EUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2014-064
Submitted to: Physics Letters B
Measurement of the cross section of high transverse
momentum Z → bb production
in proton–proton collisions at
√
s
= 8 TeV with the ATLAS
Detector
The ATLAS Collaboration
Abstract
This Letter reports the observation of a high transverse momentum Z → bb signal in proton–proton
collisions at
√
s
= 8 TeV and the measurement of its production cross section. The data analysed were
collected in 2012 with the ATLAS detector at the LHC and correspond to an integrated luminosity of
19.5 fb
−1. The Z → bb decay is reconstructed from a pair of b-tagged jets, clustered with the anti-k
t
jet algorithm with R
= 0.4, that have low angular separation and form a dijet with p
T> 200 GeV. The
signal yield is extracted from a fit to the dijet invariant mass distribution, with the dominant,
multi-jet background mass shape estimated by employing a fully data-driven technique that reduces the
dependence of the analysis on simulation. The fiducial cross section is determined to be
σ
fidZ→bb
= 2.02 ± 0.20 (stat.) ± 0.25 (syst.) ± 0.06 (lumi.) pb = 2.02 ± 0.33 pb ,
in good agreement with next-to-leading-order theoretical predictions.
c
2014 CERN for the benefit of the ATLAS Collaboration.
Measurement of the cross section of high transverse momentum Z → bb production
in proton–proton collisions at
√
s
= 8 TeV with the ATLAS Detector
ATLAS Collaboration
Abstract
This Letter reports the observation of a high transverse momentum Z → bb signal in proton–proton collisions at √s = 8 TeV and the measurement of its production cross section. The data analysed were collected in 2012 with the ATLAS detector at the LHC and correspond to an integrated luminosity of 19.5 fb−1. The Z → bb decay is reconstructed from a pair of b-tagged jets, clustered with the anti-ktjet algorithm with R= 0.4, that have low angular separation and form a dijet with pT > 200 GeV. The signal yield is extracted from a fit to the dijet invariant mass distribution, with the dominant, multi-jet background mass shape estimated by employing a fully data-driven technique that reduces the dependence of the analysis on simulation. The fiducial cross section is determined to be
σfid
Z→bb= 2.02 ± 0.20 (stat.) ± 0.25 (syst.) ± 0.06 (lumi.) pb = 2.02 ± 0.33 pb , in good agreement with next-to-leading-order theoretical predictions.
Keywords: LHC, boosted bb topologies
1. Introduction
High transverse momentum (pT), hadronically decaying,
electroweak-scale bosons have already been used in searches at the LHC [1–5], and are expected to play an increasingly signif-icant role as the LHC moves to higher centre-of-mass energies in 2015. Therefore it is important to study them directly. This Letter presents the observation of a high-pTZ → bbsignal in a fully hadronic final state, and a measurement of its production cross section. The measurement is compared to the next-to-leading-order (NLO) matrix element plus parton-shower pre-dictions of POWHEG [6–9] and aMC@NLO [10], where the parton-shower, hadronisation and underlying-event modelling are provided by Pythia-8.165 [11] and Herwig++ [12] respec-tively. This first measurement of a high-pT electroweak-scale boson in an all-hadronic final state at the LHC demonstrates the validity of both the analysis techniques used and of the state-of-the-art NLO plus parton-shower particle-level predic-tions for electroweak-scale bosons decaying to bb. It is there-fore of great relevance for the search for the H → bb signal in the (most sensitive) high Higgs boson pT range [13], as well as for searches for TeV-scale resonances decaying to bbbb via
ZZ, ZH or HH [14, 15]. A high-pT Z → bb signal can also
provide a useful benchmark for validating the performance of the ATLAS detector (for example, the b-jet energy scale1); and for testing and optimising analysis methods relevant for physics studies involving high-pTjets that contain b-hadrons (b-jets).
The analysis described in this Letter is designed to select bb decays of Z-bosons with pT> 200 GeV, in proton–proton
colli-1The use of the Z → bb peak to constrain the b-jet energy scale at the
Teva-tron experiments was demonstrated in Ref. [16].
sions at√s= 8 TeV. The high-pTrequirement helps to enhance the signal relative to bb production in multi-jet events (predomi-nantly gluon splitting to bb in this high-pTregime), which is the dominant source of background and has a more steeply-falling
pT spectrum. In order to minimise the dependence on
simu-lation, the analysis employs a fully data-driven technique for the determination of the invariant mass spectrum of the multi-jet background. This is especially important given that Monte Carlo (MC) generators have not been tested thoroughly in this region of the bb production phase space.
2. The ATLAS detector
ATLAS is a multi-purpose particle physics experiment [17] at the LHC. The detector layout2 consists of inner tracking devices surrounded by a superconducting solenoid, electro-magnetic and hadronic calorimeters, and a muon spectrome-ter. The inner tracking system provides charged-particle track-ing in the pseudorapidity region |η| < 2.5 and vertex recon-struction. It consists of a silicon pixel detector, a silicon mi-crostrip tracker, and a straw-tube transition radiation tracker. The system is surrounded by a solenoid that produces a 2 T ax-ial magnetic field. The central calorimeter system consists of a liquid-argon electromagnetic (EM) sampling calorimeter with
2ATLAS uses a right-handed coordinate system with its origin at the
nom-inal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, φ) are used in the transverse plane, φ is the azimuthal angle around the beam pipe. The pseudorapidity, η, is defined in terms of the polar angle θ as η= − ln[tan(θ/2)].
high granularity and an iron/scintillator-tile calorimeter provid-ing hadronic energy measurements in the central pseudorapidity range (|η| < 1.7). The endcap and forward regions are instru-mented with liquid-argon calorimeters for both electromagnetic
and hadronic energy measurements up to |η| = 4.9. The muon
spectrometer is operated in a magnetic field provided by air-core superconducting toroids and includes tracking chambers
for precise muon momentum measurements up to |η|= 2.7 and
trigger chambers covering the range |η| < 2.4. A three-level trigger system is used to select interesting events [18]. The Level-1 trigger reduces the event rate to below 75 kHz using hardware-based trigger algorithms acting on a subset of detec-tor information. Two software-based trigger levels, referred to collectively as the High-Level Trigger (HLT), further reduce the event rate to about 400 Hz using information from the entire de-tector.
