p - F9

Data analysis, B. Golob5helix parameterization:tiFrom raw data to summary datahelixhelix is parameterized with 5 parametersat chosen point, e.g.:y 0 , z 0 , ψ 0 , θ 0 , 1/R(x 0 =y 0 /tanψ 0 )

Data analysis, B. Golob6From raw data to summary datapattern recognitionpattern recognition:high number of detector hits → difficult association with helix;transformation of transversal helix projectionfor parts of track (in most precise tracking detector) x S , y S , z S , ψ S , φ S , 1/R Savailable - TE, Track Elementfor each other TE: calculate transformed point x’, y’;calculate φ’ ( ∠(x’, y’) and int. point);check | φ’- φ S |

Data analysis, B. Golob7From raw data to summary datapattern recognitionlab.systemtransformationinter.pointhelixcentercirclelinehitlinetrans.tangent to helixeasier to check consistentcyof hits with straight line thanwith helix

From raw data to summary datapattern recognition / track fittingalghorithm properties:minimal number of loops;α, β determined individually for each sub-detector;using int. point - not applicable to secondary tracks;each TE can be associated to several tracks;additional info can be included (energy, direction, ...)track fit:from multiple TE’s determine best helix parameters in chosen point(closest approach to int. point)N measuring pointstrack model (helix)Data analysis, B. Golobminimizationperturbations tomodel(multiple scattering)track parameters8

Data analysis, B. Golob9From raw data to summary datatrack fittingTrack fitting algorithms:divided according totrack model usage, inclusion of model distortions (mult. scatt., energy losses)Global Methods Progressive Methods Break Point MethodsGlobal Methods:simultaneous minimization of χ 2 of all measurement points;mult. scatt. included in the error matrixproperties:all meas. points used simultaneously;simultaneous pattern recognition not possible(as opposed to Progressive methods);calculation expensive (NxN matrix inversion);

Data analysis, B. Golob10Global l method - track model:expected coordinate valuesFrom raw data to summary datatrack fitting5 free parameters: p 0 =(y 0 , z 0 , ψ 0 , θ 0 , 1/R)(x 0 =y 0 /tanψ 0 )N measured 3-dimensional points ⇒ N 3-dimensional functionsdepending on 5 parameters f(p 0 )global χ 2 minimization:

Data analysis, B. Golob11Global l method -example:straight line fitmodel: y n =kx+yn 0N meas. of y at x nFrom raw data to summary datatrack fittingN k∆x σ k ∆x2 y 2 -y 1 √2σ3 (y 3 -y 1 )/2 σ/√2minimization yields4 (3y 4 +y 3 -y 2 -3y 1 )/10σ/√5for x n =n∆x andσ σ n =σ ⇒

Data analysis, B. Golob12From raw data to summary datatrack fittingProgressive method (Kalman filter):parameters after n measurement points known;extrapolate (track model) to (n+1) st point;parameters after n+1 points = average of extrapolated andmeasured parameters at (n+1) st point;properties:enables simultaneous pattern recognition and track fitting;specific scattering regions inherently included;

Data analysis, B. Golob13From raw data to summary datatrack fittingProgressive method:vector of parameters after n measurement points p nF ;error matrix after n measurement points W n ;vector of extrapolated parameters p Fen ;extrapolated error matrix WenWenT= D WnD,D=∂p pvv∂peχ 2 : sum of contribution from extrapolation and measurement:χ 2 from n pointsχ 2 from extrapolat.after minimization: set of equations for p n+1F ;if χ 2 from extrapol. larger than chosen value for specific point⇒ point not assigned to trackχ 2 of (n+1) st point

Data analysis, B. Golob14From raw data to summary datatrack fittingProgressive method -example:straight line;y nF and k nF after n measurement points;extrapolation to (n+1) st point:extrapolated error matrix:

Data analysis, B. Golob15Progressive method -example:straight line;start with first point,y F m1F =yFe 1 =y 1m ,k 1F =kFe 1 =k 1m =0Wstarting error matrix:⇒W2⎡1 / σ=⎢⎣00⎤⎥0⎦1,2From raw data to summary datatrack fittingN k F ∆x σ kF ∆x2 y 2 -y 1 √2σ3 (3y223 -y 2 - √(14/25)σ=⎡ 1/ σ − ∆x/ σ ⎤e 2y=1 )/5 0.748σW1⎢2⎣− ∆x/ σ∆x22⎡ − ∆ ⎤= e 2 / σ x / σW1+U=⎢2 2⎥⎣− ∆x/ σ ∆x/ σ2⎦22/ σ⎥⎦4 (30y 4 -y 3 -18y 2 -11y 1 )/700.524σetc.

