Study of the inclusive production of charged pions, kaons, and protons in pp collisions at sqrt(s) = 0.9, 2.76, and 7 TeV

2.4 MB·English

by  CMS Collaboration

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP/2012-202
2012/07/20
CMS-FSQ-12-014
Study of the inclusive production of charged pions, kaons,
√
and protons in pp collisions at s = 0.9, 2.76, and 7TeV
2 ∗
The CMS Collaboration
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x
e
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p Spectra of identified charged hadrons are measured in pp collisions at the LHC for
√
e
h s = 0.9, 2.76, and 7TeV. Charged pions, kaons, and protons in the transverse-
[ momentum range p ≈ 0.1–1.7GeV/c and for rapidities |y| < 1 are identified via
T
1 their energy loss in the CMS silicon tracker. The average pT increases rapidly with
v themassofthehadronandtheeventcharged-particlemultiplicity,independentlyof
4
the center-of-mass energy. The fully corrected p spectra and integrated yields are
2 T
7 comparedtovarioustunesofthe PYTHIA6and PYTHIA8eventgenerators.
4
.
7
0 SubmittedtotheEuropeanPhysicalJournalC
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1
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∗SeeAppendixAforthelistofcollaborationmembers

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1 Introduction
Thestudyofhadronproductionhasalonghistoryinhigh-energyparticleandnuclearphysics,
aswellascosmic-rayphysics. Theabsoluteyieldsandthetransversemomentum(p )spectra
T
of identified hadrons in high-energy hadron-hadron collisions are among the basic physical
observables that can be used to test the predictions for non-perturbative quantum chromody-
namicsprocesseslikehadronizationandsoftpartoninteractions, andtheirimplementationin
Monte Carlo (MC) event generators. The dependence of these quantities on the hardness of
theppcollisionprovidesvaluableinformationonmulti-partoninteractionsaswellasonother
final-state effects. In addition, the measurements of baryon (and notably proton) production
arenotreproducedbytheexistingmodels,andmoredataathigherenergymayhelpimprov-
ing the models. Spectra of identified particles in proton-proton (pp) collisions also constitute
an important reference for high-energy heavy-ion studies, where final-state effects are known
tomodifythespectralshapeandyieldsofdifferenthadronspecies.
The present analysis focuses on the measurement of the p spectra of charged hadrons, iden-
T √
tified mostly via their energy deposits in silicon detectors, in pp collisions at s = 0.9, 2.76,
and 7TeV. In certain phase space regions, particles can be identified unambiguously while
in other regions the energy loss measurements provide less discrimination power and more
sophisticatedmethodsarenecessary.
Thispaperisorganizedasfollows. TheCompactMuonSolenoid(CMS)detector,operatingat
theLargeHadronCollider(LHC),isdescribedinSection2. Elementsofthedataanalysis,such
aseventselection,trackingofchargedparticles,identificationofinteractionvertices,andtreat-
ment of secondary particles are discussed in Section 3. The applied energy loss parametriza-
tion,theestimationofenergydepositsinthesilicon,andthecalculationoftheenergylossrate
oftracksareexplainedinSection4. InSection5thevariousaspectsoftheunfoldingofparticle
yieldsaredescribed. Afteradetaileddiscussionoftheappliedcorrections(Section6),thefinal
resultsareshowninSection7andsummarizedintheconclusions.
2 The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6m internal diam-
eter. Withinthefieldvolumearethesiliconpixelandstriptracker,thecrystalelectromagnetic
calorimeter,andthebrass/scintillatorhadroncalorimeter. Inadditiontothebarrelandendcap
detectors, CMS has extensive forward calorimetry. CMS uses a right-handed coordinate sys-
tem,withtheoriginatthenominalinteractionpointandthezaxisalongthecounterclockwise
beam direction. The pseudorapidity and rapidity of a particle with energy E, momentum p,
and momentum along the z axis p are defined as η = −lntan(θ/2) where θ is the polar an-
z
gle with respect to the z axis and y = 1 ln[(E+ p )/(E− p )], respectively. A more detailed
2 z z
descriptionofCMScanbefoundinRef.[1].