3. Data, simulated samples, and event reconstruction The data sample used in this analysis, after requiring that certain quality criteria be satisfied, corresponds to an integrated
luminosity of L= 19.5±0.5 fb−1, and was recorded by ATLAS
in 2012. The uncertainty on the integrated luminosity is de-rived, following the same methodology as that detailed in Ref. [19], from a calibration of the luminosity scale using beam-separation scans performed in November 2012.
MC event samples simulated with the GEANT4-based [20] ATLAS detector simulation [21] are used to model the Z → bbsignal and the small tt, Z → cc and W → qq0background contributions. In addition, multi-jet MC event samples are used for studying the trigger modelling in simulation. The effect of multiple proton-proton interactions in the same bunch crossing (pile-up) is included in the simulation.
The Z → bb signal is modelled using Sherpa-1.4.3 [22], with the CT10 [23] NLO parton distribution function (PDF) set. An alternative Z → bb model was generated with Pythia-8.165 [11] and the CTEQ6L1 [24] leading-order (LO) PDF set and is used to determine the systematic uncertainty associated with
Z → bb modelling. The Z → cc background is also generated
with Sherpa-1.4.3 and the CT10 PDF set. The tt background is simulated with MC@NLO-4.06 [25] interfaced to Herwig-6.520 [26] for the fragmentation and hadronisation processes, including Jimmy-4.31 [27] for the underlying-event description. The top quark mass is fixed at 172.5 GeV, and the PDF set CT10
is used. The W → qq0and multi-jet MC samples are generated
using Pythia-8.165 with the CT10 PDF set.
Jets are reconstructed using the anti-kt jet clustering algo-rithm [28], with radius parameter R = 0.4 . The inputs to the reconstruction algorithm are topological calorimeter cell clus-ters [29] calibrated at the EM energy scale. The effects of pile-up on jet energies are accounted for by a jet-area-based cor-rection [30]. Jets are then calibrated to the hadronic energy scale using pT- and η-dependent calibration factors based on MC simulations and the combination of several in situ tech-niques applied to data [29]. To remove jets with a significant contribution from pile-up interactions, it is required that at least
50% of the summed scalar pTof tracks matched to a jet belongs to tracks originating from the primary vertex.3
The flavour of jets in the ATLAS simulation is defined by matching jets to hadrons with pT> 5 GeV. A jet is labelled as a b-jet if a b-hadron is found within∆R = p(∆η)2+ (∆φ)2= 0.3 of the jet axis; otherwise, if a c-hadron is found within the same distance the jet is labeled as a c-jet; and if neither is the case then the jet is labelled as a light (quark) jet. The lifetime and other properties of b-hadrons are used to identify (b-tag) b-jets with |η| < 2.5 , by exploiting the properties and topology of their decay products, such as the impact parameter of tracks (defined as a track’s distance of closest approach to the primary vertex in the transverse plane), the presence of displaced vertices, and the reconstruction of c-hadron and hadron decays. The b-tagging algorithm used in this analysis [31] combines the above information using multivariate techniques and is configured to achieve an efficiency of 70% for tagging b-jets in a MC sample of tt events, while rejecting 80% of c-jets and more than 99% of light jets in the same sample.
4. Event selection
The events of interest in this analysis were triggered by a combination of six jet-based triggers. The most efficient of these triggers (accepting about 70% of the signal events) re-quires two jets identified as b-jets by a dedicated HLT b-tagging algorithm, with transverse energies (ET) above 35 GeV, and a jet with ET > 145 GeV that may or may not be one of the b-tagged jets. The trigger efficiency for the Sherpa signal events passing the full offline event selection is 88.1%.
The event selection requires that there be at least three but no more than five jets with |η| < 2.5 and pT > 30 GeV, and that exactly two of them be b-tagged. The b-tagged jets must each
have pT > 40 GeV. The angular distance, ∆R, between them
must be smaller than 1.2 and the transverse momentum of the dijet system they form, pdijetT , must be greater than 200 GeV.
The final step of the event selection uses two variables with significant discrimination between signal and background to define two sets of events, one signal-enriched and the other signal-depleted, referred to hereafter as “Signal Region” and “Control Region”. The two variables, which are combined with an artificial neural network (ANN) into a single discriminant, SN N, are: (1) the dijet pseudorapidity, ηdijet; and (2) the pseu-dorapidity difference, ∆η, between the dijet and the balancing jet, where the balancing jet is chosen to be the one that, when added to the dijet, gives the three-jet system with the smallest transverse momentum. The correlation of these two variables with the dijet invariant mass, mdijet, is very small, allowing the ANN to be trained using selected data events outside the mass window [80, 110] GeV as background and Z → bb MC events as signal. Fig. 1 depicts the distributions of ηdijet,∆η and SN N in the signal MC sample and in the data. The data shown here in-clude all events with 60 < mdijet< 160 GeV, and are representa-tive of the background as the signal contribution is estimated to
3Amongst all reconstructed proton-proton collisions in a bunch crossing, the
| dijet η | 0 0.5 1 1.5 2 2.5 3 ) dijet η (1/N)(dN/d 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Data b b → Z ATLAS = 8 TeV s -1 Ldt = 19.5 fb
∫
(a) (Dijet - BalanceJet) η ∆ 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ) η∆ (1/N)(dN/d 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Data b b → Z ATLAS = 8 TeV s -1 Ldt = 19.5 fb∫
(b) NN S 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ) NN (1/N)(dN/dS 0 0.01 0.02 0.03 0.04 0.05 0.06 Data b b → Z ATLAS = 8 TeV s -1 Ldt = 19.5 fb∫
(c)Figure 1: The distributions of: (a) the dijet pseudorapidity, |ηdijet|; (b) the
pseu-dorapidity difference, |∆η|, between the dijet and the balancing jet; and (c) the neural network discriminant SN N, in the Z → bb signal (red squares) and in the
data (black circles), including all events with 60 < mdijet< 160 GeV. The data
is dominated by the multi-jet background. The two dashed lines in (c) indicate the SN Nvalues defining the Signal (SN N> 0.58) and Control (SN N< 0.45)
Regions.
be only about 1%. The Signal Region is defined by SN N> 0.58 and the Control Region by SN N< 0.45. The discriminating power of ηdijet and∆η stems from the fact that signal produc-tion proceeds predominantly via a quark–gluon hard scatter, as opposed to the dominant multi-jet background which is largely initiated by gluon-gluon scattering. Due to the differences be-tween the gluon and quark PDFs, the Z+ jet system tends to be more boosted along the beam axis; hence the Z-boson is pro-duced with higher η and smaller∆η separation from its recoil, compared to the background.