Data analysis, B. Golob16From raw data to summary datatrack fittingGlobal l method –multiple l scattering:error matrix:σ i : uncertainty of ind. measurem.;ε i : contr. to uncertainty due to mult. scatt.(Molièr formula:)track modelactual track (mult.scatt.)meas. erroruncertainty including mult. scatt.distribution of (y meas -y fit )/σ y (“pull”) is a measure of understanding the effect ofmult. scatt. rather than of understanding di the meas. errors

Data analysis, B. Golob21Multiple scattering:From raw data to summary datamomentum measurement

Data analysis, B. Golob22Momentum meas. ATLAS (µ):From raw data to summary datamomentum measurementintrinsic resol.10LHC: Atlas5MuonDriftTubechambers(MDT)3 meas. points in barrel;σ(x) = 50 µmL = 4 mB = 1T (BL = 3 - 9Tm)1000 GeV µ from W',Z'=> σ(p)/p ~ 10%mult. scatt.(~const.)10 100p[GeV]

Data analysis, B. Golob23From raw data to summary datacalorimeter showersCalorimetersare granulated(composed of individual id cells);charged and neutral particles depositenergy in several cells;to measure E of particle (or evenhadronic jet) need method of associatingindividual cell energy deposit toparticles (“clustering”)purpose of clustering:improved signal/noise (consideringcorrelations among cells);separation of EM/hadronic showers;search for isolated particles (e, γ, µ,...)φR2nd layerηATLAS LiAr EM calorim.:accordion geom.;3 layers in radial direction;2nd layer: ∆η x ∆φ = 0.025 025 X 0.025025η = -ln (tg Θ/2) ( ⇒ 4 cm X 4 cm)

From raw data to summary datacalorimeter showersMulguisin algorithm, implementations:cellshowersize and direction of shower const.size of shower const.,direct. recalculatedat each stepData analysis, B. Golobsize and direct. ofshower recalculatedl at each step26

From raw data to summary datacalorimeter showersResolution on dijet invariant mass:LHC simulation; event + 30 min. bias events:individual event: σ M /Mσ M M/ /M[%][%]← decreasing allowed shower size ⇒→ increasing allowed shower size ⇒ smaller fraction of E reconstr. ⇒larger fraction of E reconstr. ⇒ better resol. worse oseresol.;→ increasing allowed shower size ⇒larger fract. of E from other events ⇒worse resol.Data analysis, B. Golob27

Data analysis, B. GolobHadron identificationmost detectors use some variationof Cherenkov light detection;From raw data to summary dataparticle identificationCherenkov ring detectors:photons in detector ⇒ radius of ring⇒ Cherenkov angle ⇒ particle velocity ⇒ masslarge number of γ’s – impossible toconsider all combinations;charged track (through geometry dependentequations) determines ring center;BaBar - DIRCconsider only γ’s consistent with ring center( ) N θθ C =θ Cexp(m i ) ± Nσ θCθ c28

Data analysis, B. Golob29Cherenkov ring detectorslikelihood function:From raw data to summary dataparticle identificationL(N exp ,N bg ) = N exp , θ C =f(p i ,m i )background:uniform distrib. overdetector surfaceL(N exp ,N bg )/L(N exp =0,N bg ): measure of probability for set of γ’s s tooriginate from a particle with (p i ,m i )

Data analysis, B. Golob30From raw data to summary dataparticle identificationCherenkov ring detectorsparticle separation:from L(N exp ,N bg )/L(N exp =0,N bg ) ⇒ P(m i )P(m i i)/ )/P(m j j) particle separatione.g. HERA-B P(π, not K)/P(K, not π):

Data analysis, B. Golob31Tracking detectors calibrationindividual subdetectors must beproperly inter-orineted, i t otherwisetracks distorted;for any calibration needsample (tracks, decays, ...) withprecisely known detectorresponseCalibrationTracking detectorsactualmeasurementidealmeas.idealactualposition position

Data analysis, B. Golob32CalibrationTracking detectorsDescription of detector (mis)alignmentposition of individual subdetector w.r.t. reference(most precisely mechanically positioned detector)t described by set of small parameters α(translation, at rotation, o t-delay,...)assume linear relationqvmeas− qvext=Sv αsimplest case:α composed of 3 translations and 3 rotationsα =(η x ,η y ,η z ,ε x ,ε y ,ε z )q meas : vector of measured coordinatesq ext : vector of extrapolated coord.(from the reference detector)S: matrix depending di on measuringcoord., track model, detectorgeometry

Data analysis, B. Golob33CalibrationTracking detectorsDetermination of positionminimization:meas ext meas extk ∈meas. pointsresult:k ∈meas. pointsvector of displacements αcoordinates meas. in subdetector t are corrected by αmeasext

Data analysis, B. Golob34CalibrationTracking detectorsAppropriate sampleoften cosmic rays;other decays observed,e.g. Z 0 → µ + µ - (LEP);(needed also to checkthe alignment method)hits in otherdetectorextrap.trackhits inreferencedetector