Two elements of the CMS detector monitoring system, the beam scintillator counters (BSCs)
andthebeampick-uptimingfortheexperiments(BPTX)devices,wereusedtotriggerthede-
tectorreadout. ThetwoBSCsarelocatedatadistanceof±10.86mfromthenominalinteraction
point(IP)andaresensitivetoparticlesinthe|η|rangefrom3.23to4.65. EachBSCisasetof16
scintillatortiles. TheBSCelementsaredesignedtoprovidehitandcoincidencerates. Thetwo
BPTXdevices, locatedaroundthebeampipeatadistanceof175mfromtheIPoneitherside,
aredesignedtoprovidepreciseinformationonthebunchstructureandtimingoftheincoming
beam. Asteel/quartz-fibreforwardcalorimeter(HF)coverstheregionof|η|betweenabout3.0
and5.0. TheHF towersegmentationin η andazimuthal angle φ is0.175×0.175, except for |η|
2 2 TheCMSdetector
CMS Simulation CMS Simulation
3.5 2
e e
π π
3 K K
p p
1.1 1.5
m]) 2.5
c 1.05 c]
V/ V/
e 2 e 1
M G
ε/[ 1 [T
g( p
o 1.5
l 0.95
1 2 3 4 5 0.5
1
0.5 0
0.1 0.2 0.5 1 2 5 10 20 -3 -2 -1 0 1 2 3
p [GeV/c] y
Figure 1: Left: values of the most probable energy loss rate ε, at the reference path length
of 450µm in silicon, for electrons, pions, kaons and protons [2]. The inset shows the region
1 < p < 5GeV/c. Right: for each particle, the accessible (y,p ) area is contained between the
T
upper thicker (determined by particle identification capabilities) and the lower thinner lines
(determinedbyacceptanceandefficiency). MoredetailsaregiveninSection2.1.
above4.7wherethesegmentationis0.175×0.35.
Thetrackermeasureschargedparticleswithinthepseudorapidityrange |η| < 2.4. Ithas1440
silicon pixel and 15148 silicon strip detector modules and is located in the 3.8 T field of the
solenoid. The pixel detector [3] consists of three barrel layers (PXB) at radii of 4.4, 7.3, and
10.2cmaswellastwoendcapdisks(PXF)oneachsideofthePXB.Thedetectorunitsareseg-
mented n-on-n silicon sensors of 285µm thickness. Each readout chip serves a 52×80 array
of150µm×100µmpixels. Inthedataacquisitionsystem,zerosuppressionisperformedwith
adjustable thresholds for each pixel. Offline, pixel clusters are formed from adjacent pixels,
includingbothside-by-sideandcorner-by-corneradjacentpixels. Thestriptracker[4]employs
p-in-nsiliconwafers. Itispartitionedintodifferentsubstructures: thetrackerinnerbarrel(TIB)
andthetrackerinnerdisks(TID)aretheinnermostpartwith320µmthicksensors,surrounded
bythetrackerouterbarrel(TOB)with500µmthicksensors. Onbothsides,thetrackeriscom-
pleted by endcaps with a mixture of 320µm thick sensors (TEC3) and 500µm thick sensors
(TEC5). The first two layers of TIB and TOB and some of the TID and TEC contain “stereo”
modules: two silicon modules mounted back-to-back with a 100mrad angle to provide two-
dimensional hit resolution. Each readout chip serves 128 strips. Algorithms are run in the
Front-EndDrivers(FED)toperformpedestalsubtraction,common-modesubtractionandzero
suppression. Only a small fraction of the channels are read out in one event. Offline, clusters
are formed by combining contiguous hits. The tracker provides an impact-parameter resolu-
tionof∼15µmandanabsolutep resolutionofabout0.02GeV/cintherangep ≈0.1–2GeV/c,
T T
ofrelevancehere.
2.1 Particle identification capabilities
The identification of charged particles is often based on the relationship between energy loss
rate and total momentum (Fig. 1, left). Particle reconstruction at CMS is limited by the accep-
tance (C ) of the tracker (|η| < 2.4) and by the low tracking efficiency (C ) at low momentum
a e
(p > 0.05, 0.10, 0.20, and 0.35GeV/c for e, π, K, and p, respectively), while particle identi-
fication capabilities are restricted to p < 0.15GeV/c for electrons, p < 1.20GeV/c for pions,
3
p < 1.05GeV/c forkaons, and p < 1.70GeV/c forprotons(Fig.1, left). Pionsareaccessibleup
to a higher momentum than kaons because of their high relative abundance, as discussed in
Section 5.2. The (y,p ) region where pions, kaons and protons can all be identified is visible
T
in the rightpanel of Fig. 1. The region −1 < y < 1 was chosen for the measurement, since it
maximizesthe p coverage.