Since SN N is minimally correlated with mdijet the Control Region can be used as an unbiased model of the background in the Signal Region. Fig. 2 shows the normalised ratio of the mdijetdistributions in the Signal and Control Regions, excluding the Z mass window. A first-order polynomial fit to this distribu-tion gives a good χ2probability, 0.18, and a gradient consistent with zero, (−1.37 ± 1.10) × 10−4GeV−1. In addition, the va-lidity of assuming minimal correlation is supported by a test, performed with events from a Pythia 8 multi-jet MC sample satisfying the above analysis requirements, giving a ratio of the above distributions consistent with being flat. The impact of possible differences in the background mdijetshape between the Signal and Control Regions is considered as one of the system-atic uncertainties on the measurement.
[GeV]
dijet
m
60 70 80 90 100 110 120 130 140 150 160
Signal Region / Control Region
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 Data 1st Order Polynomial ATLAS = 8 TeV s -1 Ldt = 19.5 fb
∫
Figure 2: The normalised ratio of dijet mass distributions in the Signal and Control Regions, excluding the signal mass window, fitted with a first-order polynomial. The dashed line indicates unity.
The total number of data events satisfying the full analysis selection is 236172 in the Signal Region and 474810 in the Con-trol Region. The signal-to-background ratio in a 30 GeV win-dow around the Z-boson mass is expected to be about 6% (2%) in the Signal (Control) Region. The tt events are estimated to represent about 0.5% of the total background in both the Signal and Control Regions, and the Z → cc and W → qq0backgrounds are approximately 8% and 6% of the signal, respectively.
5. Cross-section definition
The fiducial cross section of resonant Z-boson production, with Z decaying to bb, σfid
Z→bb, is defined as follows. Particle-level jets in MC Z → bb events are reconstructed from stable particles (particles with lifetime in excess of 10 ps, exclud-ing muons and neutrinos) usexclud-ing the anti-kt algorithm with
ra-dius parameter R = 0.4 . There must be two particle-level
b-jets in the event that satisfy the following fiducial condi-tions: pT > 40 GeV, |η| < 2.5 for the individual jets; and ∆R(jet1, jet2) < 1.2, pdijet
T > 200 GeV, 60 < mdijet < 160 GeV for the dijet system.
The cross section is extracted from the measured yield of Z → bbevents in the data, NZ→bb, as
σfid Z→bb=
NZ→bb L · CZ→bb,
where CZ→bb is the efficiency correction factor to correct the detector-level Z → bb yield to the particle level. The value of CZ→bbin the Sherpa MC signal is found to be 16.2%, which can be factorised into the product of: trigger efficiency (88.1%), b-tagging and kinematic selection efficiency (52.7%), and the ef-ficiency of the SN N requirement that defines the Signal Region (35.0%). The uncertainties on CZ→bbare discussed in Section 7.
6. Signal extraction
The signal yield is extracted by fitting simultaneously the mdijet distributions of the Signal and Control Regions in the range [60, 160] GeV with a binned, extended maximum-likelihood (EML) fit, using a bin width of 1 GeV.
The Z → bb signal shape is modelled in the EML fit as the sum of three Gaussians. This empirical model describes well both the Sherpa and the Pythia signal MC samples, albeit with slightly different parameters. Given this, the Sherpa-based model is used as the baseline for the fit, and the Pythia-based model is used for an estimate of the systematic uncertainty on the measurement due to the signal shape. The only free pa-rameters of the signal model in the EML fit are the yield in the Signal Region and the shift, δMZ, of the mean of the nar-rowest Gaussian from its MC-predicted value. The widths and relative contributions of the three Gaussians, as well as the dif-ferences between the mean of each of the two wider Gaussians and the narrowest one, are fixed to the values determined by a separate fit to the signal MC mdijetdistributions. Given that the Control Region is not signal-free, the simultaneous fit in-cludes a signal component in both the Signal Region and the Control Region. The relative proportion of signal in the two re-gions, RZ = (NControl
Z→bb )/(N Signal
Z→bb), is fixed to the value predicted
by Sherpa, RZ = 0.62. This choice is supported by the good
agreement found between Sherpa and data in the SN N distribu-tion obtained from a pure sample of high-pTZ →µ+µ−events, as discussed in Section 7.
The dominant multi-jet background is modelled in the EML fit using a seventh-order Bernstein polynomial [32]. This is purely an empirical model and the order of the polynomial is
chosen by a χ2probability saturation test by fitting the mdijet dis-tribution in the Control Region with the background-only hy-pothesis and an increasing polynomial order, until no improve-ment is seen in the fit quality when adding higher-order terms. The coefficients of the Bernstein polynomial are determined by the simultaneous EML fit and are identical for the Signal and Control Regions. In this way, the signal-depleted Control Re-gion constrains the background prediction in the Signal ReRe-gion. The only additional parameters of the fit are the background normalisations in the Signal and Control Regions.
The small Z → cc, tt and W → qq0backgrounds are included as separate components in the EML fit for both the Signal and Control Regions, with their mdijet shapes being parameterised
from MC simulation as follows. The Z → cc and W → qq0
com-ponents are each modelled as three-Gaussian sums like the sig-nal, with all parameters fixed to values from fits to MC sim-ulation. The means of the Gaussians are expressed with re-spect to the mean of the narrowest Z → bb Gaussian: this cou-ples the position of these backgrounds to the Z → bb signal. The W → qq0component is normalised absolutely to its Pythia LO cross section, corrected to NLO by a K-factor derived us-ing MCFM [33]. The acceptance of the Z → cc background is taken from the simulation, but its yield is linked to the fitted Z → bbyield, since the Z → cc production differs from the sig-nal only in the well-known branching fractions of the Z decays. All properties of the tt component are fixed using the tt simula-tion, with normalisation from the NNLO+NNLL prediction of the tt production cross section [34–39]. The contribution from Higgs decays to bb is expected to be ∼ 3% of the Z → bb sig-nal and localised away from the sigsig-nal peak: therefore no such component is included in the EML fit.
