Performance of pile-up mitigation techniques for jets in [Formula: see text] collisions at [Formula: see text] TeV using the ATLAS detector

Abstract

The large rate of multiple simultaneous proton-proton interactions, or pile-up, generated by the Large Hadron Collider in Run 1 required the development of many new techniques to mitigate the adverse effects of these conditions. This paper describes the methods employed in the ATLAS experiment to correct for the impact of pile-up on jet energy and jet shapes, and for the presence of spurious additional jets, with a primary focus on the large 20.3 [Formula: see text] data sample collected at a centre-of-mass energy of [Formula: see text]. The energy correction techniques that incorporate sophisticated estimates of the average pile-up energy density and tracking information are presented. Jet-to-vertex association techniques are discussed and projections of performance for the future are considered. Lastly, the extension of these techniques to mitigate the effect of pile-up on jet shapes using subtraction and grooming procedures is presented.

Fig. 1

The luminosity-weighted distribution of the mean number of interactions per bunch crossing for the 2011 ($\sqrt{s}=7\mathrm{TeV}$) and 2012 ($\sqrt{s}=8\mathrm{TeV}$) $pp$ data samples

Fig. 2

a Per-cell electronic noise ($⟨\mathit{\mu }⟩=0$) and b total noise per cell at high luminosity corresponding to $⟨\mathit{\mu }⟩=30$ interactions per bunch crossing with a bunch spacing of $\mathrm{\Delta }t=50$ ns, in MeV, for each calorimeter layer. The different colours indicate the noise in the pre-sampler (PS), the up to three layers of the LAr calorimeter (EM), the up to three layers of the Tile calorimeter (Tile), the four layers of the hadronic end-cap calorimeter (HEC), and the three layers of the forward calorimeter (FCal). The total noise, ${\mathit{\sigma }}^{\mathrm{noise}}$, is the sum in quadrature of electronic noise and the expected RMS of the energy distribution corresponding to a single cell

Fig. 3

The mean estimated pile-up $p_{\text{T}}$ density, $\mathit{\rho }$ as a function of $\mathit{\eta }$, in simulated PYTHIA 8 dijet events

Fig. 4

The distribution of estimated pile-up $p_{\text{T}}$ density, $\mathit{\rho }$, in $Z(\to \mathit{\mu }\mathit{\mu })$+jets events using data and two independent MC simulation samples (SHERPA and POWHEG+PYTHIA  8). Both MC generators use the same pile-up simulation model (PYTHIA  8.160), and this model uses the $⟨\mathit{\mu }⟩$ distribution for $8\mathrm{TeV}$ data shown in Fig. 1. $\mathit{\rho }$ is calculated in the central region using topo-clusters with positive energy within $|\mathit{\eta }|\le 2.0$

Fig. 5

Dependence of the reconstructed jet $p_{\text{T}}$ (anti-$k_t$, $R=0.4$, LCW scale) on a in-time pile-up measured using $N_{\mathrm{PV}}$ and b out-of-time pile-up measured using $⟨\mathit{\mu }⟩$. In each case, the dependence of the jet $p_{\text{T}}$ is shown for three correction stages: before any correction, after the $\mathit{\rho }\times A^{\mathrm{jet}}$ subtraction, and after the residual correction. The error bands show the 68 % confidence intervals of the fits. The dependence was obtained by comparison with truth-particle jets in simulated dijet events, and corresponds to a truth-jet $p_{\text{T}}$ range of 20–30 GeV

Fig. 6

a RMS width of the $p_{\text{T}}^{\mathrm{reco}}-p_{\mathrm{T}}^{\mathrm{true}}$ distribution versus $⟨\mathit{\mu }⟩$ and b versus pseudorapidity $\mathit{\eta }$, for anti-$k_t$ $R=0.6$ jets at the LCW scale matched to truth-particle jets satisfying $20<p_{\mathrm{T}}^{\mathrm{true}}<30\mathrm{GeV}$, in simulated dijet events. A significant improvement is observed compared to the previous subtraction method (shown in red) [4]