T
3 Data analysis
The0.9and7TeVdataweretakenduringtheinitiallowmultiple-interactionrate(low“pileup”)
runs in early 2010, while the 2.76TeV data were collected in early 2011. The requirement of
similar amounts of produced particles at the three center-of-mass energies and that of small
√
averagenumberofpileupinteractionsledto8.80,6.74and6.20millioneventsfor s =0.9TeV,
2.76TeV,and7TeV,respectively. Thecorrespondingintegratedluminositiesare0.227±0.024nb−1,
0.143±0.008nb−1 and0.115±0.005nb−1 [5,6],respectively.
3.1 Event selection and related corrections
Theeventselectionconsistsofthefollowingrequirements:
• at the trigger level, the coincidence of signals from both BPTX devices, indicating
the presence of both proton bunches crossing the interaction point, along with the
presenceofsignalsfromeitheroftheBSCs;
• offline,thepresenceofatleastonetowerwithenergyabove3GeVineachoftheHF
calorimeters;atleastonereconstructedinteractionvertex(Section3.3);thesuppres-
sionofbeam-haloandbeam-inducedbackgroundevents,whichusuallyproducean
anomalouslylargenumberofpixelhits[7].
The efficiencies for event selection, tracking, and vertexing were evaluated by means of sim-
ulated event samples produced with the PYTHIA 6.420 [8] MC event generator at each of the
three center-of-mass energies. The events were reconstructed in the same way as the colli-
sion data. The PYTHIA tunes D6T [9], Z1, and Z2 [10] were chosen, since they describe the
measured event properties reasonably well, notably the reconstructed track multiplicity dis-
tribution. Tune D6T is a pre-LHC tune with virtuality-ordered showers using the CTEQ6L
partondistributionfunctions(PDF).ThetunesZ1andZ2arebasedontheearlyLHCdataand
generate p -orderedshowersusingtheCTEQ5LandCTEQ6LPDFs,respectively.
T
The final results were corrected to a particle level selection, which is very similar to the ac-
tual selection described above: at least one particle (τ > 10−18s) with E > 3GeV in the range
−5 < η < −3 and one in the range 3 < η < 5; this selection is referred to in the follow-
ing as “double-sided” (DS) selection. The overall efficiency of the DS selection for a zero-bias
sample,accordingto PYTHIA,isabout66-72%(0.9TeV),70-76%(2.76TeV),and73-78%(7TeV).
The ranges given represent the spread of the predictions of the different tunes. Mostly non-
diffractive (ND) events are selected, with efficiencies in the 88-98% range, but a smaller frac-
tionofdouble-diffractive(DD)events(32-38%),andsingle-diffractivedissociation(SD)events
are accepted (13-26%) as well. About 90% of the selected events are ND, while the rest are
DD or SD, in about equal measure. In order to compare to measurements with a non-single-
diffractive(NSD)selection,theparticleyieldsgiveninthisstudyshouldbedividedbyfactors
√
of 0.86, 0.89, and 0.91 according to PYTHIA, for s = 0.9, 2.76, and 7TeV, respectively. The
systematicuncertaintyonthesenumbersduetothetunedependenceisabout3%.
4 3 Dataanalysis
CMS
1.4
0.9 TeV
2.76 TeV
s 1.3 7 TeV
nt
e
v
e 1.2
S
D
o 1.1
d t
e
ect 1
el
s
of 0.9
o
ati
R 0.8
0.7
0 10 20 30 40 50 60
Reconstructed primary tracks
Figure 2: The ratio of selected events to double-sided events (ratio of the corresponding effi-
ciencies in the inelastic sample), according to the PYTHIA6 tunes (0.9TeV– D6T, 2.76TeV– Z2,
7TeV–Z1),asafunctionofthereconstructedprimarychargedtrackmultiplicity.
TheratiosofthedataselectionefficiencytotheDSselectionefficiencyareshownasafunction
of the reconstructed track multiplicity in Fig. 2 for the three center-of-mass energies studied.
