Jet energy measurement and its systematic uncertainty in proton-proton collisions at [Formula: see text] TeV with the ATLAS detector

Abstract

The jet energy scale (JES) and its systematic uncertainty are determined for jets measured with the ATLAS detector using proton-proton collision data with a centre-of-mass energy of [Formula: see text] TeV corresponding to an integrated luminosity of [Formula: see text][Formula: see text]. Jets are reconstructed from energy deposits forming topological clusters of calorimeter cells using the anti-[Formula: see text] algorithm with distance parameters [Formula: see text] or [Formula: see text], and are calibrated using MC simulations. A residual JES correction is applied to account for differences between data and MC simulations. This correction and its systematic uncertainty are estimated using a combination of in situ techniques exploiting the transverse momentum balance between a jet and a reference object such as a photon or a [Formula: see text] boson, for [Formula: see text] and pseudorapidities [Formula: see text]. The effect of multiple proton-proton interactions is corrected for, and an uncertainty is evaluated using in situ techniques. The smallest JES uncertainty of less than 1 % is found in the central calorimeter region ([Formula: see text]) for jets with [Formula: see text]. For central jets at lower [Formula: see text], the uncertainty is about 3 %. A consistent JES estimate is found using measurements of the calorimeter response of single hadrons in proton-proton collisions and test-beam data, which also provide the estimate for [Formula: see text] TeV. The calibration of forward jets is derived from dijet [Formula: see text] balance measurements. The resulting uncertainty reaches its largest value of 6 % for low-[Formula: see text] jets at [Formula: see text]. Additional JES uncertainties due to specific event topologies, such as close-by jets or selections of event samples with an enhanced content of jets originating from light quarks or gluons, are also discussed. The magnitude of these uncertainties depends on the event sample used in a given physics analysis, but typically amounts to 0.5-3 %.

Fig. 1

The energy-equivalent cell noise in the ATLAS calorimeters on the electromagnetic (EM) scale as a function of the direction $|\mathit{\eta }|$ in the detector, for the 2010 configuration with a $\mathit{\mu }=0$ and the 2011 configuration with b $\mathit{\mu }=8$. The various colours indicate the noise in the pre-sampler (PS) and the up to three layers of the LAr EM calorimeter, the up to three layers of the Tile calorimeter, the four layers for the hadronic end-cap (HEC) calorimeter, and the three modules of the forward (FCal) calorimeter

Fig. 2

Overview of the ATLAS jet reconstruction. After the jet finding, the jet four momentum is defined as the four momentum sum of its constituents

Fig. 3

Overview of the ATLAS jet calibration scheme used for the 2011 dataset. The pile-up, absolute JES and the residual in situ corrections calibrate the scale of the jet, while the origin and the $\mathit{\eta }$ corrections affect the direction of the jet

Fig. 4

Average response of simulated jets formed from topo-clusters, calculated as defined in Eq. (1) and shown in a for the EM scale (${\mathfrak{R}}^{\mathrm{EM}}$) and in b for the LCW scale (${\mathfrak{R}}^{\mathrm{LCW}}$). The response is shown separately for various truth-jet energies as function of the uncorrected (detector) jet pseudorapidity ${\mathit{\eta }}_{\det }$. Also indicated are the different calorimeter regions. The inverse of ${\mathfrak{R}}^{\mathrm{EM}}$ (${\mathfrak{R}}^{\mathrm{LCW}}$) corresponds to the average jet energy scale correction for EM (LCW) in each ${\mathit{\eta }}_{\det }$ bin. The results shown are based on the baseline Pythia inclusive jet sample

Fig. 5

Jet quality selection efficiency for anti-$k_t$ jets with $R=0.4$ measured with a tag-and-probe technique as a function of $p_{\mathrm{T}}^{\mathrm{jet}}$ in various $\mathit{\eta }$ ranges, for the four sets of selection criteria. Only statistical uncertainties are shown. Differences between data and MC simulations are also shown

Fig. 6

The average reconstructed transverse momentum $p_{\mathrm{T},\mathrm{EM}}^{\mathrm{jet}}$ on EM scale for jets in MC simulations, as function of the number of reconstructed primary vertices $N_{\mathrm{PV}}$ and $7.5\le \mathit{\mu }<8.5$, in various bins of truth-jet transverse momentum $p_{\mathrm{T}}^{\mathrm{truth}}$, for jets with a $R=0.4$ and b $R=0.6$. The dependence of $p_{\mathrm{T},\mathrm{EM}}^{\mathrm{jet}}$ on $N_{\mathrm{PV}}$ in data, in bins of track-jet transverse momentum $p_{\mathrm{T}}^{\mathrm{track}}$, is shown in c for $R=0.4$ jets, and in d for $R=0.6$ jets

Fig. 7

The average reconstructed jet transverse momentum $p_{\mathrm{T},\mathrm{EM}}^{\mathrm{jet}}$ on EM scale as function of the average number of collisions $\mathit{\mu }$ at a fixed number of primary vertices $N_{\mathrm{PV}}=6$, for truth jets in MC simulation a in the lowest bin of $p_{\mathrm{T}}^{\mathrm{truth}}$ and b in the lowest bin of track jet transverse momentum $p_{\mathrm{T}}^{\mathrm{track}\mathrm{jet}}$ considered in data