The fit procedure has been validated using a comprehensive set of tests based on pseudo-experiments, which have demon-strated that the yield and its uncertainty are accurately deter-mined by the fit procedure over a wide range of input signal yields. In particular, the fit procedure is robust against fit-ting artefacts like false dips or peaks: a consequence of fitfit-ting both signal and control regions simultaneously, with the ratio of Z → bb in each region fixed.
Fig. 3 shows the result of the simultaneous fit to the mdijet distributions of the Signal and Control Regions, as well as the corresponding background-subtracted data distributions. The rather complex shape of the background invariant mass distri-bution results from the use of the six jet-based triggers, all of which have different jet pT thresholds and hence shape di ffer-ently the invariant mass distributions. The fitted function mod-els the data well, with a signal peak compatible with Z → bb decays. The fitted signal yield is 6420 ± 640 (stat.) events.
7. Systematic uncertainties
The sources of systematic uncertainties considered in this analysis, which may affect the fitted signal yield, the efficiency correction factor or both, are listed in Table 1.
The jet energy scale (JES) and jet energy resolution (JER) uncertainties are determined using the techniques described in
[GeV] dijet m 60 70 80 90 100 110 120 130 140 150 160 Events / 5 GeV 5000 10000 15000 20000 25000 Signal Region Data Signal + Background Signal b b → Z Background ATLAS = 8 TeV s -1 Ldt = 19.5 fb
∫
(a) [GeV] dijet m 60 70 80 90 100 110 120 130 140 150 160 Events / 5 GeV 10000 20000 30000 40000 50000 Control Region Data Signal + Background Signal b b → Z Background ATLAS = 8 TeV s -1 Ldt = 19.5 fb∫
(b) [GeV] dijet m 60 70 80 90 100 110 120 130 140 150 160(Data - Background) / 5 GeV
-500 0 500 1000 1500 2000 Signal Region Data Signal b b → Z ATLAS = 8 TeV s -1 Ldt = 19.5 fb
∫
(c) [GeV] dijet m 60 70 80 90 100 110 120 130 140 150 160(Data - Background) / 5 GeV
-500 0 500 1000 1500 2000 Control Region Data Signal b b → Z ATLAS = 8 TeV s -1 Ldt = 19.5 fb
∫
(d)Figure 3: The result of the simultaneous extended maximum likelihood fit to the dijet mass distributions in (a) the Signal Region and (b) the Control Region, and the corresponding background-subtracted distributions (c) and (d), using the Sherpa signal model. The lines represent the signal (dashed), backgrounds (dotted) and the sum of the two (solid).
Refs. [29, 40]. The JES uncertainty has a relatively large im-pact on the signal efficiency, due to the pTrequirements on the individual jets and the dijet system, but a comparatively small impact on the fitted yield, because of the data-driven approach for the background determination and the fact that the location of the signal peak is a free parameter of the EML fit. The JER uncertainty affects predominantly the fitted yield, since it mod-ifies the MC-derived signal shape.
The b-tagging efficiency in the simulation is scaled to repro-duce the one in data and its uncertainty is evaluated by varying the data-to-MC scale factor applied to each jet in the simulation within a range that reflects the systematic uncertainty on the measured tagging efficiency for b-jets in ATLAS [31, 41]. The Z → ccrelative normalisation uncertainty is estimated in a sim-ilar way by varying the corresponding scale factors for charm jets in the simulation.
The uncertainty on CZ→bbdue to a potential mis-modelling of the trigger efficiency is assessed using data events collected with a prescaled trigger that is fully efficient with respect to the analysis event selection. The full offline event selection is applied to these events and the efficiency for passing the anal-ysis trigger requirements is compared to the corresponding ef-ficiency in the multi-jet MC sample, as a function of various kinematic variables. It is found that the two trigger efficiencies are consistent to within 6%. Furthermore, the trigger efficiency in the multi-jet MC sample, when considering only those events where the two b-tagged jets are labelled as true b-jets, is fully consistent with the trigger efficiency in the signal MC events. Based on these studies, a ±6% trigger efficiency modelling un-certainty is propagated to the cross-section measurement.
The uncertainty on the extracted signal yield due to poten-tial differences in the background mdijetshape between the
Sig-Table 1: The relative systematic uncertainties on the fitted yield of Z → bb,NZ→bb; the efficiency correction factor, CZ→bb; and the fiducial cross-section, σfid Z→bb,
from each of the sources of uncertainty considered.
Source of uncertainty ∆NZ→bb(%) ∆CZ→bb(%) ∆σfid
Z→bb(%)
Jet energy scale +3.0/ − 1.5 ±8.4 +6.5/ − 5.0
Jet energy resolution ±5.3 ±0.2 ±5.1
b-tagging ±0.1 ±3.6 ±3.6
Trigger modelling N/A ±6 ±6
Control Region bias +4.9/ − 5.5 N/A +4.9/ − 5.5
Signal SN Nmodelling ±0.9 ∓2.0 ±2.9
Signal mdijetshape ±2.2 N/A ±2.2
Z → ccnormalisation ±0.4 N/A ±0.4
ttnormalisation ±1.2 N/A ±1.1
W → qq0normalisation ±1.0 N/A ±1.0
nal and Control Regions (“Control Region bias”) is assessed by
repeating the EML fit for a range of SN N values around the
one used in the baseline selection to define the Control Region. These variations of the Control Region definition lead to small biases in the mdijetshape relative to the Signal Region, resulting in non-zero slopes in the first-order polynomial fits to the distri-butions equivalent to the one in Fig. 2. The non-zero slopes of these fits bracket the statistical uncertainty with which the slope of the first-order polynomial fit to Fig. 2 is determined. The largest upwards and downwards variations in the fitted signal yield from the EML fits following this procedure are propagated as systematic uncertainty to the cross-section measurement.