The ratios are used to correct the measured events; they are approximately independent of
the PYTHIA tune. The different behavior of the 2.76TeV data results from a change in the HF
configuration in 2011. The results are also corrected for the fraction of DS events without a
reconstructed track. This fraction, as given by the simulation, is about 4%, 3%, and 2.5% for
0.9, 2.76, and 7TeV, respectively. Since these events do not contain reconstructed tracks, only
theeventyieldmustbecorrected.
3.2 Tracking of charged particles
Theextrapolationofparticlespectraintotheunmeasuredregionsismodeldependent, partic-
ularly at low p . A good measurement therefore requires reliable track reconstruction down
T
to the lowest possible p . The present analysis extends to p ≈ 0.1GeV/c by exploiting spe-
T T
cial tracking algorithms [11], used in previous studies [7, 12], to provide high reconstruction
efficiencyandlowbackgroundrate.
The performance of the charged-particle tracking was quantified in terms of the geometrical
acceptance, thetrackingefficiency, andthefractionofmisreconstructedtracks; allthesequan-
tities were evaluated by means of simulated events and validated in previous studies [7, 12].
The acceptance of the tracker (when at least two pixel hits are required) is flat in the region
−2 < η < 2 and p > 0.4GeV/c, and its value is about 96–98%. The loss of acceptance at
T
p < 0.4GeV/c is caused by energy loss and multiple scattering of particles, which both de-
T
pend on the particle mass. Likewise, the reconstruction efficiency is about 80-90%, degrading
at low p , also in a mass-dependent way. The misreconstructed-track rate (C ) is very small,
T f
reaching 0.3% only for p < 0.25GeV/c; it rises slightly above 2GeV/c because of the steeply
T
falling p distribution. The probability of reconstructing multiple tracks (C ) from a true sin-
T m
gle track is about 0.1% – mostly due to particles spiralling in the strong magnetic field. The
efficiencies and background rates largely factorize in η and p , but for the final corrections an
T
(η,p )gridisused.
T
3.3 Vertexingandsecondaryparticles 5
Table 1: Standard deviation of the vertex z coordinate distribution (σ ) and average number
z
ofpileupeventsforthethreecenter-of-massenergiesstudied. Thelasttwocolumnsshowthe
estimatedfractionofmergedandsplitvertices. Moredetailsaregiveninthetext.
Energy σ (cid:104)pileup(cid:105) Merged Split
z
0.9TeV 6.67cm 0.016 5·10−4 ∼10−3
2.76TeV 6.23cm 0.094 3·10−3 ∼10−3
7TeV 3.08cm 0.009 6·10−4 ∼10−3
3.3 Vertexing and secondary particles
The region where pp collisions occur (beam spot) is well measured by reconstructing vertices
frommanyevents. Sincethebunchesareverynarrow,thetransversepositionoftheinteraction
vertices is well constrained; conversely, their z coordinates are spread over a relatively long
distance and must be determined on an event-by-event basis. Reconstructed tracks are used
fordeterminingthevertexpositioniftheyhave p > 0.1GeV/candoriginatefromthevicinity
T
of the beam spot, i.e. their transverse impact parameter satisfies the condition d < 3σ ; here
T T
σ is the quadratic sum of the uncertainty of d and the RMS of the beam spot distribution in
T T
the transverse plane. The agglomerative vertex-reconstruction algorithm [13] was used, with
the z coordinates (and their uncertainty) of the tracks at the point of closest approach to the
beamaxisasinput. Thisalgorithmkeepsclusteringtracksintoverticesaslongasthesmallest
distance between the vertices of the remaining groups of tracks, divided by its uncertainty,
is below 35. Simulations indicate that this value minimizes the number of merged vertices
(vertices with tracks from two or more true vertices) and split vertices (two or more vertices
with tracks from a single true vertex). For single-vertex events, there is no lower limit on the
number of tracks associated to the vertex. If multiple vertices are present, only those with at
leastthreetracksarekept.
The distribution of the z coordinates of the reconstructed primary vertices is Gaussian, with
standard deviations of 6cm at 0.9 and 2.76TeV, and 3cm at 7TeV. The simulated data were
reweightedsoastohavethesamevertexzcoordinatedistributionsasthedata. Thedistribution
ofthedistance∆zbetweenverticeswasusedtoquantifytheeffectofpileupandthequalityof
vertexreconstruction. Thereisanemptyregionaround∆z = 0,whichcorrespondstocasesin
whichtwotrueverticesarecloserthanabout0.4cmtoeachotherandaremergedduringvertex
reconstruction. The ∆z distribution was therefore used to determine the fraction of merged
(and thus lost) vertices, and to estimate the fraction of split vertices (via the non-Gaussian
tails). Botheffectsareatthe0.1%levelandwereneglectedinthisstudy.