Fig. 8

The pile-up contribution per additional vertex, measured as ${\mathit{\alpha }}^{\mathrm{EM}}=\mathit{\partial }{p}_{\mathrm{T},\mathrm{EM}}^{\mathrm{jet}}/\mathit{\partial }{N}_{\mathrm{PV}}$, as function of $|{\mathit{\eta }}_{\det }|$, for the various methods discussed in the text, for a $R=0.4$ and b $R=0.6$ jets. The contribution from $\mathit{\mu }$, calculated as ${\mathit{\beta }}^{\mathrm{EM}}=\mathit{\partial }{p}_{\mathrm{T},\mathrm{EM}}^{\mathrm{jet}}/\mathit{\partial }\mathit{\mu }$ and displayed for the various methods as function of $|{\mathit{\eta }}_{\det }|$, is shown for the two jet sizes in c and d, respectively. The points for the determination of ${\mathit{\alpha }}^{\mathrm{EM}}$ and ${\mathit{\beta }}^{\mathrm{EM}}$ from MC simulations use the offset calculated from the reconstructed $p_{\mathrm{T},\mathrm{EM}}^{\mathrm{jet}}$ and the true (particle level) $p_{\mathrm{T}}^{\mathrm{truth}}$, as indicated in Eq. 4

Fig. 9

Overview of the $(p_{\mathrm{T}}^{\mathrm{avg}},{\mathit{\eta }}_{\det })$ bins of the dijet balance measurements for jets reconstructed with distance parameter $R=0.4$ calibrated using the EM+JES scheme. The solid lines indicate the $(p_{\mathrm{T}}^{\mathrm{avg}},{\mathit{\eta }}_{\det }^{\mathrm{probe}})$ bin edges, and the points show the average transverse momentum and pseudorapidity of the probe jet within each bin. The measurements within the ${\mathit{\eta }}_{\det }$ range spanned by the two thick, dashed lines are used to derive the residual calibration

Fig. 10

Relative jet response ($1/c$) for anti-$k_t$ jets with $R=0.4$ calibrated with the EM+JES scheme as a function of the probe jet pseudorapidity measured using the matrix and the central reference methods. Results are presented in a for $40\le p_{\mathrm{T}}^{\mathrm{avg}}<55$ GeV and in b for $220\le p_{\mathrm{T}}^{\mathrm{avg}}<300$ GeV. The lower parts of the figures show the ratios between relative response in data and MC

Fig. 11

Relative jet response ($1/c$) as a function of the jet pseudorapidity for anti-$k_t$ jets with $R=0.4$ calibrated with the EM+JES scheme, separately for a $22\le p_{\mathrm{T}}^{\mathrm{avg}}<30$ GeV, b $55\le p_{\mathrm{T}}^{\mathrm{avg}}<75$ GeV, c $170\le p_{\mathrm{T}}^{\mathrm{avg}}<220$ GeV and d $600\le p_{\mathrm{T}}^{\mathrm{avg}}<800$ GeV. The lower parts of the figures show the ratios between the data and MC relative response. These measurements are performed using the matrix method. The applied correction is shown as a thick line. The line is solid over the range where the measurements is used to constrain the calibration, and dashed in the range where extrapolation is applied

Fig. 12

Relative jet response ($1/c$) as a function of the average jet $p_{\mathrm{T}}$ of the dijet system for anti-$k_t$ jets with $R=0.4$ calibrated with the EM+JES scheme, separately for a $-1.2\le {\mathit{\eta }}_{\det }<-0.8$ and b $2.1\le {\mathit{\eta }}_{\det }<2.8$. The lower parts of the figures show the ratios between the data and MC relative response. The applied correction is shown as a thick line

Fig. 13

Summary of uncertainties on the intercalibration as a function of the jet ${\mathit{\eta }}_{\det }$ for anti-$k_t$ jets with $R=0.4$ calibrated with the EM+JES scheme, separately for a $p_{\mathrm{T}}=35$ GeV and b $p_{\mathrm{T}}=350$ GeV. The individual components are added in quadrature to obtain the total uncertainty. The MC modelling uncertainty is the dominant component

Fig. 14

The $Z$ boson $p_{\mathrm{T}}$ distribution in selected $Z$ events. Data and prediction from the $Z\to ee$ Pythia simulation, normalised to the observed number of events, are compared

Fig. 15

The $p_{\mathrm{T}}^{\text{jet}}/p_{\mathrm{T}}^{\text{ref}}$ distribution in the data for $20\le p_{\mathrm{T}}^{\text{ref}}<25\mathrm{GeV}$ and $\mathit{\pi }-\mathrm{\Delta }\mathit{\varphi }(\mathrm{jet},Z)<0.05$ is shown in a. The black solid histogram represents the fit function, a Poisson distribution extended to non-integer values, multiplied by a turn-on curve. The value used in each bin is the mean value of that function in the bin. The gray dashed line shows the underlying Poisson distribution, from which the mean is taken as the measurement of the $p_{\mathrm{T}}$ balance. In b the measured widths of the $p_{\mathrm{T}}^{\text{jet}}/p_{\mathrm{T}}^{\text{ref}}$ distributions as a function of $p_{\mathrm{T}}^{\text{ref}}$ is shown for data and MC simulations, for events with $\mathit{\pi }-\mathrm{\Delta }\mathit{\varphi }(\mathrm{jet},Z)<0.05$. The fitted functional form defined by Eq. (11) is superimposed. In both figures, anti-$k_t$ jets with distance parameter $R=0.4$ calibrated with the EM+JES scheme are used. Only statistical uncertainties are shown