The impact on CZ→bbof a possible mis-modelling of the dis-tributions of the analysis selection variables, except SN N, in the MC signal is assessed by comparing the Sherpa and Pythia MC signal samples. It is found to be less than 1% and therefore it is considered negligible. There is a 15% discrepancy between the Pythia and Sherpa predictions for the efficiency of the Signal Region SN Nrequirement. Since the input variables to SN N de-pend primarily on the dynamics of Z-boson production, the modelling by Sherpa is tested by comparing a sample of events
in the ATLAS 2012 data containing high-pT Z → µ+µ−
de-cays to a corresponding Sherpa MC sample, with the dimuon system replacing the dijet system. The agreement is found to be very good, at the level of 2%, and the residual discrepancies are propagated as the “Signal SN N modelling” uncertainty on both CZ→bband the RZfit parameter. This uncertainty also cov-ers the impact from possible differences between the PDFs used in the Sherpa signal sample and the data, given that the above Z →µ+µ−Sherpa sample uses the same PDF set as the Z → bb Sherpa signal sample.
The difference obtained in the fitted signal yield when using the Pythia signal model rather than the Sherpa one is used as an estimate of the uncertainty on the measurement due to possible mis-modelling of the mdijetshape in the MC signal.
The impact on the measurement from the uncertainty on the W → qq0and tt normalisations is assessed by varying the fixed number of events of each background in the Signal and Control
Regions independently by 50% and repeating the EML fit.
8. Results
Using the extracted Z → bb yield, the estimated signal-efficiency correction factor and the integrated luminosity of the dataset, the cross section in the fiducial region defined in Sec-tion 5 is measured to be
σfid
Z→bb= 2.02 ± 0.20 (stat.) ± 0.25 (syst.) ± 0.06 (lumi.) pb . The total systematic uncertainty is the result of adding in quadrature all the individual systematic uncertainties on σfid
Z→bb listed in Table 1. It is further found that the signal mdijetpeak position is consistent with the Z → bb expectation: δMZ = −1.5 ± 0.7 (stat.)+3.4−2.5(syst.) GeV. The good agreement with zero provides an independent confirmation of the good agreement between data and MC on the energy scale of b-jets in ATLAS.
The robustness of the measurement is supported by several cross-checks and complementary studies. In particular, a con-sistent cross-section measurement is obtained by applying a tighter b-tagging selection (with an efficiency of 60% for tag-ging b-jets in a MC sample of tt events) or when the require-ment on pdijetT is raised to 250 GeV or 300 GeV. Furthermore, when the same methodology is repeated on two independent classes of events, those accepted by the dominant trigger de-scribed above and all other events, both measured cross sections (1.99 ± 0.25 (stat.) pb and 1.87 ± 0.44 (stat.) pb respectively) are fully consistent with the baseline measurement, even though the mdijetdistributions are significantly different in the two classes of events. In addition, when the background shape obtained from the baseline EML fit is used to fit for a signal in the sam-ple of events with 0.45 < SN N< 0.58, the fitted signal yield in this sample is consistent with the number of signal events cal-culated based on the measured cross section and the shape of SN N predicted by Sherpa. Finally, repeating the analysis with
a number of alternative functional forms for the empirical de-scription of the background shape (such as a log-normal func-tion convolved with a fourth-order Bernstein polynomial) leads to negligible variations in the measured cross section compared to the systematic uncertainties of the measurement.
The measured cross section is compared to the particle-level, NLO-plus-parton-shower predictions of two MC generators, POWHEG and aMC@NLO, in the same fiducial region. In both cases, the cross section of the Z+ 1-jet process is calculated to NLO accuracy. For aMC@NLO, the Z decay is simulated with MadSpin [42]. POWHEG is interfaced to Pythia for parton showering, hadronisation and underlying-event contributions, whilst aMC@NLO is interfaced to Herwig++. The particle-level predictions are then derived by applying to the generated events the fiducial selection defined in Section 5. The predicted cross sections are:
POWHEG : σfid Z→bb= 2.02 +0.25 −0.19(scales)+0.03−0.04(PDF) pb aMC@NLO : σfid Z→bb= 1.98 +0.16 −0.08(scales) ± 0.03(PDF) pb . Both generators use the CT10 PDF set for the central value of the prediction, and the renormalisation and factorisation scales are set to the pT of the Z boson. The uncertainty due to the ambiguity in the renormalisation and factorisation scales is es-timated by doubling or halving them simultaneously. The PDF uncertainty is evaluated by varying the 52 PDFs in the CT10 NLO error set, following the Hessian method and rescaling to the 68% confidence level. Within the experimental and theo-retical uncertainties, both predictions are completely consistent with the measured cross section.
POWHEG and aMC@NLO can also be used to provide an estimate of the fraction of the total cross section for Z → bb
pro-duction at the LHC, with pT > 200 GeV, that is contained
within the measured fiducial region. The ratio of the above cross sections to the cross sections calculated without applying any particle-level requirements, only requiring pT > 200 GeV for the Z-boson before parton showering, is 0.53 for POWHEG and 0.47 for aMC@NLO.
In conclusion, the high-pTZ → bbsignal has been observed and its production cross section measured in a fully hadronic fi-nal state, in 19.5 fb−1of proton–proton collisions at √s= 8 TeV recorded in 2012 by the ATLAS detector at the LHC. Within the fiducial region defined in Section 5, the production cross section is measured to be
σfid
Z→bb= 2.02 ± 0.20 (stat.) ± 0.25 (syst.) ± 0.06 (lumi.) pb and is found to be in good agreement with the NLO-plus-parton-shower predictions from POWHEG and aMC@NLO.
Acknowledgements
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.
We acknowledge the support of ANPCyT, Argentina; Yer-PhI, Armenia; ARC, Australia; BMWF and FWF, Austria;
ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colom-bia; MSMT CR, MPO CR and VSC CR, Czech Repub-lic; DNRF, DNSRC and Lundbeck Foundation, Denmark; EPLANET, ERC and NSRF, European Union; IN2P3-CNRS,
CEA-DSM/IRFU, France; GNSF, Georgia; BMBF, DFG, HGF,
MPG and AvH Foundation, Germany; GSRT and NSRF, Greece; ISF, MINERVA, GIF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Mo-rocco; FOM and NWO, Netherlands; BRF and RCN, Nor-way; MNiSW and NCN, Poland; GRICES and FCT, Portugal;
MNE/IFA, Romania; MES of Russia and ROSATOM, Russian
Federation; JINR; MSTD, Serbia; MSSR, Slovakia; ARRS and
MIZ ˇS, Slovenia; DST/NRF, South Africa; MINECO, Spain;
SRC and Wallenberg Foundation, Sweden; SER, SNSF and Cantons of Bern and Geneva, Switzerland; NSC, Taiwan; TAEK, Turkey; STFC, the Royal Society and Leverhulme Trust, United Kingdom; DOE and NSF, United States of Amer-ica.