ThenumberofprimaryverticesinabunchcrossingfollowsaPoissondistribution. Thefraction
ofeventswithmorethanonevertex(duetopileup)issmallinthe0.9and7TeVdata(1.6%and
0.9%, respectively), but is 9.4% at 2.76TeV. The interaction-region and pileup parameters are
summarized in Table 1. For the 0.9 and 2.76TeV data, bunch crossings with either one or two
reconstructedverticeswereused,whileforthe7TeVdatatheanalysiswasrestrictedtoevents
with a single reconstructed vertex to suppress the larger background from pileup, split and
mergedvertices.
The hadron spectra were corrected for particles of non-primary origin. The main source of
secondary particles is the feed-down from weakly decaying particles, mostly K0, Λ/Λ, and
S
Σ+/Σ−. Whilethecorrection(C )isaround1%forpions,itisupto15%forprotonswith p ≈
s T
0.2GeV/c. This is expected because the daughter p or p takes most of the momentum of the
6 4 Energydepositsandestimationofenergylossrate
Table 2: Properties of several strip subdetectors evaluated by using hits on tracks with close-
to-normal incidence: readout threshold t, coupling parameter α , standard deviation σ of the
c n
Gaussiannoise. Thethreevaluesgivenforα andσ areforthe0.9,2.76,and7TeVdatasets.
c n
t σ
n
Detector α
c
[keV] [keV]
TIB 9.6 0.091,0.077,0.096 6.9,7.0,6.9
TID 8.5 0.076,0.068,0.081 7.2,7.6,7.2
TOB 15.3 0.116,0.094,0.124 9.2,10.3,9.6
TEC3 8.5 0.059,0.059,0.072 6.3,6.9,6.4
TEC5 14.1 0.094,0.086,0.120 8.6,9.7,9.0
Λ Λ
primary / ,andthereforehasahigherprobabilityofbeing(mistakenly)fittedtotheprimary
vertex than a pion from a K0 decay. Since none of the weakly decaying particles mentioned
S
decayintokaons,thecorrectionforkaonsissmall. Thecorrectionswerederivedfrom PYTHIA
and cross-checked with data [14] by comparing measured and predicted spectra of particles.
Λ Λ
Whiledataandsimulationgenerallyagree,the / correctionhadtobemultipliedbyafactor
of1.6.
For p < 0.15GeV/c, electrons can be clearly identified. According to PYTHIA, the overall e±
contaminationofthehadronyieldsisbelow0.2%. Althoughmuonscannotbeseparatedfrom
pions,theirfractionisnegligible,below0.05%. Sincebothcontaminationsaresmallnocorrec-
tionswereapplied.
4 Energy deposits and estimation of energy loss rate
The silicon layers of the tracker are thin and the energy depositions do not follow a Gaussian
distribution,butexhibitalongtailathighvalues. Ideally,theestimatesoftheenergylossrate
should not depend on the path lengths of the track through the sensitive parts of the silicon
or on the detector details. However this is not the case with the often used truncated, power,
or weighted means of the differential deposits, ∆E/∆x. Some of the dependence on the path
length can be corrected for, but a method based on the proper knowledge of the underlying
physicalprocessesispreferable.
In the present paper a novel analytical parametrization [15] has been used to approximate
the energy loss of charged particles. The method provides the probability density p(y|ε,l) of
energy deposit y, if the most probable energy loss rate ε at a reference path-length l and the
0
path-length l are known. The method can be used in conjunction with a maximum likelihood
estimation. Thedepositedenergyisestimatedfromthemeasuredchargedepositsinindividual
channels (pixels or strips) contributing to hit clusters. Deposits below the readout threshold
or above the saturation level of the readout electronics are estimated from the length of the
tracksegmentinthesilicon. Thisresultsinawideraccessibleenergydepositrangeandbetter
particle identification power. The method can be applied to the energy loss rate estimation of
tracksandtocalibratethegainofthetrackerdetectorfront-endelectronics. Inthisanalysis,for
each track, the estimated ε value at l = 450µm was used for particle identification and yield
0
determination.