Fig. 16

Mean $p_{\mathrm{T}}^{\mathrm{jet}}/p_{\mathrm{T}}^{\text{ref}}$ balance vs $\mathrm{\Delta }\mathit{\varphi }(\mathrm{jet},Z)$ for $20\le p_{\mathrm{T}}^{\text{ref}}<25\mathrm{GeV}$ in the data and in the simulation. A linear function used to extrapolate the balance to $\mathrm{\Delta }\mathit{\varphi }=\mathit{\pi }$ is superimposed. Anti-$k_t$ jets with distance parameter $R=0.4$ calibrated with the EM+JES scheme are used. Only statistical uncertainties are shown

Fig. 17

Mean $p_{\mathrm{T}}$ balance obtained in the data and with the Pythia simulation. Results for anti-$k_t$ jets with distance parameter a $R=0.4$ and b $R=0.6$ calibrated with the EM+JES scheme are shown. Only statistical uncertainties are shown

Fig. 18

Transverse momentum profile of tracks around the leading jet axis for events with $20\le p_{\mathrm{T}}^{\mathrm{ref}}<25\mathrm{GeV}$ in $Z$-jet events. The radii $R$ and $R_0$ are those used in Eq. (12) to define the IC and IC+OC regions. The hatched area indicates the contribution from the underlying event (UE). Anti-$k_t$ jets with $R=0.4$ calibrated with the EM+JES scheme are considered

Fig. 19

Summary of the $Z$-jet uncertainties on the data-to-MC ratio of the mean $p_{\mathrm{T}}$ balance, for anti-$k_t$ jets with distance parameter a $R=0.4$ and b $R=0.6$ calibrated with the EM+JES scheme

Fig. 20

Data-to-MC ratio of the mean $p_{\mathrm{T}}$ balance for $Z$-jet events as a function of $p_{\mathrm{T}}^{\text{ref}}$ for anti-$k_t$ jets with distance parameter (a, c) $R=0.4$ and (b, d) $R=0.6$ calibrated with the (a, b) EM+JES and the (c, d) LCW+JES schemes. The total uncertainty on this ratio is depicted by grey bands. Dashed lines show the $-$1, $-$2, and $-$5 % shifts

Fig. 21

MPF response distributions in the $\mathit{\gamma }\text{-jet}$ data for a $25\le p_{\mathrm{T}}^{\mathit{\gamma }}<45$ GeV and b $160\le p_{\mathrm{T}}^{\mathit{\gamma }}<210$  GeV when using topo-clusters at the EM scale. The dashed lines represent the fits with a Gaussian function. The mean value from the fit in each $p_{\mathrm{T}}^{\mathit{\gamma }}$ bin is the value used as the measured average MPF response

Fig. 22

Jet response distributions in the $\mathit{\gamma }\text{-jet}$ data for a $25\le p_{\mathrm{T}}^{\mathit{\gamma }}<45$ GeV and b $160\le p_{\mathrm{T}}^{\mathit{\gamma }}<210$ GeV as measured by the DB technique for anti-$k_t$ jets with $R=0.6$ at the EM+JES scale. The dashed lines represent fits of Gaussian functions, except in the lowest bin ($25\le p_{\mathrm{T}}^{\mathit{\gamma }}<45$ GeV), where the fit function is a Poisson distribution. The mean value from the fit in each $p_{\mathrm{T}}^{\mathit{\gamma }}$ bin is the value used as the measured average jet response in DB

Fig. 23

Average jet response as determined by the MPF technique in $\mathit{\gamma }\text{-jet}$ events using topo-clusters at the a EM and b LCW energy scales, for both data and MC simulations, as a function of the photon transverse momentum. The data-to-MC response ratio is shown in the bottom inset of each figure. Only the statistical uncertainties are shown

Fig. 24

Average jet response as determined by the DB technique in $\mathit{\gamma }\text{-jet}$ events for anti-$k_t$ jets with (a, b) $R=0.4$ and (c, d) $R=0.6$, calibrated with the (a, c) EM+JES scheme and with the (b, d) LCW+JES scheme, for both data and MC simulations, as a function of the photon transverse momentum

Fig. 25

Average jet response as determined by the a MPF and b DB techniques, using anti-$k_t$ jets with $R=0.4$ at the EM and EM+JES energy scales respectively, for Pythia (circles) and Herwig (squares) MC simulations, as a function of the photon transverse momentum. The HERWIG-to-PYTHIA response ratio is shown in the bottom inset of each figure. Only the statistical uncertainties are shown

