A measurement of the calorimeter response to single hadrons and determination of the jet energy scale uncertainty using LHC Run-1 pp-collision data with the ATLAS detector

Abstract

A measurement of the calorimeter response to isolated charged hadrons in the ATLAS detector at the LHC is presented. This measurement is performed with 3.2 nb[Formula: see text] of proton-proton collision data at [Formula: see text] [Formula: see text] from 2010 and 0.1 nb[Formula: see text] of data at [Formula: see text] [Formula: see text] from 2012. A number of aspects of the calorimeter response to isolated hadrons are explored. After accounting for energy deposited by neutral particles, there is a 5% discrepancy in the modelling, using various sets of Geant4 hadronic physics models, of the calorimeter response to isolated charged hadrons in the central calorimeter region. The description of the response to anti-protons at low momenta is found to be improved with respect to previous analyses. The electromagnetic and hadronic calorimeters are also examined separately, and the detector simulation is found to describe the response in the hadronic calorimeter well. The jet energy scale uncertainty and correlations in scale between jets of different momenta and pseudorapidity are derived based on these studies. The uncertainty is 2-5% for jets with transverse momenta above 2 [Formula: see text], where this method provides the jet energy scale uncertainty for ATLAS.

Fig. 1

An illustration (a) of the construction of the $E/p$ variable used throughout this paper. The particle is identified by matching a track (green) with momentum p to topological energy clusters in the EM and hadronic calorimeters (red), while nearby topological energy clusters from neutral-particle background (light blue) must be removed. The red (black) dashed circle on the horizontal plane has a radius $\mathrm{\Delta }R=0.1$ (0.2) around the track. The same diagram is shown for the neutral-particle background selection (b) using late-showering hadrons, described in Sect. 4.2. The construction is similar, but the energy deposited in the EM calorimeter by the particle is required to be consistent with a minimally-ionising particle (MIP). No attempt is made to identify individual clusters as originating from background particles. The subtraction is done on average

Fig. 2

The $E/p$ distribution for isolated tracks with a $|\mathit{\eta }|<0.6$ and $1.2<p/\mathrm{GeV}<1.8$; b $|\mathit{\eta }|<0.6$ and $2.2<p/\mathrm{GeV}<2.8$; c $1.9<|\mathit{\eta }|<2.3$ and $2.8<p/\mathrm{GeV}<3.6$; d $|\mathit{\eta }|<0.6$ and $1.2<p/\mathrm{GeV}<1.8$ and high $⟨\mathit{\mu }⟩$ ($9.6<⟨\mathit{\mu }⟩<20.6$). The bottom portion of each panel shows the ratio of MC simulation to data, separately for the two sets of hadronic physics models. The error bars represent statistical uncertainties

Fig. 3

The fraction of tracks as a function (a, b) of momentum and (c, d) of $|\mathit{\eta }|$ with $E\le 0$ for tracks with positive (a, c) and negative (b, d) charge. The bottom portion of each panel shows the ratio of MC simulation to data, separately for 2010 and 2012, and separately for the two sets of hadronic physics models. The error bars represent statistical uncertainties

Fig. 4

The fraction of tracks as a function of interaction lengths of material in front of the detector with $E\le 0$ for tracks with $1.2<p/\mathrm{GeV}<1.8$ and a positive or b negative charge. The bottom portion of each panel shows the ratio of MC simulation to data, separately for 2010 and 2012, and separately for the two sets of hadronic physics models. The error bars represent statistical uncertainties

Fig. 5

Ratio of the number of tracks with $E<0$ to the number with $E=0$ as a function of track momentum, for tracks with a $|\mathit{\eta }|<0.6$ and b $0.6<|\mathit{\eta }|<1.1$. The bottom portion of each panel shows the ratio of MC simulation to data, separately for the two sets of hadronic physics models. The error bars represent statistical uncertainties

Fig. 6

${⟨E/p⟩}_{\mathrm{BG}}$ as a function of the track momentum, for tracks with at least 20 TRT hits and a $|\mathit{\eta }|<0.6$, b $0.6<|\mathit{\eta }|<1.1$, c $1.8<|\mathit{\eta }|<1.9$, and d $1.9<|\mathit{\eta }|<2.3$. The bottom portion of each panel shows the ratio of MC simulation to data. The error bars represent statistical uncertainties

