can be observed that the when adding track information, the response remains centered at 1 within 1%. An ultimate performace is achieved when combining H1 + track-based jet corrections. As addressed before, it is known that dead material accounts for about 80% of the Local Hadron Calibration and therefore it is suitable to associate that the improvement in the transverse jet momentum resolution after applying the correction comes from correcting for dead material effects. The bulk of the dead material takes place in the LAr cryostat, between the EM and the HAD calorimeters. At low , pions interact more in the EM, the cryostat does not completely contribute to dead material and therefore the tracks provide a handle on how to improve the transverse jet momentum resolution. On the other hand, at high , has no information about how many tracks went through from the EM to the HAD, whereas H1(LC) does know it, since the have both the cells(clusters) in the TILE and in the EM. In consecuence, at high H1(LC) fully accounts for this effect and hence does not give further improvement. This feature suggests that more information to enhance this technique may be provided by combining clusters' information to tracks in order to get a handle on which the cryostat effect is. One possibility it is being under study is to analyse the response as a function of in bins of number of clusters. In addition, the response sensitivity to the number of clusters in the TILE is being investigated.

Data-Driven Track-Based Jet Corrections

Track-based jet corrections can be derived using either only data or MC information and tested with data using the strategy summarized next ( method). In a sample of back-to-back leading jets, a jet may be defined as a reconstructed jet pointing to the central region. The energy imbalance of the jet with respect to a tag jet, a back-to-back reconstructed jet in the same region, can then be studied as a function of the $probe$ jet most promising track variable. This method can be used to calibrate the transverse momentum response of probe jets with a particular value of the most promising track variable relative to the average transverse momentum response of the tag jets. In addition, and .

Further Documentation

• Talks:

• Notes:

Athena Implementation

We are currently looking into implementing this correction as part of the JetCalibTools package. This twiki will be updated as soon as progress is made on this implementation.

Appendix:

---

Major updates:
-- GastonRomeo - 06 May 2009

-- GastonRomeo - 06 May 2009