Topological cell clustering in the ATLAS calorimeters and its performance in LHC Run 1

Abstract

The reconstruction of the signal from hadrons and jets emerging from the proton-proton collisions at the Large Hadron Collider (LHC) and entering the ATLAS calorimeters is based on a three-dimensional topological clustering of individual calorimeter cell signals. The cluster formation follows cell signal-significance patterns generated by electromagnetic and hadronic showers. In this, the clustering algorithm implicitly performs a topological noise suppression by removing cells with insignificant signals which are not in close proximity to cells with significant signals. The resulting topological cell clusters have shape and location information, which is exploited to apply a local energy calibration and corrections depending on the nature of the cluster. Topological cell clustering is established as a well-performing calorimeter signal definition for jet and missing transverse momentum reconstruction in ATLAS.

Fig. 1

Cutaway view on the ATLAS calorimeter system

Fig. 2

The peak luminosities measured by the ATLAS online luminosity monitor system throughout the run years are shown in (a). The mean number of additional proton–proton interactions at the beginning of each LHC fill is shown in (b) for the same period in time

Fig. 3

The pulse shape in the ATLAS LAr calorimeters. The unipolar triangular pulse is the current pulse in the liquid argon generated by fast ionising particles. Its characteristic time is the drift time (charge collection time) $t_{\text{d}}$, with $t_{\text{d}}\approx 450\text{ns}$ in the example for the central EMB calorimeter shown here. The shaped pulse is superimposed, with a characteristic duration of ${\mathit{\tau }}_{\text{signal}}\approx 600\text{ns}$. The full circles on the shaped pulse indicate the nominal bunch crossings at $25\text{ns}$ intervals. The figure has been adapted from Ref. [14]

Fig. 4

The energy-equivalent cell noise in the ATLAS calorimeters on the electromagnetic (EM) scale as a function of the direction $\left|\mathit{\eta }\right|$ in the detector, for a the 2010 configuration with $\mathit{\mu }=0$, b the 2011 configuration with $\mathit{\mu }=8$ (both plots from Ref. [16]), and c the 2012 configuration with $\mathit{\mu }=30$. The various colours indicate the noise in the pre-sampler (PS) and the three layers of the LAr EM calorimeter, the three layers of the Tile calorimeter, the four layers of the hadronic end-cap (HEC) calorimeter, and the three modules of the forward (FCAL) calorimeter

Fig. 5

Signal significance (${\mathit{\varsigma }}_{\text{cell}}^{\text{EM}}$) distributions for all cells (blue/cyan) and for cells after the noise suppression in the topological cell clustering is applied (red/yellow), in selected sampling layers of the LAr calorimeters: a the first sampling of the central electromagnetic LAr calorimeter (EMB), b the first sampling of the electromagnetic LAr end-cap calorimeter (EMEC), c the first sampling of the hadronic LAr end-cap calorimeter (HEC), and d the first module of the LAr forward calorimeter (FCAL). The spectra are extracted from 2012 zero-bias data at $\sqrt{s}=8\text{TeV}$ with an average number of pile-up interactions $⟨\mathit{\mu }⟩=28$. The dashed lines indicate $S=\pm 4$, $N=\pm 2$, and $P=0$

Fig. 6

Stages of topo-cluster formation in the first module (FCAL0) of the FCAL calorimeter for a simulated dijet event with at least one jet entering this calorimeter. Shown in a are cells with signal significance $|{\mathit{\varsigma }}_{\text{cell}}^{\text{EM}}|>4$ that can seed topo-clusters, in b cells with $|{\mathit{\varsigma }}_{\text{cell}}^{\text{EM}}|>2$ controlling the topo-cluster growth, and in c all clustered cells and the outline of topo-clusters and topo-cluster fragments in this module. All clusters shown in c which do not contain a seed cell from this module are seeded in other modules of the FCAL, or in other calorimeters surrounding it. Pile-up is not included in this simulation, but electronic noise is modelled. Cells not colour coded but inside a topo-cluster have a negative signal, while cells shaded grey are completely surrounded by clustered cells but not part of a topo-cluster themselves. The cell and cluster boundaries are displayed on a dimensionless grid using the polar angle $\mathit{\theta }$ and the azimuthal angle $\mathit{\varphi }$. This view maintains the cell shapes and proportions. For the definition of the cell signal significance ${\mathit{\varsigma }}_{\text{cell}}^{\text{EM}}$ see Eq. (2)