Data analysis, B. Golob35CalibrationTracking detectorsAppropriate samplee.g. Z 0 → µ + µ - (LEP);●meas. hits●extrap. hitsreferencedet.δextrapolations ofmeas. tracksdo not intersectin interaction point

Data analysis, B. Golob36CalibrationTracking detectorsExampleDelphi detector at LEPbefore< >=36 µmσ =58µmδ [cm][(1/p t )-(1/pextt )]/(1/pextt )µ + µ -beforeafterafter=1.7 µmσ = 41 µm

Data analysis, B. Golob37CalibrationData and simulationCalibration of data and MC simulationexample of RICH (Delphi at LEP)sample with known detector response:cosθ C = 1/βntracks with p>6 GeV; even protons at p>6 GeV β=1 - 10 -2sample yields value of n;expected error on θ C , σ (θ C ) needed for fits;(θ( meas - θexpC C )/σ(θ C ) ”pull” examined;pull distribution properties:for gaussian distribution of θmeasC :=0σ=1 if σ ≠1 ⇒ correct σ(θ C )

Data analysis, B. Golob38example of RICH(Delphi at LEP)CalibrationData and simulationbeforeafter=4.9 ±0.2 mrad=0.01 ±0.08mradθ Cmeas- θ Cexp[rad]same method andcorrections appliedto MC simulationto match the databeforeafterσ=1.30 ±0.03σ=1.01 ±0.01(θ Cmeas- θ Cexp)/σ(θ C )

Analysis of dataHadronic jets reconstructionquark productionobservable jetsexample of jet formationreconstructed jets ⇒interpretation ofprocesses at parton levelData analysis, B. Golobenergy scale (LEP)91 10 1 E [GeV]39

Data analysis, B. Golob40Analysis of dataHadronic jets reconstructionjet reconstructionexperimental method(assigning tracks to jets, calculation of energy, ....);observables (# jets, # tracks in jet, angular distributions,...)must be expressed in terms of theory parametersin order to test predictions;definition of jetshould be appropriate p for exp. usage and theoretical calculations in orderto confront theory & experimentsAlgorithm for track associationresolution parameter combination of tracksy cut ; e.g. p jet = p i + p j ;if y ij < y cut two tracks insame jet

Data analysis, B. Golob41Analysis of dataHadronic jets reconstructionjet reconstructionalgorithmsname resolution parameter combination commentpreserves E, ppreserves pin Table:pvpii→→4 − momentum3 − momentumpreserves E, p;resummableNLO log’shigher order calculations in perturbative QCD performed for massless partons⇒ resolution parameters calculated for massless partons;summing two jets 4-momenta in general leads to a non-zero mass object (new jet);several algorithms exist to avoid the problem

Data analysis, B. Golob42Analysis of dataHadronic jets reconstructionalghorithms comparisonfor all alghorithms perturbative calculations exist to O(α s2 ),e.g. relative rate of n jets:using above predictions + models of hadronizationcomparison of parton and hadron distributions

Data analysis, B. GolobAnalysis of dataHadronic jets reconstructionalghorithms comparisonn jet rates vs. y cutbefore hadronization(parton level)2 jets3 jets4jets-- after hadronizationJADEsmallest hadronizationcorrections forJADE and DURHAMPDURHAMy cuty t43

Data analysis, B. Golob44alghorithms comparisonn jet rates vs. EAnalysis of dataHadronic jets reconstructionsmallest hadronizationcorrections forJADEJADE

Data analysis, B. Golob45Heavy y( (b)quark tagginggAnalysis of dataHeavy quark taggingH(m >150 GeV) → bb > 50%; CPV in B system; ....try to discriminate b initiated jets from others;use properties of hadrons composed of b quarks:lifetime mass energy1.6 ps 5.3 GeV in fragmentation higherthan for other hadronslifetime:γcτ B >γcτ D δ B > δ Ddecay prod.of Bdecay prod.of Dimpactparameterinter. point

Data analysis, B. Golob46Heavy y( (b)quark tagginggmass:example ofrapidity forB(M) →X(E 1 )Y(E 2 );Analysis of dataHeavy quark tagginglarge M ⇒ small y;average # of decay products higher for B than D⇒ y even smaller

Data analysis, B. Golob47Heavy y( (b)quark tagginggcombination of severaldiscriminating variablesinto single one(likelihood ratio);example for Delphiat LEP;actual method forb-tagging depends onspecific experimentalconditionsAnalysis of dataHeavy quark taggingrated)N B (sele ected)/NB (geneN B (selected)/N all (selected)

Data analysis, B. Golob48Analysis of dataSummaryPath from electronic signal detection to result for measured physicalquantities involves a number of stepsEach of those represents a specific problem and requires specificmethods and solutions (some of those illustrated here)Quality (correctness and accuracy) of the final results depends cruciallyon the quality of reconstruction of raw data