The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN and the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF
(Den-mark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA
(Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA) and in the Tier-2 facilities worldwide.
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L. De Nooij106, D. De Pedis133a, A. De Salvo133a, U. De Sanctis165a,165b, A. De Santo150, J.B. De Vivie De Regie116, W.J. Dearnaley71, R. Debbe25, C. Debenedetti46, B. Dechenaux55, D.V. Dedovich64, I. Deigaard106, J. Del Peso81,
T. Del Prete123a,123b, F. Deliot137, C.M. Delitzsch49, M. Deliyergiyev74, A. Dell’Acqua30, L. Dell’Asta22, M. Dell’Orso123a,123b, M. Della Pietra103a,g, D. della Volpe49, M. Delmastro5, P.A. Delsart55, C. Deluca106, S. Demers177, M. Demichev64, A. Demilly79, S.P. Denisov129, D. Derendarz39, J.E. Derkaoui136d, F. Derue79, P. Dervan73, K. Desch21, C. Deterre42, P.O. Deviveiros106, A. Dewhurst130, S. Dhaliwal106, A. Di Ciaccio134a,134b, L. Di Ciaccio5, A. Di Domenico133a,133b, C. Di Donato103a,103b, A. Di Girolamo30, B. Di Girolamo30, A. Di Mattia153, B. Di Micco135a,135b, R. Di Nardo47, A. Di Simone48, R. Di Sipio20a,20b, D. Di Valentino29, M.A. Diaz32a, E.B. Diehl88, J. Dietrich42, T.A. Dietzsch58a, S. Diglio84, A. Dimitrievska13a, J. Dingfelder21, C. Dionisi133a,133b, P. Dita26a, S. Dita26a, F. Dittus30, F. Djama84, T. Djobava51b, M.A.B. do Vale24c, A. Do Valle Wemans125a,125g, T.K.O. Doan5, D. Dobos30, C. Doglioni49, T. Doherty53, T. Dohmae156, J. Dolejsi128, Z. Dolezal128, B.A. Dolgoshein97,∗, M. Donadelli24d, S. Donati123a,123b, P. Dondero120a,120b, J. Donini34, J. Dopke30, A. Doria103a, M.T. Dova70, A.T. Doyle53, M. Dris10, J. Dubbert88, S. Dube15, E. Dubreuil34, E. Duchovni173, G. Duckeck99, O.A. Ducu26a, D. Duda176, A. Dudarev30, F. Dudziak63, L. Duflot116, L. Duguid76, M. D¨uhrssen30, M. Dunford58a, H. Duran Yildiz4a, M. D¨uren52, A. Durglishvili51b, M. Dwuznik38a, M. Dyndal38a, J. Ebke99, W. Edson2, N.C. Edwards46, W. Ehrenfeld21, T. Eifert144, G. Eigen14, K. Einsweiler15, T. Ekelof167, M. El Kacimi136c, M. Ellert167, S. Elles5, F. Ellinghaus82, N. Ellis30, J. Elmsheuser99, M. Elsing30, D. Emeliyanov130, Y. Enari156, O.C. Endner82, M. Endo117, R. Engelmann149, J. Erdmann177, A. Ereditato17, D. Eriksson147a, G. Ernis176, J. Ernst2, M. Ernst25, J. Ernwein137, D. Errede166, S. Errede166, E. Ertel82, M. Escalier116, H. Esch43, C. Escobar124, B. Esposito47, A.I. Etienvre137, E. Etzion154, H. Evans60, A. Ezhilov122, L. Fabbri20a,20b, G. Facini31, R.M. Fakhrutdinov129, S. Falciano133a, R.J. Falla77, J. Faltova128, Y. Fang33a, M. Fanti90a,90b, A. Farbin8, A. Farilla135a, T. Farooque12, S. Farrell164, S.M. Farrington171, P. Farthouat30, F. Fassi168, P. Fassnacht30, D. Fassouliotis9, A. Favareto50a,50b, L. Fayard116, P. Federic145a, O.L. Fedin122,i, W. Fedorko169, M. Fehling-Kaschek48, S. Feigl30, L. Feligioni84, C. Feng33d, E.J. Feng6, H. Feng88, A.B. Fenyuk129,
S. Fernandez Perez30, S. Ferrag53, J. Ferrando53, A. Ferrari167, P. Ferrari106, R. Ferrari120a, D.E. Ferreira de Lima53, A. Ferrer168, D. Ferrere49, C. Ferretti88, A. Ferretto Parodi50a,50b, M. Fiascaris31, F. Fiedler82, A. Filipˇciˇc74, M. Filipuzzi42, F. Filthaut105, M. Fincke-Keeler170, K.D. Finelli151, M.C.N. Fiolhais125a,125c, L. Fiorini168, A. Firan40, J. Fischer176, W.C. Fisher89, E.A. Fitzgerald23, M. Flechl48, I. Fleck142, P. Fleischmann88, S. Fleischmann176, G.T. Fletcher140, G. Fletcher75, T. Flick176, A. Floderus80, L.R. Flores Castillo174, A.C. Florez Bustos160b, M.J. Flowerdew100, A. Formica137, A. Forti83, D. Fortin160a, D. Fournier116, H. Fox71, S. Fracchia12, P. Francavilla79, M. Franchini20a,20b, S. Franchino30, D. Francis30, M. Franklin57, S. Franz61, M. Fraternali120a,120b, S.T. French28, C. Friedrich42, F. Friedrich44, D. Froidevaux30, J.A. Frost28, C. Fukunaga157, E. Fullana