For pixel clusters, the energy deposits (and their variances) were calculated as the sum of in-
dividual pixel deposits (and variances). The noise contribution is Gaussian, with a standard
deviation σ ≈ 10keV per pixel. In the case of strips, the energy deposits were corrected for
n
4.1 Detectorgaincalibrationwithtracks 7
capacitive coupling and cross-talk between neighboring strips. The readout threshold t, the
coupling parameter α , and the standard deviation σ of the Gaussian noise for strips were
c n
determinedfromthedata,bymeansoftrackswithclose-to-normalincidence(Table2).
Table 3: Tight requirements for approximate particle identification. All ε values are functions
of p. Subscripts π, K, and p refer to the most probable value for a given particle species, as
expectedfromsimulation.
Particle Momentum Mostprobableenergylossrate
pion 0.15 < p < 0.70GeV/c ε < (ε +ε )/2
π K
kaon p < 0.70GeV/c (ε +ε )/2 < ε < (ε +ε )/2
π K K p
proton p < 1.40GeV/c (ε +ε )/2 < ε
K p
4.1 Detector gain calibration with tracks
Foranaccuratedeterminationofε,itiscrucialtocalibratetheresponseofallreadoutchips. Itis
alsoimportanttocomparethemeasuredenergydepositspectratotheenergylossparametriza-
tion,andintroducecorrectionsifneeded.
The value of ε was estimated for each track using an initial gain calibration of the pixel and
stripreadoutchips. Approximateparticleidentificationwasperformedstartingfromasample
of identified tracks selected as follows: a track was identified as pion, kaon, or proton if its
momentum pandmostprobableenergylossrateεsatisfiedthetightrequirementslistedinTa-
ble3. Inaddition,trackswith p > 2GeV/c,orε < 3.2MeV/cm,orfromidentifiedK0 two-body
S
charged decays were assumed to be pions. Identified electrons were not used. The expected
ε,pathlength l,andenergydeposit y werecollectedforeachhit,andstoredforeveryreadout
chip separately. For each chip, the joint energy deposit log-likelihood, −2∑ logp(g·y |ε ,l ),
j j j j
ofallselectedhits(index j)wasminimizedbyvaryingthemultiplicativegaincorrection g. At
each center-of-mass energy, approximately 10% of the data were sufficient to perform a gain
calibration with sufficient resolution. The expected gain uncertainty is 0.5% on average for
pixelchipsand0.5-2%forstripsreadoutchips,dependingonthechipposition.
Afterthedetectorgaincalibration,theenergylossparametrizationwasvalidatedwithparticles
identifiedbytheselectiondiscussedabove. Asexamples, themeasuredenergydepositdistri-
butions of positively charged hadrons for different path lengths at βγ = p/m = 1.39 and 3.49
are shown for PXB and TIB in Fig. 3, for the 7TeV dataset. Similar results were obtained from
thedatatakenat0.9and2.76TeV. Separatecorrectionsforpositiveandnegativeparticleswere
necessary since some effects are not charge symmetric. The energy loss parametrization [15]
(solidlinesinthefigures)givesagooddescriptionofthedata. Inordertodescribedeviations
fromtheparametrization,weallowforanaffinetransformationofthetheoreticaldistributions
(logε → αlogε+δ),theparametersofwhicharedeterminedfromthehit-levelresiduals. The
scale factors (α) and the shifts (δ) are both functions of the βγ value of the particle and the
length of the track segment l in silicon. The scale factors are around unity for most βγ values
and increase to 1.2–1.4 for βγ < 2. Shifts (δ) are generally a few keV with deviations up to
10keVforβγ < 1. Aslightpath-lengthdependencewasfoundforbothscalefactorsandshifts.
Theobservedbehaviorofthesehit-levelresiduals,asafunctionof βγandl,wasparametrized
withpolynomials. Thesecorrectionswereappliedtoindividualhitsduringthedetermination
ofthelogεtemplates,asdescribedbelow.