Fig. 7

${⟨E/p⟩}_{\mathrm{BG}}$ as a function of the track pseudorapidity, for tracks with at least 20 TRT hits and a $1.2<p/\mathrm{GeV}<1.8$, b $1.8<p/\mathrm{GeV}<2.2$, c $3.6<p/\mathrm{GeV}<4.6$, and d $4.6<p/\mathrm{GeV}<5.6$. The bottom portion of each panel shows the ratio of MC simulation to data. The error bars represent statistical uncertainties

Fig. 8

Comparison of the ${⟨E/p⟩}_{\mathrm{COR}}$ for tracks with a less than and b greater than 20 hits in the TRT. The bottom portion of each panel shows the ratio of MC simulation to data, separately for the two sets of hadronic physics models, and separately for 2010 and 2012 data. The error bars represent statistical uncertainties

Fig. 9

${⟨E/p⟩}_{\mathrm{COR}}$ as a function of track momentum, for tracks with a $|\mathit{\eta }|<0.6$, b $0.6<|\mathit{\eta }|<1.1$, c $1.8<|\mathit{\eta }|<1.9$, and d $1.9<|\mathit{\eta }|<2.3$. Tracks not matching any topological energy clusters in the calorimeter are included. The bottom portion of each panel shows the ratio of MC simulation to data. The error bars represent statistical uncertainties

Fig. 10

Ratio of ${⟨E/p⟩}_{\mathrm{COR}}$ calculated with cells to ${⟨E/p⟩}_{\mathrm{COR}}$ calculated with topological clusters as a function of track momentum, for tracks with a $|\mathit{\eta }|<0.6$ and b $0.6<|\mathit{\eta }|<1.1$. The bottom portion of each panel shows the ratio of MC simulation to data. The error bars represent statistical uncertainties

Fig. 11

Comparison of the ${⟨E/p⟩}_{\mathrm{COR}}$ calculated using LCW-calibrated topological clusters as a function of track momentum, corrected for the neutral-particle background, for tracks with $|\mathit{\eta }|<0.6$, and a zero or more associated topological clusters or b one or more associated topological clusters. Figure 9a shows the same quantity as Fig. 11a, calculated using EM-scale topological clusters. The bottom portion of each panel shows the ratio of MC simulation to data, separately for the two sets of hadronic physics models, and separately for 2010 and 2012 data. The error bars represent statistical uncertainties

Fig. 12

Comparison of the ${⟨E/p⟩}_{\mathrm{COR}}$ for a positive and b negative tracks as a function of track momentum, corrected for the neutral-particle background, for tracks with $|\mathit{\eta }|<0.6$, in simulation with the FTFP_BERT and QGSP_BERT sets of hadronic physics models. The bottom portion of each panel shows the ratio of MC simulation to data, separately for the two sets of hadronic physics models, and separately for 2010 and 2012 data. The error bars represent statistical uncertainties

Fig. 13

Comparison of the $E/p$ distributions for a positive and b negative tracks with $0.8<p/\mathrm{GeV}<1.2$ and $|\mathit{\eta }|<0.6$, in simulation with the FTFP_BERT and QGSP_BERT sets of hadronic physics models. The bottom portion of each panel shows the ratio of the two sets of hadronic physics models. The error bars represent statistical uncertainties

Fig. 14

The a ${⟨E/p⟩}_{\text{RAW}}$, b ${⟨E/p⟩}_{\mathrm{BG}}$, and c ${⟨E/p⟩}_{\mathrm{COR}}$ with $1.2<p/\mathrm{GeV}<1.8$ and d ${⟨E/p⟩}_{\mathrm{COR}}$ with $1.8<p/\mathrm{GeV}<50$ as a function of the number of reconstructed primary vertices, for tracks with $|\mathit{\eta }|<0.6$ and for $⟨\mathit{\mu }⟩<20.6$. Here, low-$⟨\mathit{\mu }⟩$ refers to data taken with average pile-up $⟨\mathit{\mu }⟩\ll 1$. The bottom portion of each panel shows the ratio of MC simulation to data. The error bars represent statistical uncertainties