Torregrosa82, B.G. Fulsom144, J. Fuster168, C. Gabaldon55, O. Gabizon173, A. Gabrielli20a,20b, A. Gabrielli133a,133b, S. Gadatsch106, S. Gadomski49, G. Gagliardi50a,50b, P. Gagnon60, C. Galea105, B. Galhardo125a,125c, E.J. Gallas119, V. Gallo17, B.J. Gallop130, P. Gallus127, G. Galster36, K.K. Gan110, R.P. Gandrajula62, J. Gao33b, f, Y.S. Gao144,e, F.M. Garay Walls46, F. Garberson177, C. Garc´ıa168, J.E. Garc´ıa Navarro168, M. Garcia-Sciveres15, R.W. Gardner31, N. Garelli144, V. Garonne30, C. Gatti47, G. Gaudio120a, B. Gaur142, L. Gauthier94, P. Gauzzi133a,133b, I.L. Gavrilenko95, C. Gay169, G. Gaycken21, E.N. Gazis10, P. Ge33d, Z. Gecse169, C.N.P. Gee130, D.A.A. Geerts106, Ch. Geich-Gimbel21, K. Gellerstedt147a,147b, C. Gemme50a, A. Gemmell53, M.H. Genest55, S. Gentile133a,133b, M. George54, S. George76, D. Gerbaudo164, A. Gershon154, H. Ghazlane136b, N. Ghodbane34,
B. Giacobbe20a, S. Giagu133a,133b, V. Giangiobbe12, P. Giannetti123a,123b, F. Gianotti30, B. Gibbard25, S.M. Gibson76, M. Gilchriese15, T.P.S. Gillam28, D. Gillberg30, G. Gilles34, D.M. Gingrich3,d, N. Giokaris9, M.P. Giordani165a,165c,
R. Giordano103a,103b, F.M. Giorgi20a, F.M. Giorgi16, P.F. Giraud137, D. Giugni90a, C. Giuliani48, M. Giulini58b, B.K. Gjelsten118, S. Gkaitatzis155, I. Gkialas155, j, L.K. Gladilin98, C. Glasman81, J. Glatzer30, P.C.F. Glaysher46, A. Glazov42, G.L. Glonti64, M. Goblirsch-Kolb100, J.R. Goddard75, J. Godfrey143, J. Godlewski30, C. Goeringer82, S. Goldfarb88, T. Golling177, D. Golubkov129, A. Gomes125a,125b,125d, L.S. Gomez Fajardo42, R. Gonc¸alo125a, J. Goncalves Pinto Firmino Da Costa137, L. Gonella21, S. Gonz´alez de la Hoz168, G. Gonzalez Parra12, M.L. Gonzalez Silva27, S. Gonzalez-Sevilla49, L. Goossens30, P.A. Gorbounov96, H.A. Gordon25, I. Gorelov104, B. Gorini30, E. Gorini72a,72b, A. Goriˇsek74, E. Gornicki39, A.T. Goshaw6, C. G¨ossling43, M.I. Gostkin64, M. Gouighri136a, D. Goujdami136c, M.P. Goulette49, A.G. Goussiou139, C. Goy5, S. Gozpinar23, H.M.X. Grabas137, L. Graber54, I. Grabowska-Bold38a, P. Grafstr¨om20a,20b, K-J. Grahn42, J. Gramling49, E. Gramstad118, S. Grancagnolo16, V. Grassi149, V. Gratchev122, H.M. Gray30, E. Graziani135a, O.G. Grebenyuk122, Z.D. Greenwood78,k, K. Gregersen77, I.M. Gregor42, P. Grenier144, J. Griffiths8, A.A. Grillo138, K. Grimm71, S. Grinstein12,l, Ph. Gris34, Y.V. Grishkevich98, J.-F. Grivaz116, J.P. Grohs44, A. Grohsjean42, E. Gross173, J. Grosse-Knetter54, G.C. Grossi134a,134b, J. Groth-Jensen173, Z.J. Grout150, L. Guan33b, F. Guescini49, D. Guest177, O. Gueta154, C. Guicheney34, E. Guido50a,50b,
T. Guillemin116, S. Guindon2, U. Gul53, C. Gumpert44, J. Gunther127, J. Guo35, S. Gupta119, P. Gutierrez112, N.G. Gutierrez Ortiz53, C. Gutschow77, N. Guttman154, C. Guyot137, C. Gwenlan119, C.B. Gwilliam73, A. Haas109, C. Haber15, H.K. Hadavand8,
N. Haddad136e, P. Haefner21, S. Hageboeck21, Z. Hajduk39, H. Hakobyan178, M. Haleem42, D. Hall119, G. Halladjian89, K. Hamacher176, P. Hamal114, K. Hamano170, M. Hamer54, A. Hamilton146a, S. Hamilton162, P.G. Hamnett42, L. Han33b,
K. Hanagaki117, K. Hanawa156, M. Hance15, P. Hanke58a, R. Hanna137, J.B. Hansen36, J.D. Hansen36, P.H. Hansen36, K. Hara161, A.S. Hard174, T. Harenberg176, S. Harkusha91, D. Harper88, R.D. Harrington46, O.M. Harris139, P.F. Harrison171, F. Hartjes106, S. Hasegawa102, Y. Hasegawa141, A. Hasib112, S. Hassani137, S. Haug17, M. Hauschild30, R. Hauser89, M. Havranek126,
C.M. Hawkes18, R.J. Hawkings30, A.D. Hawkins80, T. Hayashi161, D. Hayden89, C.P. Hays119, H.S. Hayward73, S.J. Haywood130, S.J. Head18, T. Heck82, V. Hedberg80, L. Heelan8, S. Heim121, T. Heim176, B. Heinemann15, L. Heinrich109, S. Heisterkamp36, J. Hejbal126, L. Helary22, C. Heller99, M. Heller30, S. Hellman147a,147b, D. Hellmich21, C. Helsens30, J. Henderson119,