Fig. 7

The number of reconstructed clusters for simulated charged and neutral single pions without actual pile-up added but with nominal pile-up noise used in the reconstruction. In a the distribution of the number of clusters $N_{\text{clus}}$ is shown for neutral and charged pions injected into the ATLAS calorimeters at $|\mathit{\eta }|=0.3$ with an energy of $E=100\text{GeV}$, together with the $N_{\text{clus}}$ distribution for empty events (topo-clusters generated by electronic noise only). The distributions are individually normalised to unity. The dependence of the average $⟨N_{\text{clus}}⟩$ on the generated ${\mathit{\eta }}_{\text{gen}}$ is shown in b again for ${\mathit{\pi }}^0$, ${\mathit{\pi }}^{-}$ and empty events. The shaded area and the dashed lines indicate the spread (in terms of RMS) around the central value

Fig. 8

Schematic view of geometrical moments for topo-clusters

Fig. 9

Overview of the local hadronic cell-weighting (LCW) calibration scheme for topo-clusters. Following the topo-cluster formation, the likelihood for a cluster to be generated by electromagnetic energy deposit (${\mathcal{P}}_{\text{clus}}^{\text{EM}}$) is calculated. After this, the sequence of calibration and corrections indicated in the schematics is executed, each yielding cell signal weights for the two possible interpretations of the cluster signals. These weights are indicated in the figure. They are then used together with ${\mathcal{P}}_{\text{clus}}^{\text{EM}}$ to calculate the topo-cluster energy and barycentre from the contributing calorimeter cells, as described in the text

Fig. 10

Distribution of the likelihood ${\mathcal{P}}_{\text{clus}}^{\text{EM}}({\mathit{\rho }}_{\text{clus}}/E_{\text{clus}}^{\text{EM}},{\mathit{\lambda }}_{\text{clus}})$ for reconstructed topo-clusters to originate from an electromagnetic shower as a function of the shower depth ${\mathit{\lambda }}_{\text{clus}}$ and the normalised cluster signal density ${\mathit{\rho }}_{\text{clus}}/E_{\text{clus}}^{\text{EM}}$, with ${\mathit{\rho }}_{\text{clus}}=⟨{\mathit{\rho }}_{\text{cell}}⟩$ being the energy-weighted average of ${\mathit{\rho }}_{\text{cell}}$. The shown distribution is determined as described in the text, in a selected bin of the cluster energy $E_{\text{clus}}^{\text{EM}}$ and the cluster direction ${\mathit{\eta }}_{\text{clus}}$. The red line indicates the boundary of the ${\mathcal{P}}_{\text{clus}}^{\text{EM}}>50$% selection, below which the topo-cluster is classified as mostly electromagnetic (“EM-like”) and above which it is classified as mostly hadronic (“HAD-like”). The small EM-like area at the edge of the HAD-like region stems from neutral pions showering late. These areas are typical in regions of the detector where the second layer of the EM calorimeter is thinner and substantial parts of the shower are deposited in its last layer. The larger volume of the cells in this last layer leads to the reduced energy density while the position at the back of the EM calorimeter means a larger ${\mathit{\lambda }}_{\text{clus}}$

Fig. 11

The distribution of the longitudinal depth ${\mathit{\lambda }}_{\text{clus}}$ of topo-cluster inside anti-$k_t$ jets with $R=0.6$, $|y|<2.8$, and $p_{\text{T}}>20$ GeV, for clusters classified as (a) electromagnetic (EM) and (b) hadronic (HAD), in 2010 data and MC simulations (no pile-up). Also shown is the average topo-cluster depth $⟨{\mathit{\lambda }}_{\text{clus}}⟩$ as function of the cluster energy $E_{\text{clus}}^{\text{EM}}$ for the same topo-clusters classified as (c) EM and (d) HAD, respectively. The figures are adapted from Ref. [38]

Fig. 12

Distributions of the cell energy $E_{\text{cell}}^{\text{EM}}$ in the a central pre-sampler (PreSamplerB) and the cell energy density ${\mathit{\rho }}_{\text{cell}}$ in the second sampling of b the central (EMB2) electromagnetic calorimeter in ATLAS, as observed inside anti-$k_t$ jets with $R=0.6$, calibrated with the global sequential (GCW+JES) calibration scheme described in Ref. [38], in 2010 data (no pile-up) and the corresponding MC simulations. The data/MC ratio of the spectra is shown below the corresponding distributions. The figure uses plots from Ref. [38]