Fig. 26

Out-of-cone radiation factor $k_{\mathrm{OOC}}$ relating the $p_{\mathrm{T}}$ of the photon with the $p_{\mathrm{T}}$ of the truth jet as a function of the photon transverse momentum, measured using charged particles, for anti-$k_t$ jets with a $R=0.4$ and b $R=0.6$, in data and in MC simulations. The data-to-MC response ratio is shown in the bottom inset of each plot. Statistical and systematic uncertainties are added in quadrature

Fig. 27

Systematic uncertainties on the data-to-MC ratio of the jet response, as determined by the MPF technique for $\mathit{\gamma }\text{-jet}$ events using topo-clusters at the a EM and b LCW energy scales, as a function of the photon transverse momentum

Fig. 28

Systematic uncertainties on the data-to-MC ratio of the jet response, as determined by the DB technique in $\mathit{\gamma }\text{-jet}$ events, for anti-$k_t$ jets with (a, b) $R=0.4$ and (c, d) $R=0.6$, calibrated with the (a, c) EM+JES scheme and with the (b, d) LCW+JES scheme, as a function of the photon transverse momentum

Fig. 29

Multijet balance as a function of the recoil system $p_{\mathrm{T}}^{\mathrm{recoil}}$ for anti-$k_t$ jets with (a, b) $R=0.4$ and (c, d) $R=0.6$, calibrated with the (a, c) EM+JES scheme and with the (b, d) LCW+JES scheme, for both data and MC simulations. The non-leading jets in the data with $p_{\mathrm{T}}<750$ GeV are corrected by the combination of $\mathit{\gamma }\text{-jet}$ and $Z$-jet in situ calibrations as described in Sect. 11.1. The open points in the bottom panel show the ratio of the MJB values between data and MC simulations. The curve in the same panel shows the data-to-MC ratio of the jet $p_{\mathrm{T}}$ relative to the $p_{\mathrm{T}}$ of a photon ($p_{\mathrm{T}}^{\mathit{\gamma }}$) or a $Z$ boson ($p_{\mathrm{T}}^Z$) as a function of the $p_{\mathrm{T}}^{\mathit{\gamma }}$ or $p_{\mathrm{T}}^Z$ in $\mathit{\gamma }\text{-jet}$ or $Z$-jet events, obtained in the combination mentioned above. Only the statistical uncertainties are shown

Fig. 30

Multijet balance with the nominal and varied $Z$-jet in situ calibrations as a function of the recoil system $p_{\mathrm{T}}^{\mathrm{recoil}}$ for anti-$k_t$ jets with (a, b) $R=0.4$ and (c, d) $R=0.6$, calibrated with the (a, c) EM+JES scheme and with the (b, d) LCW+JES scheme. The varied distributions are obtained by fluctuating the jet energy scale for the non-leading jets by $\pm 1\mathit{\sigma }$ for each of the systematic uncertainties for the $Z$-jet calibration and repeating the analysis over the data sample. The bottom panel shows the relative variations of the MJB with respect to the nominal case. The uppermost (lowermost) thick line in the bottom panel shows the total variation obtained by adding all the positive (negative) variations in quadrature. The colour coding used in the lower part of the figure is the same as that used in the upper one

Fig. 31

Multijet balance with the nominal and varied $\mathit{\gamma }\text{-jet}$ in situ calibrations as a function of the recoil system $p_{\mathrm{T}}^{\mathrm{recoil}}$ for anti-$k_t$ jets with (a, b) $R=0.4$ and (c, d) $R=0.6$, calibrated with the (a, c) EM+JES scheme and with the (b, d) LCW+JES scheme. The varied distributions are obtained by fluctuating the jet energy scale for the non-leading jets by $\pm 1\mathit{\sigma }$ for each of the systematic uncertainties and repeating the analysis over the data sample. The bottom panel shows the relative variations of the MJB with respect to the nominal case. The uppermost (lowermost) thick line in the bottom panel shows the total variation obtained by adding all the positive (negative) variations in quadrature. The colour coding used in the lower part of the figure is the same as that used in the upper one

Fig. 32

Relative uncertainties on the MJB due to the systematic uncertainty sources considered in the analysis as a function of the recoil system $p_{\mathrm{T}}$ for anti-$k_t$ jets with (a, b) $R=0.4$ and (c, d) $R=0.6$, calibrated with the (a, c) EM+JES scheme and with the (b, d) LCW+JES scheme. The black line shows the total uncertainty obtained as a sum of all uncertainties in quadrature

Fig. 33

Multijet balance and systematic uncertainties related to the multijet balance technique and to the propagated uncertainties from the $\mathit{\gamma }\text{-jet}$ and $Z$-jet balance as a function of the recoil system $p_{\mathrm{T}}^{\mathrm{recoil}}$ for anti-$k_t$ jets with (a, b) $R=0.4$ and (c, d) $R=0.6$, calibrated with the (a, c) EM+JES scheme and with the (b, d) LCW+JES scheme. The subleading jets in the data are corrected by the combination of $\mathit{\gamma }\text{-jet}$ and $Z$-jet in situ calibrations at $p_{\mathrm{T}}<750$ GeV and MJB calibration at higher $p_{\mathrm{T}}$ as described in Sect. 11.1. The three systematic uncertainty bands are obtained by adding individual systematic uncertainties for each calibration technique in quadrature. Also shown are predictions of the MJB from MC simulations for the three highest $p_{\mathrm{T}}^{\mathrm{recoil}}$-values, together with their systematic uncertainties propagated by using distribution from MC simulations. The bottom panel shows the relative variations of the MJB with respect to the nominal case