R.C.W. Henderson71, C. Hengler42, A. Henrichs177, A.M. Henriques Correia30, S. Henrot-Versille116, C. Hensel54, G.H. Herbert16, Y. Hern´andez Jim´enez168, R. Herrberg-Schubert16, G. Herten48, R. Hertenberger99, L. Hervas30, G.G. Hesketh77, N.P. Hessey106, R. Hickling75, E. Hig´on-Rodriguez168, E. Hill170, J.C. Hill28, K.H. Hiller42, S. Hillert21, S.J. Hillier18, I. Hinchliffe15, E. Hines121, M. Hirose158, D. Hirschbuehl176, J. Hobbs149, N. Hod106, M.C. Hodgkinson140, P. Hodgson140, A. Hoecker30, M.R. Hoeferkamp104, J. Hoffman40, D. Hoffmann84, J.I. Hofmann58a, M. Hohlfeld82, T.R. Holmes15, T.M. Hong121, L. Hooft van Huysduynen109, J-Y. Hostachy55, S. Hou152, A. Hoummada136a, J. Howard119, J. Howarth42, M. Hrabovsky114, I. Hristova16, J. Hrivnac116,
T. Hryn’ova5, P.J. Hsu82, S.-C. Hsu139, D. Hu35, X. Hu25, Y. Huang42, Z. Hubacek30, F. Hubaut84, F. Huegging21, T.B. Huffman119, E.W. Hughes35, G. Hughes71, M. Huhtinen30, T.A. H¨ulsing82, M. Hurwitz15, N. Huseynov64,b, J. Huston89, J. Huth57,
G. Iacobucci49, G. Iakovidis10, I. Ibragimov142, L. Iconomidou-Fayard116, E. Ideal177, P. Iengo103a, O. Igonkina106, T. Iizawa172, Y. Ikegami65, K. Ikematsu142, M. Ikeno65, Y. Ilchenko31,m, D. Iliadis155, N. Ilic159, Y. Inamaru66, T. Ince100, P. Ioannou9,
M. Iodice135a, K. Iordanidou9, V. Ippolito57, A. Irles Quiles168, C. Isaksson167, M. Ishino67, M. Ishitsuka158, R. Ishmukhametov110, C. Issever119, S. Istin19a, J.M. Iturbe Ponce83, R. Iuppa134a,134b, J. Ivarsson80, W. Iwanski39, H. Iwasaki65, J.M. Izen41, V. Izzo103a, B. Jackson121, M. Jackson73, P. Jackson1, M.R. Jaekel30, V. Jain2, K. Jakobs48, S. Jakobsen30, T. Jakoubek126, J. Jakubek127, D.O. Jamin152, D.K. Jana78, E. Jansen77, H. Jansen30, J. Janssen21, M. Janus171, G. Jarlskog80, N. Javadov64,b, T. Jav˚urek48, L. Jeanty15, J. Jejelava51a,n, G.-Y. Jeng151, D. Jennens87, P. Jenni48,o, J. Jentzsch43, C. Jeske171, S. J´ez´equel5, H. Ji174, W. Ji82, J. Jia149, Y. Jiang33b, M. Jimenez Belenguer42, S. Jin33a, A. Jinaru26a, O. Jinnouchi158, M.D. Joergensen36, K.E. Johansson147a, P. Johansson140, K.A. Johns7, K. Jon-And147a,147b, G. Jones171, R.W.L. Jones71, T.J. Jones73, J. Jongmanns58a, P.M. Jorge125a,125b, K.D. Joshi83, J. Jovicevic148, X. Ju174, C.A. Jung43, R.M. Jungst30, P. Jussel61, A. Juste Rozas12,l, M. Kaci168, A. Kaczmarska39, M. Kado116, H. Kagan110, M. Kagan144, E. Kajomovitz45, C.W. Kalderon119, S. Kama40, N. Kanaya156, M. Kaneda30, S. Kaneti28, T. Kanno158, V.A. Kantserov97, J. Kanzaki65, B. Kaplan109, A. Kapliy31, D. Kar53, K. Karakostas10, N. Karastathis10,
M. Karnevskiy82, S.N. Karpov64, K. Karthik109, V. Kartvelishvili71, A.N. Karyukhin129, L. Kashif174, G. Kasieczka58b,
R.D. Kass110, A. Kastanas14, Y. Kataoka156, A. Katre49, J. Katzy42, V. Kaushik7, K. Kawagoe69, T. Kawamoto156, G. Kawamura54, S. Kazama156, V.F. Kazanin108, M.Y. Kazarinov64, R. Keeler170, R. Kehoe40, M. Keil54, J.S. Keller42, J.J. Kempster76,
H. Keoshkerian5, O. Kepka126, B.P. Kerˇsevan74, S. Kersten176, K. Kessoku156, J. Keung159, F. Khalil-zada11,
H. Khandanyan147a,147b, A. Khanov113, A. Khodinov97, A. Khomich58a, T.J. Khoo28, G. Khoriauli21, A. Khoroshilov176, V. Khovanskiy96, E. Khramov64, J. Khubua51b, H.Y. Kim8, H. Kim147a,147b, S.H. Kim161, N. Kimura172, O. Kind16, B.T. King73, M. King168, R.S.B. King119, S.B. King169, J. Kirk130, A.E. Kiryunin100, T. Kishimoto66, D. Kisielewska38a, F. Kiss48,
T. Kitamura66, T. Kittelmann124, K. Kiuchi161, E. Kladiva145b, M. Klein73, U. Klein73, K. Kleinknecht82, P. Klimek147a,147b, A. Klimentov25, R. Klingenberg43, J.A. Klinger83, T. Klioutchnikova30, P.F. Klok105, E.-E. Kluge58a, P. Kluit106, S. Kluth100, E. Kneringer61, E.B.F.G. Knoops84, A. Knue53, T. Kobayashi156, M. Kobel44, M. Kocian144, P. Kodys128, P. Koevesarki21, T. Koffas29, E. Koffeman106, L.A. Kogan119, S. Kohlmann176, Z. Kohout127, T. Kohriki65, T. Koi144, H. Kolanoski16, I. Koletsou5, J. Koll89, A.A. Komar95,∗, Y. Komori156, T. Kondo65, N. Kondrashova42, K. K¨oneke48, A.C. K¨onig105, S. K¨onig82, T. Kono65,p, R. Konoplich109,q, N. Konstantinidis77, R. Kopeliansky153, S. Koperny38a, L. K¨opke82, A.K. Kopp48, K. Korcyl39, K. Kordas155,