Fig. 13

Distributions of the cell energy density ${\mathit{\rho }}_{\text{cell}}$ in the a second sampling of the end-cap (EME2) electromagnetic calorimeter, and the b first module of the forward calorimeter (FCAL0) in ATLAS, as observed inside anti-$k_t$ jets with $R=0.6$, calibrated with the GCW + JES scheme described in Ref. [38], in 2010 data and MC simulations (no pile-up). The data/MC ratio of the spectra is shown below the corresponding distributions. The figure uses plots from Ref. [38]

Fig. 14

Distributions of the cell energy density ${\mathit{\rho }}_{\text{cell}}$ in the central a and end-cap b hadronic calorimeters in ATLAS, as observed inside anti-$k_t$ jets with $R=0.6$ calibrated with the GCW + JES scheme described in Ref. [38], in 2010 data and MC simulations (no pile-up). The data/MC ratio of the spectra is shown below the corresponding distributions. The figure uses plots from Ref. [38]

Fig. 15

Illustration of the assignment scheme for cells inside the calorimeter with true signal not captured in a topo-cluster in the context of the out-of-cluster correction (see Sect. 5.4) and for dead material cells outside the calorimeter for the dead material correction discussed in Sect. 5.5. The deposited energy in cells inside the topo-cluster is used to determine the hadronic calibration described in Sect. 5.3. A schematic depiction of a typical section of the ATLAS end-cap calorimeter with four highly granular electromagnetic samplings and four coarser hadronic samplings is shown in a view with $\mathit{\eta }$ as the horizontal and the depth z as the vertical coordinate. The boxes at small z in front of the EM calorimeter symbolise upstream energy losses collected into dead material cells

Fig. 16

The distribution of the isolation moment $f_{\text{iso}}$ in a clusters classified as electromagnetic, and b clusters classified as hadronic. The average isolation $⟨f_{\text{iso}}⟩$ as a function of the cluster signal $E_{\text{clus}}^{\text{EM}}$ is shown in c for electromagnetic and in d for hadronic topo-clusters. The figures are taken from Ref. [38]

Fig. 17

The average energy loss in the virtual dead material cells for charged 100 GeV pions. The numbers 1–7 indicate the different regions, with region 8 (not displayed) being everywhere outside regions 1–7. The dead material cells are superimposed on a schematic (r, z) view showing a quarter of the ATLAS calorimeter system with its read-out segmentation

Fig. 18

The average ratio of reconstructed to EM-scale energy after each calibration step, as a function of the cluster energy $E_{\text{clus}}^{\text{EM}}$ (a, c, e) for topo-clusters in anti-$k_t$ jets with $R=0.6$ and $p_{\text{T}}>20$ GeV and with rapidities $|y_{\text{jet}}|<0.3$. The corresponding average ratios as a function of ${\mathit{\eta }}_{\text{clus}}$ are shown in b, d, and f. Data recorded in 2010 is compared to the corresponding MC simulations. The figures are adapted from Ref. [38]

Fig. 19

The distribution of $E/p$, the ratio of the calorimeter energy E and the track momentum p, for (a) central tracks with $1.2\text{GeV}<p<1.8\text{GeV}$ and (b) forward-going tracks with $2.8\text{GeV}<p<3.6\text{GeV}$, for data and MC simulations of proton–proton collisions at $\sqrt{s}=900\text{GeV}$ and no pile-up (from Ref. [38])

Fig. 20

In a, the likelihood ${\mathcal{P}}_{E=0}(d_{\text{dm}})$ to find no matching energy in the calorimeter ($E=0$) for reconstructed isolated charged-particle tracks is shown as a function of the thickness $d_{\text{dm}}$ of the inactive material in front of the calorimeter, for data and MC simulations in proton–proton collisions at $\sqrt{s}=900\text{GeV}$. The thickness of the inactive material is measured in terms of the nuclear interaction length ${\mathit{\lambda }}_{\text{nucl}}$. The tracks are reconstructed within $|\mathit{\eta }|<1$. The likelihood to reconstruct $E=0$ as a function of the incoming track momentum is shown for the same data and MC simulations in b, for reconstructed tracks within $|\mathit{\eta }|<0.6$. Both figures are taken from Ref. [38]

Fig. 21

The average $⟨E/p⟩$ ratio as a function of the track momentum p, for a tracks within $|\mathit{\eta }|<0.6$ and b tracks within $1.9<|\mathit{\eta }|<2.3$. Data from isolated tracks recorded in 2010 and 2012 with insignificant pile-up are shown together with MC simulations employing two different hadronic shower models