Fig. 34

Relative jet response, $1/c$, as a function of the jet ${\mathit{\eta }}_{\det }$ for anti-$k_t$ jets with $R=0.4$ calibrated with the EM+JES scheme and in addition the derived $\mathit{\eta }$-intercalibration. Results are shown separately for a $55\le p_{\mathrm{T}}^{\mathrm{avg}}<75$ GeV and b $300\le p_{\mathrm{T}}^{\mathrm{avg}}<400$ GeV. For all points included in the original calibration ($|{\mathit{\eta }}_{\det }|<2.8$), the data are corrected to be consistent with the response in MC simulations using Pythia, as intended. The resulting calibration derived from the already calibrated data is shown as a thick line and is consistent with unity. The lower parts of the figures show the ratios between the relative jet response in data and MC

Fig. 35

The (a, b) $Z$-jet and (a, b) $\mathit{\gamma }\text{-jet}$ balance for anti-$k_t$ jets with $R=0.4$, calibrated with the EM+JES scheme. In a and b the results for events with $25\le p_{\mathrm{T}}^{\mathrm{ref}}<35$  GeVand $50\le p_{\mathrm{T}}^{\mathrm{ref}}<80$  GeV are shown, respectively. Here $p_{\mathrm{T}}^{\mathrm{ref}}$ is the $p_{\mathrm{T}}$ of the reconstructed $Z$ boson projected onto the axis of the balancing jet. The $p_{\mathrm{T}}$ balance for $\mathit{\gamma }\text{-jet}$ events with photons with transverse momenta $p_{\mathrm{T}}^{\mathit{\gamma }}$ within $85\le p_{\mathrm{T}}^{\mathit{\gamma }}<100$ GeV is shown in c, while d shows the $p_{\mathrm{T}}$ balance for higher photon transverse momenta ($210\le p_{\mathrm{T}}^{\mathit{\gamma }}<260$ GeV). As no in situ calibration is applied to these measurements, it is expected that data and MC simulations using Pythia are shifted relative to each other by the absolute correction multiplied by the relative (${\mathit{\eta }}_{\det }$ dependent) correction presented herein. The resulting JES calibration is shown as a solid line in the lower part of the figures. The dijet modelling uncertainty is shown as a filled band around the in situ correction

Fig. 36

Weight carried by each in situ technique in the combination to derive the residual jet energy scale calibration as a function of the jet transverse momentum $p_{\mathrm{T}}^{\mathrm{jet}}$ for anti-$k_t$ jets with $R=0.4$ calibrated with the a EM+JES and the b LCW+JES scheme. The $p_{\mathrm{T}}^{\mathrm{jet}}$ dependence of the weights is discussed in Sect. 13.4

Fig. 37

Individual uncertainty sources applicable to the combined response ratio as a function of the jet $p_{\mathrm{T}}$ for the three in situ techniques: a, b $Z$-jet direct balance, c, d $\mathit{\gamma }\text{-jet}$ MPF and e, f multijet balance for anti-$k_t$ jets with $R=0.4$ calibrated with the a, c, e EM+JES and the b, d, f LCW+JES scheme. The systematic uncertainties displayed here correspond to the components listed in Table 10

Fig. 38

Ratio of the average jet response $⟨p_{\mathrm{T}}^{\mathrm{jet}}/p_{\mathrm{T}}^{\mathrm{ref}}⟩$ measured in data to that measured in MC simulations for jets within $|\mathit{\eta }|<1.2$ as a function of the transverse jet momentum $p_{\mathrm{T}}^{\mathrm{jet}}$. The data-to-MC jet response ratios are shown separately for the three in situ techniques used in the combined calibration: direct balance in $Z$-jet events, MPF in $\mathit{\gamma }\text{-jet}$ events, and multijet $p_{\mathrm{T}}$ balance in inclusive jet events. The error bars indicate the statistical and the total uncertainties (adding in quadrature statistical and systematic uncertainties). Results are shown for anti-$k_t$ jets with $R=0.4$ calibrated with the a EM+JES and the b LCW+JES scheme. The light band indicates the total uncertainty from the combination of the in situ techniques. The inner dark band indicates the statistical component only

Fig. 39

Difference between the data-to-MC response ratio $R$ measured using the direct balance (DB) and the missing momentum fraction (MPF) methods for jets reconstructed with the anti-$k_t$ algorithm with $R=0.4$ calibrated with the EM+JES and LCW+JES schemes. The error bars shown only contain the uncorrelated uncertainties

Fig. 40

Systematic (effective) relative uncertainties displayed as a function of jet $p_{\mathrm{T}}$ for anti-$k_t$ jets with $R=0.4$ calibrated with the a EM+JES and the b LCW+JES calibration schemes for the reduced scheme with six nuisance parameters. Each curve can be interpreted as a $1\mathit{\sigma }$ JES systematic nuisance parameter, symmetric around zero. They represent eigenvectors of the covariance matrix (continuous lines) and the residual component (dashed line)