Fig. 7

a $N_{\mathrm{PV}}$ dependence of the reconstructed $p_{\text{T}}$ of anti-$k_t$ $R=0.4$ LCW jets after the area subtraction as a function of track-jet $p_{\text{T}}$. b Validation results from $Z$+jets events showing the $⟨\mathit{\mu }⟩$ dependence as a function of the $Z$ boson $p_{\text{T}}$, denoted by $p_{\text{T}}^{\mathrm{ref}}$, for anti-$k_t$ $R=0.4$ LCW jets in the central region after the area subtraction. The points represent central values of the linear fit to $\mathit{\partial }⟨\mathrm{\Delta }{p}_{\text{T}}⟩/\mathit{\partial }⟨\mathit{\mu }⟩$ and the error bars correspond to the associated fitting error

Fig. 8

a Comparisons of the uncorrected (filled blue circles), corrected (red) distributions of the ratio of 3-subjettiness to 2-subjettiness (${\mathit{\tau }}_{32}$) for data (points) and for MC simulation (solid histogram) for leading jets in the range $600\le p_{\text{T}}<800\mathrm{GeV}$. The distribution of ${\mathit{\tau }}_{32}$ computed using stable truth particles (filled green triangles) is also included. The lower panel displays the ratio of the data to the MC simulation. b Dependence of ${\mathit{\tau }}_{32}$ on $⟨\mathit{\mu }⟩$ for the uncorrected (filled blue circles), corrected (filled red squares) and trimmed (open purple squares) distributions for reconstructed jets in MC simulation for leading jets in the range $600\le p_{\text{T}}<800\mathrm{GeV}$. The mean value of ${\mathit{\tau }}_{32}$ computed using stable truth particles (green) is also included

Fig. 9

The mean anti-$k_t$ $R=0.4$ LCW jet multiplicity as a function of $⟨\mathit{\mu }⟩$ in $Z$+jets events for jets with $p_{\text{T}}>20\mathrm{GeV}$ and $|\mathit{\eta }|<2.1$. Events in this plot are required to have at least 1 jet both before and after the application of the jet-area based pile-up correction

Fig. 10

a Schematic representation of the jet vertex fraction $\mathrm{JVF}$ principle where f denotes the fraction of track $p_{\text{T}}$ contributed to jet 1 due to the second vertex (PV2). b $\mathrm{JVF}$ distribution for hard-scatter (blue) and pile-up (red) jets with $20<p_{\text{T}}<50\mathrm{GeV}$ and $|\mathit{\eta }|<2.4$ after pile-up subtraction and jet energy scale correction in simulated $Z+$jets events

Fig. 11

The mean anti-$k_t$ $R=0.4$ LCW+JES jet multiplicity as a function of $⟨\mathit{\mu }⟩$ in $Z$+jets events for jets with $|\mathit{\eta }|<2.1$, back-to-back with the $Z$ boson, before and after several $|\mathrm{JVF}|$ cuts were applied to jets with $p_{\text{T}}<50\mathrm{GeV}$. Results for jets with a $p_{\text{T}}>20\mathrm{GeV}$, b $p_{\text{T}}>30\mathrm{GeV}$ and c $p_{\text{T}}>40\mathrm{GeV}$ are shown requiring at least one jet of that $p_{\text{T}}$. To remove effects of hard-scatter modelling the dependence on $⟨\mathit{\mu }⟩$ was fit and the MC simulation shifted so that data and simulation agree at zero pile-up, $⟨\mathit{\mu }⟩=0$. The upper ratio plots show results before and after applying a $|\mathrm{JVF}|$ cut of 0.25 and the lower ratio plots show the same for a cut of 0.50. The $\mathrm{JVF}$ uncertainty is very small when counting jets with $p_{\text{T}}>40\mathrm{GeV}$