Fig. 22

The distribution of the transverse momentum of topo-clusters reconstructed on the EM scale ($p_{\text{T},\text{clus}}^{\text{EM}}$) for an inclusive $Z\to \mathit{\mu }\mathit{\mu }$ event sample recorded in 2012. Data are compared to distributions from MC simulations (a, c, e) including fully simulated pile-up and (b, d, f) with pile-up overlaid from data for all topo-clusters within (a, b) $|{\mathit{\eta }}_{\text{clus}}|<0.2$, (c, d) $2.0<|{\mathit{\eta }}_{\text{clus}}|<2.2$ , (e, f) $3.8<|{\mathit{\eta }}_{\text{clus}}|<4.0$. The ratio of the distribution from data to the one from MC simulation is evaluated bin-by-bin and shown below the respective distribution. The shaded bands indicate the statistical uncertainties from MC simulations for both the spectra and the ratios

Fig. 23

The average $⟨\mathrm{\Sigma }{p}_{\text{T},\text{clus}}^{\text{EM}}⟩$ of clusters at the EM scale, calculated as function of $\mathit{\eta }$ using Eq. (41), for clusters with a $p_{\text{T},\text{clus}}^{\text{EM}}>0$, b $p_{\text{T},\text{clus}}^{\text{EM}}>100\text{MeV}$, c $p_{\text{T},\text{clus}}^{\text{EM}}>250\text{MeV}$, d $p_{\text{T},\text{clus}}^{\text{EM}}>500\text{MeV}$, e $p_{\text{T},\text{clus}}^{\text{EM}}>1\text{GeV}$, and f $p_{\text{T},\text{clus}}^{\text{EM}}>2\text{GeV}$. Results are obtained from a 2012 $Z\to \mathit{\mu }\mathit{\mu }$  sample without jets with $p_{\text{T}}>20\text{GeV}$ in data and MC simulation. The ratios of $⟨\mathrm{\Sigma }{p}_{\text{T},\text{clus}}^{\text{EM}}⟩(\mathit{\eta })$ from data and MC simulations are shown below each plot

Fig. 24

The average transverse momentum flow $⟨\mathrm{\Sigma }{p}_{\text{T},\text{clus}}^{\text{EM}}⟩$ evaluated as function of the pile-up activity measured by the number of proton–proton interactions per bunch crossing $\mathit{\mu }$, in several calorimeter regions. In a, c, and e, $⟨\mathrm{\Sigma }{p}_{\text{T},\text{clus}}^{\text{EM}}⟩(\mathit{\mu })$ is shown in the central ($|\mathit{\eta }|<0.2$), end-cap ($2.0<|\mathit{\eta }|<2.2$), and the forward ($3.8<|\mathit{\eta }|<4.0$) region, respectively, using topo-clusters with $p_{\text{T},\text{clus}}^{\text{EM}}>0$. The corresponding results using topo-clusters with $p_{\text{T},\text{clus}}^{\text{EM}}>1\text{GeV}$ are presented in b, d, and f. Results are obtained from a 2012 $Z\to \mathit{\mu }\mathit{\mu }$ sample without jets with $p_{\text{T}}>20\text{GeV}$ in data and MC simulations. The narrow shaded bands around the results for MC simulations indicate statistical uncertainties, both for $⟨\mathrm{\Sigma }{p}_{\text{T},\text{clus}}^{\text{EM}}⟩(\mathit{\mu })$ and the corresponding data-to-MC simulation ratios shown below each plot

Fig. 25

Average topo-cluster number density $⟨\mathit{\partial }N/\mathit{\partial }\mathit{\eta }⟩$ as a function of ${\mathit{\eta }}_{\text{clus}}$, for clusters with $p_{\text{T},\text{clus}}^{\text{EM}}>p_{\text{T},\text{min}}$, for various $p_{\text{T},\text{min}}$ values. Results are obtained from a 2012 $Z\to \mathit{\mu }\mathit{\mu }$ sample without jets with $p_{\text{T}}>20\text{GeV}$ in data and MC simulations. The corresponding data-to-MC simulation ratios are shown below each figure

Fig. 26

The reconstructed average transverse momentum flow on EM scale, measured with topo-clusters in bins of $\mathit{\eta }$ using $⟨\mathrm{\Sigma }{p}_{\text{T},\text{clus}}^{\text{EM}}⟩(\mathit{\eta })$ in Eq. (41) and with all calorimeter cells in the same $\mathit{\eta }$-bins using $\mathrm{\Sigma }{p}_{\text{T},\text{cell}}^{\text{EM}}(\mathit{\eta })$ given in Eq. (42), in 2012 MB data