Fig. 41

In a, the nominal JES correlation matrix is shown. The difference between the correlation matrices of the interpretations resulting in stronger and weaker correlations for anti-$k_t$ jets with $R=0.4$ calibrated using the EM+JES calibration scheme in the central calorimeter region ($\mathit{\eta }=0.5$) is depicted in b

Fig. 42

Relative uncertainties for reduced (effective) components within a single category displayed as a fraction of jet $p_{\mathrm{T}}$ for anti-$k_t$ jets with $R=0.4$, calibrated with the EM+JES scheme. The convention from Fig. 40 is followed here. The 54 nuisance parameters that are input to the reduction for each of the categories are listed in Table 10. The reduction is performed for all nuisance parameters belonging to any given category, which are statistical and method components (a), detector components (b), modelling components (c), and mixed detector and modelling components (d). Each of the curves can be interpreted as an effective $1\mathit{\sigma }$ JES systematic nuisance parameter, symmetric around zero. They represent eigenvectors of the covariance matrix (continuous lines) and the residual component (dashed line), for the specified category

Fig. 43

Relative calorimeter jet response ratio between data and MC simulations, as estimated from the single-hadron response measurements as a function of the jet transverse momentum, is shown in a. The total systematic uncertainty together with the uncertainty from the individual components is shown as a lighter band. The black circles denote the estimated mean shift of the calorimeter response to jets in data over the one in MC simulations. In b, the uncertainty from the single-hadron response measurements is shown as a lighter (yellow) band, while the JES uncertainty, as derived from the in situ methods based on $p_{\mathrm{T}}$ balance, is shown as a dark (gray) band. The closed markers denote the estimated shift of the calorimeter response to jets in data over the one in MC simulations, and the line shows the JES correction derived from the $p_{\mathrm{T}}$ balance in situ methods

Fig. 44

The three templates distributions for the reconstructed $W$ mass in $t\overline{t}$ events obtained by shifting the jet energy by a factor ${\mathit{\alpha }}_l=0.95$, 1 and 1.05 in the Monte Carlo simulation with respect to the one in data (a). The Monte Carlo simulation templates are also compared to the data distribution. The ${\mathit{\alpha }}_l$ measurement as a function of mean jet $p_{\mathrm{T}}$ using the maximum $p_{\mathrm{T}}$ reconstruction approach, is shown in b. Error bars are statistical while hashed rectangles represent the total uncertainties

Fig. 45

The difference from the average ${\mathit{\alpha }}^{\mathrm{EM}}({\mathit{\eta }}_{\det })$ of the in-time pile-up signal contribution per reconstructed primary vertex ($\mathrm{\Delta }(\mathit{\partial }{p}_{\mathrm{T},\mathrm{EM}}^{\mathrm{jet}}/\mathit{\partial }{N}_{\mathrm{PV}})(p_{\mathrm{T}}^{\mathrm{truth}})$) as a function of the true jet transverse momentum $p_{\mathrm{T}}^{\mathrm{truth}}$, for MC-simulated jets reconstructed with anti-$k_t$ $R=0.4$ and $R=0.6$ at the EM scale, in two different regions a $|{\mathit{\eta }}_{\det }|<0.3$ and b $1.2\le |{\mathit{\eta }}_{\det }|<2.1$ of the ATLAS calorimeter. In c and d, the variations of the out-of-time pile-up signal contribution per interaction with $p_{\mathrm{T}}^{\mathrm{truth}}$ around its average ${\mathit{\beta }}^{\mathrm{EM}}({\mathit{\eta }}_{\det })$ ($\mathrm{\Delta }(\mathit{\partial }{p}_{\mathrm{T},\mathrm{EM}}^{\mathrm{jet}}/\mathit{\partial }\mathit{\mu })(p_{\mathrm{T}}^{\mathrm{truth}})$) are shown for the same jet samples and the same respective ${\mathit{\eta }}_{\det }$ regions. Logarithmic functions of $p_{\mathrm{T}}^{\mathrm{truth}}$ are fitted to the points obtained from MC simulations

Fig. 46

The fractional systematic shift due to mis-modelling of the effect of in-time pile-up on the transverse momentum $p_{\mathrm{T},\mathrm{EM}+\mathrm{JES}}^{\mathrm{jet}}$ of jets reconstructed with the anti-$k_t$ algorithm with $R=0.4$, and calibrated with the EM+JES scheme, is shown as a function of $(N_{\mathrm{PV}}-N_{\mathrm{PV}}^{\mathrm{ref}})$ in a, c, and e for various $p_{\mathrm{T},\mathrm{EM}+\mathrm{JES}}^{\mathrm{jet}}$ bins. The same systematic shift is shown in b, d, and f for jets calibrated with the LCW+JES scheme, now in bins of $p_{\mathrm{T},\mathrm{LCW}+\mathrm{JES}}^{\mathrm{jet}}$