Fig. 15

The a ${⟨E/p⟩}_{\text{RAW}}$, b ${⟨E/p⟩}_{\mathrm{BG}}$, and c ${⟨E/p⟩}_{\mathrm{COR}}$ with $1.2<p/\mathrm{GeV}<1.8$ and d ${⟨E/p⟩}_{\mathrm{COR}}$ with $1.8<p/\mathrm{GeV}<50$ as a function of $⟨\mathit{\mu }⟩$ for tracks with $|\mathit{\eta }|<0.6$. Here, low-$⟨\mathit{\mu }⟩$ refers to data taken with average pile-up $⟨\mathit{\mu }⟩\ll 1$. The bottom portion of each panel shows the ratio of MC simulation to data. The error bars represent statistical uncertainties

Fig. 16

Comparison of the response of the hadronic calorimeter as a function of track momentum between the data and MC simulation in $|\mathit{\eta }|<0.6$ a at the EM-scale and b after the LCW calibration. The bottom portion of each panel shows the ratio of MC simulation to data, separately for the two sets of hadronic physics models. The error bars represent statistical uncertainties

Fig. 17

Response of the hadronic calorimeter as a function of track momentum in a $0.6<|\mathit{\eta }|<1.1$ and b $1.1<|\mathit{\eta }|<1.4$ at the EM-scale. The bottom portion of each panel shows the ratio of MC simulation to data, separately for the two physics sets of hadronic physics models. The error bars represent statistical uncertainties

Fig. 18

Comparison of the response of the EM calorimeter as a function of track momentum between the data and MC simulation in $|\mathit{\eta }|<0.6$, a at the EM-scale and b with the LCW calibration. The bottom portion of each panel shows the ratio of MC simulation to data, separately for the two physics sets of hadronic physics models. The error bars represent statistical uncertainties

Fig. 19

Comparison of the response of the calorimeter between the nominal topological cluster threshold and the threshold corresponding to $⟨\mathit{\mu }⟩=30$ with $|\mathit{\eta }|<0.6$. a With no requirement on E / p, and b with $E/p>0$. The bottom portion of each panel shows the ratio of the response with the different thresholds. The error bars represent statistical uncertainties

Fig. 20

Comparison of the response of the calorimeter between the nominal topological cluster threshold and the threshold corresponding to $⟨\mathit{\mu }⟩=30$ with $0.6<|\mathit{\eta }|<1.1$. a With no requirement on E / p, and b with $E/p>0$. The bottom portion of each panel shows the ratio of the response with the different thresholds. The error bars represent statistical uncertainties

Fig. 21

Ratio of the response of the calorimeter between the threshold corresponding to $⟨\mathit{\mu }⟩=30$ and the nominal topological cluster threshold with a $|\mathit{\eta }|<0.6$ and b $0.6<|\mathit{\eta }|<1.1$, excluding tracks with $E\le 0$. The bottom portion of each panel shows the ratio of MC simulation to data. The error bars represent statistical uncertainties

Fig. 22

Comparison of the response of the hadronic calorimeter with the nominal topological cluster threshold to that with the threshold corresponding to $⟨\mathit{\mu }⟩=30$ for a $|\mathit{\eta }|<0.6$ and b $0.6<|\mathit{\eta }|<1.1$. The bottom portion of each panel shows the ratio of the response with the different thresholds. The error bars represent statistical uncertainties

Fig. 23

The reconstructed mass peaks of a $K_{\text{S}}^0$, b $\mathrm{\Lambda }$, and c $\overline{\mathrm{\Lambda }}$ candidates in data and MC simulation with the QGSP_BERT and FTFP_BERT sets of hadronic physics models, for candidates with at least one track with $|\mathit{\eta }|<0.6$. The distributions are normalised to unit area, and the error bars represent statistical uncertainties

Fig. 24

The $E/p$ distribution for isolated a ${\mathit{\pi }}^{+}$, b ${\mathit{\pi }}^{-}$, c proton, and d anti-proton tracks with $|\mathit{\eta }|<0.6$ and $2.2<p/\mathrm{GeV}<2.8$. The bottom portion of each panel shows the ratio of MC simulation to data. The error bars represent statistical uncertainties

Fig. 25

The fraction of tracks with $E\le 0$ for identified a ${\mathit{\pi }}^{+}$ and ${\mathit{\pi }}^{-}$, and b proton and anti-proton tracks with $|\mathit{\eta }|<0.6$. For anti-protons, $E_a\gtrsim 2$ $\mathrm{GeV}$. The uncertainties shown are statistical only