Fig. 27

The dependence of the average number of positive-energy topo-clusters on the pile-up activity measured by the number of proton–proton collisions per bunch crossings $\mathit{\mu }$ in several regions of the detector is shown in a, b for $|\mathit{\eta }|<0.2$, in c, d for $2.0<|\mathit{\eta }|<2.2$, and in e, f for $3.8<|\mathit{\eta }|<4.0$. Plots a, c and e show the results for counting all clusters with $p_{\text{T},\text{clus}}^{\text{EM}}>0$, while b, c and f show the results for only counting clusters with $p_{\text{T},\text{clus}}^{\text{EM}}>1\text{GeV}$. The corresponding ratio of data to MC simulations is shown below each plot. All results are obtained from a 2012 $Z\to \mathit{\mu }\mathit{\mu }$  sample without jets with $p_{\text{T}}>20\text{GeV}$ in data and MC simulations. The narrow shaded bands indicate the statistical uncertainties associated with the results from MC simulations for the mean values and the ratios

Fig. 28

The distribution of the topo-cluster depth location, measured in terms of ${log}_{10}({\mathit{\lambda }}_{\text{clus}}/{\mathit{\lambda }}_0)$, for clusters in various bins of ${\mathit{\eta }}_{\text{clus}}$ for an inclusive $Z\to \mathit{\mu }\mathit{\mu }$ event sample recorded in 2012. Data is compared to distributions from MC simulations including fully simulated pile-up for all topo-clusters within a $|{\mathit{\eta }}_{\text{clus}}|<0.2$, c $2.0<|{\mathit{\eta }}_{\text{clus}}|<2.2$, and e $3.8<|{\mathit{\eta }}_{\text{clus}}|<4.0$. The corresponding distributions for MC simulations with pile-up from data overlaid are depicted in b, d, and f. The ratios of the distributions for data and MC simulations are shown below the respective distributions. The shaded bands indicate the statistical uncertainties for MC simulations

Fig. 29

The distribution of the topo-cluster depth location, measured in terms of ${log}_{10}({\mathit{\lambda }}_{\text{clus}}/{\mathit{\lambda }}_0)$, for selected topo-clusters within $|{\mathit{\eta }}_{\text{clus}}|<0.2$ and with a transverse momentum $p_{\text{T},\text{clus}}^{\text{EM}}$, evaluated on the EM scale, larger than various thresholds. Results are shown for an inclusive $Z\to \mathit{\mu }\mathit{\mu }$ event sample recorded in 2012. Data are compared to distributions from MC simulations including fully simulated pile-up for all topo-clusters with a $p_{\text{T},\text{clus}}^{\text{EM}}>1\text{GeV}$, c $p_{\text{T},\text{clus}}^{\text{EM}}>2\text{GeV}$, and e $p_{\text{T},\text{clus}}^{\text{EM}}>5\text{GeV}$. The corresponding distributions for MC simulations with pile-up from data overlaid are depicted in b, d, and f. The shaded bands indicate the statistical uncertainties for the distributions obtained from MC simulations and the corresponding uncertainties in the ratio plots

Fig. 30

In a, the fully calibrated and corrected jet $p_{\text{T}}$ response measured by $p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}$ is shown as a function of the pile-up activity measured by $\mathit{\mu }$, in three different detector regions for $Z\to \mathit{\mu }\mathit{\mu }$ events with one anti-$k_t$ jet with $R=0.4$ with $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$, for 2012 data and MC simulations with fully simulated pile-up. The $\mathit{\mu }$ dependence of the uncorrected jet $p_{\text{T}}$ response is shown in b. It is measured in terms of its ratio to the fully calbrated jet response, $p_{\text{T},\text{jet}}^{\text{LCW}}/p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}(\mathit{\mu })$, for the same events and in the same detector regions. The shaded bands shown for the results from MC simulations indicate statistical uncertainties

Fig. 31

The distribution of the number of topo-clusters inside anti-$k_t$ jets formed with $R=0.4$ in the (a, b) central ($|\mathit{\eta }|<0.6$), the (c, d) end-cap ($2.0<|\mathit{\eta }|<2.5$), and the (e, f) forward detector region ($3.5<|\mathit{\eta }|<4.5$) of ATLAS. Shown are results from the analysis of $Z\to \mathit{\mu }\mathit{\mu }$ events with at least one jet with $30\text{GeV}<p_{\text{T}}<40\text{GeV}$ in 2012 data and MC simulations with fully simulated pile-up in a, c and e, and with pile-up from data overlaid in b, d and f. The ratios of results for data and MC simulations are shown below the distributions. The shaded bands show the statistical uncertainties for the distributions obtained from MC simulations and the corresponding uncertainty bands in the ratio plots