Fig. 47

The fractional systematic shift due to mis-modelling of the effect of in-time pile-up on the transverse momentum $p_{\mathrm{T},\mathrm{EM}+\mathrm{JES}}^{\mathrm{jet}}$ of jets reconstructed with the anti-$k_t$ algorithm with $R=0.6$ and calibrated with the EM+JES scheme, is shown as a function of $(N_{\mathrm{PV}}-N_{\mathrm{PV}}^{\mathrm{ref}})$ in a, c, and e for various $p_{\mathrm{T},\mathrm{EM}+\mathrm{JES}}^{\mathrm{jet}}$ bins. The same systematic shift is shown in b, d, and f for jets calibrated with the LCW+JES scheme, now in bins of $p_{\mathrm{T},\mathrm{LCW}+\mathrm{JES}}^{\mathrm{jet}}$

Fig. 48

The fractional systematic shift due to mis-modelling of the effect of out-of-time pile-up on the transverse momentum $p_{\mathrm{T},\mathrm{EM}+\mathrm{JES}}^{\mathrm{jet}}$ of jets reconstructed with the anti-$k_t$ algorithm with $R=0.4$ and calibrated with the EM+JES scheme, is shown as a function of $(\mathit{\mu }-{\mathit{\mu }}^{\mathrm{ref}})$ in a, c, and e for various $p_{\mathrm{T},\mathrm{EM}+\mathrm{JES}}^{\mathrm{jet}}$ bins. The same systematic shift is shown in b, d, and f for jets calibrated with the LCW+JES scheme, now in bins of $p_{\mathrm{T},\mathrm{LCW}+\mathrm{JES}}^{\mathrm{jet}}$

Fig. 49

The fractional systematic shift due to mis-modelling of the effect of out-of-time pile-up on the transverse momentum $p_{\mathrm{T},\mathrm{EM}+\mathrm{JES}}^{\mathrm{jet}}$ of jets reconstructed with the anti-$k_t$ algorithm with $R=0.6$ and calibrated with the EM+JES scheme, is shown as a function of $(\mathit{\mu }-{\mathit{\mu }}^{\mathrm{ref}})$ in a, c, and e for various $p_{\mathrm{T},\mathrm{EM}+\mathrm{JES}}^{\mathrm{jet}}$ bins. The same systematic shift is shown in b, d, and f for jets calibrated with the LCW+JES scheme, now in bins of $p_{\mathrm{T},\mathrm{LCW}+\mathrm{JES}}^{\mathrm{jet}}$

Fig. 50

In a, the deviation from unity of the data-to-MC ratio of the track-jet $p_{\mathrm{T}}$ for non-isolated jets divided by the track-jet $p_{\mathrm{T}}$ for isolated jets, is shown as a function of the jet $p_{\mathrm{T}}$. The deviation from unity of the data-to-MC ratio of the relative response of non-isolated jets with respect to that of isolated jets as a function of the jet $p_{\mathrm{T}}$ is shown in b. As described in the text, the distributions show the ratios given in a Eq. (16) and b Eq. (15) for the four jet calibration schemes. Only statistical uncertainties are shown

Fig. 51

Difference in jet response $\mathcal{R}=p_{\mathrm{T}}^{\mathrm{jet}}/p_{\mathrm{T}}^{\mathrm{truth}}$ of isolated jets initiated by light quarks and gluons as a function of the true jet $p_{\mathrm{T}}$, for anti-$k_t$ jets with $R=0.4$ in the barrel calorimeter. Three different calibration schemes are shown for a the EM+JES calibration, b the LCW+JES calibration, and c the alternative Global Sequential (GS) [3] scheme. Three different MC simulation samples are also shown, Pythia (solid red circles), Herwig++ (open blue circles) and Pythia Perugia2011 (open black squares)

Fig. 52

Jet $p_{\mathrm{T}}$ response for the two leading jets in the dijet sample for different tagger light-quark operating points for jets with a $40\mathrm{GeV}<p_{\mathrm{T}}<60\mathrm{GeV}$ and b $260\mathrm{GeV}<p_{\mathrm{T}}<310\mathrm{GeV}$, and $|{\mathit{\eta }}_{\det }|<0.8$. Jets are labelled as light quark or gluon using the MC-simulation record and are further required to be isolated

Fig. 53

Average response to b-jets in some of the different samples used to calculate the b-jet energy scale systematic uncertainties is depicted in a. The resulting uncertainties in the ratio of the b-jet response to the response of jets in an inclusive sample are shown in b. These results are obtained for b-jets built with the anti-$k_t$ algorithm with resolution parameter $R=0.4$

Fig. 54

Ratio of the average $r_{\mathrm{trk}}$ given in Eq. (19) in data and MC simulations for a inclusive jets and c tagged b-jets. In e, the $b$-tagged to inclusive sample ratio variable $R^{\prime }$ from Eq. (21) is shown. The contributions of the systematic uncertainties to the total uncertainty in the different measurements are shown in b, d, and f, respectively. Jets within $|\mathit{\eta }|<1.2$ are used

Fig. 55

Ratio of the average $r_{\mathrm{trk}}$ given in Eq. (19) in $t\overline{t}$ events in data and MC simulations for a light-jets and tagged c b-jets. In e, the ratio of $R_{r_{\mathrm{trk}}}$ from Eq. (20) between the b-jet and the light-jet sample is shown. The total systematic uncertainty is shown as a band, and the dotted lines correspond to unity and the 2.5 % deviation from unity. The contributions of the systematic uncertainties to the total uncertainty in the different measurements are shown in b, d, and f, respectively. The contributions to the total systematic uncertainty due to the jet resolution, $b$-tagging calibration, background contamination and the modelling of the initial- and final-state radiation are grouped under “Other systematics”. Jets with $|\mathit{\eta }|<1.2$ are used