Fig. 12

a Distribution of $\mathrm{corrJVF}$ for pile-up (PU) and hard-scatter (HS) jets with $20<p_{\text{T}}<30\mathrm{GeV}$. b Primary-vertex dependence of the hard-scatter jet efficiency for $20<p_{\text{T}}<30\mathrm{GeV}$ (solid markers) and $30<p_{\text{T}}<40\mathrm{GeV}$ (open markers) jets for fixed cuts of $\mathrm{corrJVF}$ (blue square) and $\mathrm{JVF}$ (violet circle) such that the inclusive efficiency is $90\%$. The selections placed on $\mathrm{corrJVF}$ and $\mathrm{JVF}$, which depend on the $p_{\text{T}}$ bin, are specified in the legend

Fig. 13

a Distribution of $R_{\mathrm{pT}}$ for pile-up (PU) and hard-scatter (HS) jets with $20<p_{\text{T}}<30\mathrm{GeV}$. b Primary-vertex dependence of the hard-scatter jet efficiency for $20<p_{\text{T}}<30\mathrm{GeV}$ (solid markers) and $30<p_{\text{T}}<40\mathrm{GeV}$ (open markers) jets for fixed cuts of $R_{\mathrm{pT}}$ (blue square) and $\mathrm{JVF}$ (violet circle) such that the inclusive efficiency is $90\%$. The cut values imposed on $R_{\mathrm{pT}}$ and $\mathrm{JVF}$, which depend on the $p_{\text{T}}$ bin, are specified in the legend

Fig. 14

a Fake rate from pile-up jets versus hard-scatter jet efficiency curves for $\mathrm{JVF}$, $\mathrm{corrJVF}$, $R_{\mathrm{pT}}$ and $\mathrm{JVT}$. The widely used $\mathrm{JVF}$ working points with cut values 0.25 and 0.5 are indicated with gold and green stars. b Primary vertex dependence of the hard-scatter jet efficiency for $20<p_{\text{T}}<30\mathrm{GeV}$ (solid markers) and $30<p_{\text{T}}<40\mathrm{GeV}$ (open markers) jets for fixed cuts of $\mathrm{JVT}$ (blue square) and $\mathrm{JVF}$ (violet circle) such that the inclusive efficiency is $90\%$

Fig. 15

The distributions of a $\mathrm{corrJVF}$, b $R_{\mathrm{pT}}$ and c $\mathrm{JVT}$ for light-quark and gluon initiated hard-scatter jets

Fig. 16

The fake rate from pile-up jets versus hard-scatter jet efficiency curves for $\mathrm{JVT}$ separating jets initiated by light quarks, gluons and b-quarks

Fig. 17

Efficiency measured in $Z(\to \mathit{\mu }\mathit{\mu })$+jets events as a function of $p_{\text{T}}^{\mathrm{ref}}$ in data and MC simulation for a $\mathrm{JVT}>0.2$, b $\mathrm{JVT}>0.4$ and c $\mathrm{JVT}>0.7$, where $p_{\text{T}}^{\mathrm{ref}}=p_{\text{T}}^Z$. The bottom panels of each figure show the ratio of efficiencies measured in data and MC simulation

Fig. 18

Rapidity–$\mathit{\varphi }$ view of a simulated event of a $W^{\prime }$ boson with a mass of 1 TeV decaying to a $W$ boson and a $Z$ boson, both of which decay to jet pairs

Fig. 19

a Correlation of subjet $p_{\text{T}}$ fraction, defined as the ratio of the subjet $p_{\text{T}}$ to the ungroomed jet $p_{\text{T}}$, and subjet $\mathrm{corrJVF}$ for anti-$k_t$ $R=1.0$ jets with $p_{\text{T}}>300\mathrm{GeV}$ and $|\mathit{\eta }|<1.5$. The dotted line indicates the standard calorimeter-based trimming $f_{\mathrm{cut}}$ of $5\%$. b Distribution of jet mass for calorimeter- and track-based trimming configurations and jet cleansing. The default trimmed jet mass (purple filled circles) with $f_{\mathrm{cut}}=0.05$ is compared to calorimeter-based trimming with $(f_{\mathrm{cut}}=0.04)$ and $\mathrm{corrJVF}>0.6$ (blue open squares), linear cleansing (green upward triangles) and $\mathrm{JVF}$ cleansing (black downward triangles). The dashed blue histogram is the mass distribution for ungroomed jets, with no pile-up subtraction applied