Fig. 32

The distribution of the number of topo-clusters with $p_{\text{T},\text{clus}}^{\text{EM}}>1\text{GeV}$ inside anti-$k_t$ jets with $R=0.4$ in the (a, b) central ($|\mathit{\eta }|<0.6$), the (c, d) end-cap ($2.0<|\mathit{\eta }|<2.5$), and the (e, f) forward detector region ($3.5<|\mathit{\eta }|<4.5$) of ATLAS. Shown are results from the analysis of $Z\to \mathit{\mu }\mathit{\mu }$ events with at least one jet with $30\text{GeV}<p_{\text{T}}<40\text{GeV}$ in 2012 data and MC simulations with fully simulated pile-up in a, c and e, and with pile-up from data overlaid in b, d and f. The data-to-MC simulation ratios are shown below the respective distributions. The shaded bands indicate statistical uncertainties for the distributions from MC simulations and the corresponding statistical uncertainty bands for the ratios

Fig. 33

The average number of topo-clusters $⟨N_{\text{clus}}^{\text{jet}}⟩$ in anti-$k_t$ jets reconstructed with $R=0.4$ within $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ as a function of $\mathit{\mu }$, in $Z\to \mathit{\mu }\mathit{\mu }$ events in 2012 data and MC simulations (a). The pile-up dependence of the average number of topo-clusters $⟨N_{\text{clus}}^{\text{core}}⟩$ in the core of the jet, defined by the distance to jet axis $\mathrm{\Delta }R<0.3$, is shown in b. Selecting topo-clusters by $p_{\text{T},\text{clus}}^{\text{EM}}>2\text{GeV}$ inside jets and in the core of the jet yields the $\mathit{\mu }$ dependencies shown in c and d. The shaded bands shown for the results obtained from MC simulations indicate statistical uncertainties

Fig. 34

The distribution of the depth location, measured in terms of ${log}_{10}({\mathit{\lambda }}_{\text{clus}}/{\mathit{\lambda }}_0)$ with ${\mathit{\lambda }}_0=1\text{mm}$, of all topo-clusters in jets reconstructed with the anti-$k_t$ algorithm with $R=0.4$ and with $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in $Z\to \mathit{\mu }\mathit{\mu }$ events in 2012 data and MC simulations with (a, c, e) fully simulated pile-up and with (b, d, f) overlaid pile-up from data. Distributions are shown for jets in the (a, b) central ($|\mathit{\eta }|<0.6$), the (c, d) end-cap ($2.0<|\mathit{\eta }|<2.5$), and the (e, f) forward detector region ($3.5<|\mathit{\eta }|<4.5$). The bin-by-bin ratios of the distributions from data and MC simulations are shown below the plots. The shaded bands indicate statistical uncertainties for the distributions from MC simulations and the corresponding uncertainty bands in the ratio plots

Fig. 35

The distribution of the depth location, measured in terms of ${log}_{10}({\mathit{\lambda }}_{\text{clus}}/{\mathit{\lambda }}_0)$ with ${\mathit{\lambda }}_0=1\text{mm}$, of topo-clusters with $p_{\text{T},\text{clus}}^{\text{EM}}>1\text{GeV}$ in jets reconstructed with the anti-$k_t$ algorithm with $R=0.4$ and with $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in $Z\to \mathit{\mu }\mathit{\mu }$ events in 2012 data and MC simulations with (a, c, e) fully simulated pile-up and with (b, d, f) overlaid pile-up from data. Distributions are shown for jets in the (a, b) central ($|\mathit{\eta }|<0.6$), the (c, d) end-cap ($2.0<|\mathit{\eta }|<2.5$), and the (e, f) forward detector region ($3.5<|\mathit{\eta }|<4.5$). The data-to-MC simulation ratios are shown below the distributions. The shaded bands shown for the distributions obtained from MC simulations indicate statistical uncertainties and the corresponding uncertainty bands in the ratio plots