8 4 Energydepositsandestimationofenergylossrate
CMS CMS
00000.....11111 000000......111111444444
pp √s = 7 TeV pp √s = 7 TeV
l = 270 µm, σ = 14.5 keV
00000.....0000099999 n
l = 300 µm, σ = 17.5 keV 000000......111111222222 l = 300 µm, σ = 9.5 keV
n n
-1-1-1-1-1MeV]MeV]MeV]MeV]MeV] 0000000000..........00000000007878787878 ll == 450000 µµmm,, σσnn == 1199..55 kkeeVV -1-1-1-1-1-1MeV]MeV]MeV]MeV]MeV]MeV] 000000......111111 ll == 450000 µµmm,, σσnn == 1102..55 kkeeVV
y [y [y [y [y [ 00000.....0000066666 l = 600 µm, σn = 22.5 keV y [y [y [y [y [y [ l = 600 µm, σn = 13.5 keV
ensitensitensitensitensit 00000.....0000055555 ensitensitensitensitensitensit 000000......000000888888 ll == 795000 µµmm,, σσn == 1145..55 kkeeVV
ddddd dddddd n
bility bility bility bility bility 00000.....0000044444 bility bility bility bility bility bility 000000......000000666666
bababababa 00000.....0000033333 babababababa 000000......000000444444
ooooo oooooo
PrPrPrPrPr 00000.....0000022222 PXB pos βγ = 1.39 PrPrPrPrPrPr TIB pos βγ = 3.49
000000......000000222222
00000.....0000011111
00000 000000
00000 00000.....11111 00000.....22222 00000.....33333 00000.....44444 00000.....55555 00000.....66666 000000 000000......111111 000000......222222 000000......333333 000000......444444 000000......555555 000000......666666
DDDDDeeeeepppppooooosssssiiiiittttt [[[[[MMMMMeeeeeVVVVV]]]]] DDDDDDeeeeeeppppppoooooossssssiiiiiitttttt [[[[[[MMMMMMeeeeeeVVVVVV]]]]]]
Figure 3: An example from the 7TeV dataset of the validation of the energy deposit
parametrization. The measured energy deposit distributions of identified hadrons at given
βγvaluesinthePXB(left)andTIB(right)areshown. Valuesaregivenforsiliconpathlengths
of l = 270, 300, 450, 600, 750, 900 and 1050µm, together with predictions of the parametriza-
tion(curves)alreadycontainingthehit-levelcorrections(scalefactorsandshifts). Theaverage
clusternoiseσ isalsogiven.
n
4.2 Estimation of the most probable energy loss rate for tracks
The best value of ε for each track was calculated with the corrected energy deposits. The logε
values in (η,p ) bins were then used in the yield unfolding (Section 5). Removal of hits with
T
incompatibleenergydepositsandthecreationoffittemplates,givingtheexpectedlogεdistri-
butionsforallparticlespecies(electrons,pions,kaons,andprotons),arediscussedhere.
Thevalueofεwasestimatedbyminimizingthejointenergydepositnegativelog-likelihoodof
allhitsonthetrajectory(indexi),χ2 = −2∑ logp(y |ε,l ). Distributionsoflogεasafunctionof
i i i
totalmomentum pareplottedinFig.4forelectrons,pions,kaons,andprotons,andcompared
tothepredictionsoftheenergylossmethod. Theobserveddeviationsweretakenintoaccount
bymeansoftrack-levelcorrections(cf. Section5).
Sincetheassociationofhitstotracksisnotalwaysunambiguous,somehits,usuallyfromnoise
orhitoverlap,donotbelongtotheactualtrack. Thesefalsehits,or“outliers”,canberemoved.
Thetracksconsideredforhitremovalwerethosewithatleastthreehitsandforwhichthejoint
√
energy-deposit χ2 is larger than 1.3 n +4 1.3n , where n denotes the number of hits
hits hits hits
on the track. If the exclusion of a hit decreased the χ2 by at least 12, the hit was removed. At
most one hit was removed; this affected about 1.5% of the tracks. If there is an outlier, it is
usuallythehitwiththelowest∆E/∆xvalue.
Inadditiontothemostprobablevalueoflogε, theshapeofthelogε distributionwasalsode-
termined from the data. The template distribution for a given particle species was built from
tracks with estimated ε values within three standard deviations of the theoretical value at a
given βγ. All kinematical parameters and hit-related observables were kept, but the energy
deposits were re-generated by sampling from the analytical parametrization. This procedure
exploitsthesuccessofthemethodatthehitleveltoensureameaningfultemplatedetermina-
tion,evenfortrackswithveryfewhits.