Fig. 26

The difference in $⟨E/p⟩$ between ${\mathit{\pi }}^{+}$ and ${\mathit{\pi }}^{-}$ with a $|\mathit{\eta }|<0.6$ and b $0.6<|\mathit{\eta }|<1.1$. The error bars represent statistical uncertainties

Fig. 27

The difference in $⟨E/p⟩$ between protons and ${\mathit{\pi }}^{+}$ with a $|\mathit{\eta }|<0.6$ and b $0.6<|\mathit{\eta }|<1.1$. The error bars represent statistical uncertainties

Fig. 28

The difference in $⟨E/p⟩$ between anti-protons and ${\mathit{\pi }}^{-}$ with a $|\mathit{\eta }|<0.6$ and b $0.6<|\mathit{\eta }|<1.1$. The error bars represent statistical uncertainties

Fig. 29

${⟨E/p⟩}_{\mathrm{COR}}$ as a function of track momentum, corrected for the neutral background, for ${\mathit{\pi }}^{+}$ tracks with a $|\mathit{\eta }|<0.6$ and b $0.6<|\mathit{\eta }|<1.1$ and for ${\mathit{\pi }}^{-}$ tracks with c $|\mathit{\eta }|<0.6$ and d $0.6<|\mathit{\eta }|<1.1$. The bottom portion of each panel shows the ratio of MC simulation to data, separately for the two sets of hadronic physics models. The error bars represent statistical uncertainties

Fig. 30

The ratio of the calorimeter response to single particles of various species to the calorimeter response to ${\mathit{\pi }}^{+}$ with the FTFP_BERT set of hadronic physics models. Only statistical uncertainties are shown

Fig. 31

The spectra of true particles inside anti-$k_t$, $R=0.4$ jets with a $90<p_{\mathrm{T}}/\mathrm{GeV}<100$, b $400<p_{\mathrm{T}}/\mathrm{GeV}<500$, and c $1800<p_{\mathrm{T}}/\mathrm{GeV}<2300$

Fig. 32

The fractional contribution to the total jet energy of particles in a certain range of momenta, for particles inside anti-$k_t$, $R=0.4$ jets with a $90<p_{\mathrm{T}}/\mathrm{GeV}<100$, b $400<p_{\mathrm{T}}/\mathrm{GeV}<500$, and c $1800<p_{\mathrm{T}}/\mathrm{GeV}<2300$

Fig. 33

a The energy response of anti-$k_t$, $R=0.4$ jets with $|\mathit{\eta }|<0.6$, based on a convolution of the response functions for isolated charged hadrons with the particle spectrum from Pythia8. b The ratio of the response of the categories of jets to the inclusive jet response. Jets are separated into those containing a b-hadron (b-jets), those initiated by light quarks (quark), and those initiated by gluons (gluon). The response distribution for b-jets is truncated at 800 $\mathrm{GeV}$

Fig. 34

The fraction of jet energy carried by particles in several categories (hadrons and EM particles, in several ranges of particle p), for anti-$k_t$, $R=0.4$ jets with $90<p_{\mathrm{T}}/\mathrm{GeV}<100$, $400<p_{\mathrm{T}}/\mathrm{GeV}<500$, or $1800<p_{\mathrm{T}}/\mathrm{GeV}<2300$

Fig. 35

The fraction of jet energy carried by particles in several categories (hadrons and EM particles, in several ranges of particle p), for anti-$k_t$, $R=0.4$ jets with $|\mathit{\eta }|<0.6$, as a function of jet $p_{\mathrm{T}}$

Fig. 36

The spectra of energy deposited in the calorimeter by particles inside anti-$k_t$, $R=0.4$ jets with $|\mathit{\eta }|<0.6$, for jets with a $90<p_{\mathrm{T}}/\mathrm{GeV}<100$ and b $400<p_{\mathrm{T}}/\mathrm{GeV}<500$

Fig. 37

The jet energy scale uncertainty contributions, as well as the total jet energy scale uncertainty, as a function of jet $p_{\mathrm{T}}$ for a $|\mathit{\eta }|<0.6$ and b $0.6<|\mathit{\eta }|<1.1$

Fig. 38

The jet energy scale correlations as a function of jet $p_{\mathrm{T}}$ and $|\mathit{\eta }|$ for jets in the central region of the detector