Fig. 36

The distribution of the leading topo-cluster depth location measure ${log}_{10}({\mathit{\lambda }}_{\text{clus}}/{\mathit{\lambda }}_0)$ in fully calibrated jets reconstructed with the anti-$k_t$ algorithm with $R=0.4$ and $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in regions of a the central ($|{\mathit{\eta }}_{\text{jet}}|<0.6$), b the end-cap ($2.0<|{\mathit{\eta }}_{\text{jet}}|<2.5$), and the c forward ($3.5<|{\mathit{\eta }}_{\text{jet}}|<4.5$) calorimeters in ATLAS. Data is compared to MC simulations with fully simulated pile-up for $Z\to \mathit{\mu }\mathit{\mu }$ events recorded in 2012. The ratio of the distribution from data to the one from MC simulations is shown below each plot. The shaded bands show statistical uncertainties for the distributions from MC simulations and the corresponding uncertainty bands in the ratio plots. The reference scale for ${\mathit{\lambda }}_{\text{clus}}$ is ${\mathit{\lambda }}_0=1\text{mm}$

Fig. 37

The distribution of the leading topo-cluster signal density measure ${log}_{10}({\mathit{\rho }}_{\text{clus}}/{\mathit{\rho }}_0)-{log}_{10}(E_{\text{clus}}^{\text{EM}}/E_0)$ in fully calibrated jets reconstructed with the anti-$k_t$ algorithm with $R=0.4$ and $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in regions of a the central ($|{\mathit{\eta }}_{\text{jet}}|<0.6$), b the end-cap ($2.0<|{\mathit{\eta }}_{\text{jet}}|<2.5$), and c the forward ($3.5<|{\mathit{\eta }}_{\text{jet}}|<4.5$) calorimeters in ATLAS. Data is compared to MC simulations with fully simulated pile-up for $Z\to \mathit{\mu }\mathit{\mu }$ events recorded in 2012. The ratio of the distribution from data to the one from MC simulations is shown below each plot. The shaded bands show statistical uncertainties for the distributions from MC simulations and the corresponding uncertainty bands in the ratio plots. The reference scale for ${\mathit{\rho }}_{\text{clus}}$ is ${\mathit{\rho }}_0=1\text{MeV}/{\text{mm}}^3$, and for the energy $E_0=1\text{MeV}$

Fig. 38

The distribution of the ratio of the cluster signal reconstructed on EM scale $E_{\text{clus}}^{\text{EM}}$ to the fully calibrated signal $E_{\text{clus}}^{\text{LCW}}$ for the leading topo-cluster in fully calibrated jets reconstructed with the anti-$k_t$ algorithm with $R=0.4$ and $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in regions of a the central ($|{\mathit{\eta }}_{\text{jet}}|<0.6$), b the end-cap ($2.0<|{\mathit{\eta }}_{\text{jet}}|<2.5$), and c the forward ($3.5<|{\mathit{\eta }}_{\text{jet}}|<4.5$) calorimeters in ATLAS. Data is compared to MC simulations with fully simulated pile-up for $Z\to \mathit{\mu }\mathit{\mu }$ events recorded in 2012. The ratio of the distribution from data to the one from MC simulations is shown below each plot. The shaded bands show statistical uncertainties for the distributions from MC simulations and the corresponding uncertainty bands in the ratio plots. The reference scale for ${\mathit{\rho }}_{\text{clus}}$ is ${\mathit{\rho }}_0=1\text{MeV}/{\text{mm}}^3$, and for the energy $E_0=1\text{MeV}$

Fig. 39

The distribution of the signal fraction $f_{\text{lead}}$ carried by the leading topo-cluster in jets, as defined in Eq. (45), in a the central, b the end-cap, and c the forward detector region. The jets are reconstructed using the anti-$k_t$ algorithm with $R=0.4$ and with $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in $Z\to \mathit{\mu }\mathit{\mu }$ events in 2012 data and MC simulations with fully simulated pile-up. The data-to-MC simulation ratios are shown below the distributions. The shaded bands shown for the distributions obtained from MC simulations indicate statistical uncertainties and the corresponding uncertainty bands in the ratio plots

Fig. 40

The pile-up dependence of a $f_{\text{lead}}$ defined in Eq. (45), b $E_{\text{clus}}^{\text{EM}}/E_{\text{clus}}^{\text{LCW}}$, and c the depth location ${\mathit{\lambda }}_{\text{clus}}$ of the leading topo-cluster in fully calibrated anti-$k_t$ jets reconstructed with $R=0.4$ and with $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in $Z\to \mathit{\mu }\mathit{\mu }$ events in 2012 data and MC simulations with fully simulated pile-up. The reference scale for ${\mathit{\lambda }}_{\text{clus}}$ is ${\mathit{\lambda }}_0=1\text{mm}$. The pile-up activity is measured in terms of the number of pile-up interactions $\mathit{\mu }$. The shaded bands shown for the results obtained from MC simulations indicate statistical uncertainties