Fig. 56

Average jet response as a function of true transverse momentum of jets built using all stable particles, for a sample of inclusive jets (solid circles), a sample of b-jets tagged with the MV1 tagging algorithm (open circles) and a sample of semileptonically decaying b-jets with a reconstructed muon inside (open squares), is shown in a. The resulting semileptonic correction, as a function of calorimeter jet $p_{\mathrm{T}}$, used to transform the $p_{\mathrm{T}}$ of a jet in the semileptonic sample to the $p_{\mathrm{T}}$ of a jet in an inclusive sample of b-jets, is displayed in b. Associated systematic uncertainties are shown around the central value, and the combined uncertainty is shown as a coloured band

Fig. 57

Relative response of the semileptonic sample with respect to the inclusive b-jet sample as calculated from the dijet $p_{\mathrm{T}}$ asymmetry. The uncertainty band around the data denotes systematic uncertainties in the asymmetry measurement

Fig. 58

Average relative response of the probe jets with respect to the tag jets as a function of various impact points in the azimuthal direction ($\mathit{\varphi }$) of the probe jet. The average $p_{\mathrm{T}}$ of the two leading jets is $300\le p_{\mathrm{T}}^{\mathrm{avg}}<400$ GeV. The vertical solid lines indicate the location of the Tile calorimeter modules. The non-operating Tile calorimeter module is at $\mathit{\varphi }=1.03$. The markers indicate the results for no correction (triangles), the cell-based corrections (squares) and the corrections based on the jet shape (circles). The lower part of the figure shows the respective average values of the two corrections as a function of the azimuthal angle of the probe jet

Fig. 59

Fractional in situ jet energy scale systematic uncertainty as a function of a, b $p_{\mathrm{T}}^{\mathrm{jet}}$ and c, d jet pseudorapidity for anti-$k_t$ jets with distance parameter of $R=0.4$ calibrated using the EM+JES calibration scheme. The contributions from each in situ method are shown separately. Uncertainties from pile-up, flavour, and topology are not included

Fig. 60

Fractional in situ jet energy scale systematic uncertainty as a function of a, b $p_{\mathrm{T}}^{\mathrm{jet}}$ and c, d jet pseudorapidity for anti-$k_t$ jets with distance parameter of $R=0.4$ calibrated using the LCW+JES calibration scheme. The contributions from each in situ method are shown separately. Uncertainties from pile-up, flavour, and topology are not included

Fig. 61

Sample-dependent fractional jet energy scale systematic uncertainty as a function of a, b $p_{\mathrm{T}}^{\mathrm{jet}}$ and c, d jet pseudorapidity for anti-$k_t$ jets with distance parameter of $R=0.4$ calibrated using the EM+JES calibration scheme. The uncertainty shown applies to semileptonic top-decays with average 2011 pile-up conditions, and does not include the uncertainty on the jet energy scale of b-jets

Fig. 62

Sample-dependent fractional jet energy scale systematic uncertainty as a function of a, b $p_{\mathrm{T}}^{\mathrm{jet}}$ and c, d jet pseudorapidity for anti-$k_t$ jets with distance parameter of $R=0.4$ calibrated using the LCW+JES calibration scheme. The uncertainty shown applies to semileptonic top-decays with average 2011 pile-up conditions, and does not include the uncertainty on the jet energy scale of b-jets

Fig. 63

Sample-dependent fractional jet energy scale systematic uncertainty as a function of a, b $p_{\mathrm{T}}^{\mathrm{jet}}$ and c, d jet pseudorapidity for anti-$k_t$ jets with distance parameter of $R=0.4$ calibrated using the EM+JES calibration scheme. The uncertainty shown applies to inclusive QCD jets with average 2011 pile-up conditions, and does not include the uncertainty on the jet energy scale of b-jets

Fig. 64

Sample-dependent fractional jet energy scale systematic uncertainty as a function of a, b $p_{\mathrm{T}}^{\mathrm{jet}}$ and c, d jet pseudorapidity for anti-$k_t$ jets with distance parameter of $R=0.4$ calibrated using the LCW+JES calibration scheme. The uncertainty shown applies to inclusive QCD jets with average 2011 pile-up conditions, and does not include the uncertainty on the jet energy scale of b-jets

Fig. 65

Fractional jet energy scale systematic uncertainty as a function of $p_{\mathrm{T}}^{\mathrm{jet}}$ for anti-$k_t$ jets with distance parameter of $R=0.4$ calibrated using the a EM+JES and b LCW+JES calibration schemes. The uncertainty shown applies to b-jets with average 2011 pile-up conditions

Fig. 66

Fractional jet energy scale systematic uncertainty for inclusive jets as a function of $p_{\mathrm{T}}^{\mathrm{jet}}$ for jets with a, c $R=0.4$ and b, d $R=0.6$ calibrated with the a, b EM+JES and c, d LCW+JES schemes and with $\mathit{\eta }=0.5$