Fig. 41

The distribution of the normalised (a, c, e) lateral (${\mathfrak{m}}_{\text{lat}}^2$) and (b, d, f) longitudinal (${\mathfrak{m}}_{\text{long}}^2$) extension measures of the leading topo-cluster in fully calibrated anti-$k_t$ jets with $R=0.4$ and $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in $Z\to \mathit{\mu }\mathit{\mu }$ events in 2012 data and MC simulations with fully simulated pile-up, for jets in the (a, b) central ($|\mathit{\eta }|<0.6$), the (c, d) end-cap ($2.0<|\mathit{\eta }|<2.5$), and the (e, f) forward detector region ($3.5<|\mathit{\eta }|<4.5$) of ATLAS. The ratios of data and MC simulation distributions are shown below the plots. The shaded bands shown for the distributions obtained from MC simulations indicate statistical uncertainties and the corresponding uncertainty bands in the ratio plots

Fig. 42

The length of the leading topo-cluster, measured in terms of the longitudinal spread (second moment) $⟨{\mathit{\lambda }}^2⟩$ of the cell coordinates along the principal cluster axis by $\sqrt{⟨{\mathit{\lambda }}^2⟩/{\mathit{\lambda }}_0^2}$, in anti-$k_t$ jets reconstructed with $R=0.4$ and $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in $Z\to \mathit{\mu }\mathit{\mu }$ events in 2012 data and MC simulations with fully simulated pile-up. Distributions are shown for jets in the a central ($|\mathit{\eta }|<0.6$), the b end-cap ($2.0<|\mathit{\eta }|<2.5$), and the c forward detector region ($3.5<|\mathit{\eta }|<4.5$). The normalisation of the longitudinal spread is given by ${\mathit{\lambda }}_0=1\text{mm}$. The ratios of data-to-MC simulations are shown below the distributions. The shaded bands indicate statistical uncertainties of the distributions from MC simulations and the resulting uncertainty bands in the ratio plots

Fig. 43

The size $R_{\mathit{\eta }\mathit{\varphi }}^{\text{lead}}$ of the leading topo-cluster in $(\mathit{\eta },\mathit{\varphi })$ space, measured using Eq. (20), in anti-$k_t$ jets reconstructed with $R=0.4$ and with $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in $Z\to \mathit{\mu }\mathit{\mu }$ events in 2012 data and MC simulations with fully simulated pile-up. Distributions are shown for jets in the a central ($|\mathit{\eta }|<0.6$), the b end-cap ($2.0<|\mathit{\eta }|<2.5$), and the c forward detector region ($3.5<|\mathit{\eta }|<4.5$) in ATLAS. The ratios of data to MC simulations are shown below the distributions. The shaded bands shown for the distributions obtained from MC simulations indicate statistical uncertainties and the corresponding uncertainty bands in the ratio plots

Fig. 44

The average pile-up dependence of various geometric observables reconstructed from the leading topo-cluster in anti-$k_t$ jets reconstructed with $R=0.4$ and $30\text{GeV}<p_{\text{T},\text{jet}}^{\text{LCW}+\text{JES}}<40\text{GeV}$ in $Z\to \mathit{\mu }\mathit{\mu }$ events in 2012 data and MC simulations with fully simulated pile-up. The average cluster length, represented by ${log}_{10}({⟨{\mathit{\lambda }}^2/{\mathit{\lambda }}_0^2⟩}^{1/2})$ with the reference scale ${\mathit{\lambda }}_0=1\text{mm}$, is shown as a function of $\mathit{\mu }$ in a, for three detector regions. The average size $⟨R_{\mathit{\eta }\mathit{\varphi }}^{\text{lead}}⟩$ of the leading topo-cluster in $(\mathit{\eta },\mathit{\varphi })$ space is displayed for the same detector regions and as a function of $\mathit{\mu }$ in b. The average normalised lateral energy dispersion $⟨{\mathfrak{m}}_{\text{lat}}^2⟩$ of the cluster, as a function of $\mathit{\mu }$ for the three detector regions, is shown in c. The shaded bands shown around the results obtained from MC simulations indicate statistical uncertainties