Photon reconstruction Photon reconstruction and matchingand matching

Prokudin MikhailProkudin Mikhail

OutlineOutline

►RequirementsRequirements►Cluster finderCluster finder

algorithm and performancealgorithm and performance

►Cluster fittingCluster fitting requirementsrequirements

►Matching algorithmMatching algorithm

Photon reco. RequirementsPhoton reco. Requirements

►Robust reconstruction of single Robust reconstruction of single photonsphotons

►Two close photons case:Two close photons case: robust reconstruction of parameters in robust reconstruction of parameters in

case of two separate maximumscase of two separate maximums separation one/two photons in case of one separation one/two photons in case of one

local maximumlocal maximum

►Fast!Fast!

Cluster finderCluster finderCluster formationCluster formation

► Remove maximums near charged Remove maximums near charged trackstracks real trackingreal tracking

► Precluster:Precluster: formed near local maximumformed near local maximum

► cut on maximum energycut on maximum energy find maximum 2x2 matrix near find maximum 2x2 matrix near

maximummaximum add a neighbor to local maximum cell add a neighbor to local maximum cell

with minimal energy depositionwith minimal energy deposition► to add informationto add information

check precluster energycheck precluster energy► >0.5GeV>0.5GeV

► Cluster: group of preclusters with Cluster: group of preclusters with common cellscommon cells--------------------------------------------------------------------------------------------------

► Clusters with 2 maximums >10%Clusters with 2 maximums >10% Fit procedure is necessarily!Fit procedure is necessarily! >3 (<1% >3 (<1% γγ) maximums can be omitted) maximums can be omitted

RequirementsRequirements► Clusters should be largeClusters should be large

information for unfoldinginformation for unfolding► Clusters should be smallClusters should be small

hadrons backgroundhadrons background

Fitting basicsFitting basics

► 2 clusters2 clusters► Simple Simple

methodsmethods Fit not requiredFit not required

► 1 cluster1 cluster 2 maximums2 maximums

► FitFit shower shapeshower shape

► 1 cluster1 cluster 1 maximum1 maximum 2 photons2 photons

► Should be Should be rejectedrejected

► FitFit shower shapeshower shapeSame photons, but different distance between

them.

Fitting basicsFitting basics

► 2 clusters2 clusters► Simple Simple

methodsmethods Fit not requiredFit not required

► 1 cluster1 cluster 2 maximums2 maximums

► FitFit shower shapeshower shape

► 1 cluster1 cluster 1 maximum1 maximum 2 photons2 photons

► Should be Should be rejectedrejected

► FitFit shower shapeshower shapeSame photons, but different distance between

them.

Fitting basics. Shower shapeFitting basics. Shower shape

+

or

?

Precise knowledge of shower shape is essential. If χ2 is used, than what is σ2

(error)?

cells cell

predcell

meascell EE

2

22 )(

Fitting basics. Shower libraryFitting basics. Shower library

► Store mean energy Store mean energy deposition vs. (x, y) for deposition vs. (x, y) for eacheach EnergyEnergy ThetaTheta PhiPhi

► Energy deposition in Energy deposition in cluster cells are not cluster cells are not independentindependent RMS value storing uselessRMS value storing useless

► Should use analytical Should use analytical formula for formula for σσ22

with correlationswith correlationsh4 h5

h4

h5

σσ22 formula formula

►σσ22=c=c22(E(Emeasmeas(1-E(1-Emeasmeas/E/Eclustercluster)+c)+c00+c+c11EE22clustercluster))

cc22 is normalization is normalization►95% of photons have 95% of photons have χχ22<2<2

cc11 and c and c0 0

►exact values are found requiring:exact values are found requiring: χχ22 should not depend on photon’s energy should not depend on photon’s energy independence from independence from φφ

►due to shower librarydue to shower library

cci is different for each calorimeter region/cell is different for each calorimeter region/cell sizesize

Energy reconstruction quality Energy reconstruction quality

Calibration is goodCalibration is good

Photon separation.Photon separation.Cluster with 2 maximumsCluster with 2 maximums

► χχ22 criteria allows criteria allows identify ~40% of identify ~40% of two photons two photons clustersclusters efficiency highly efficiency highly

depend on depend on distance between distance between photons/calorimetephotons/calorimeter regionr region

Inner calorimeter region

Energy reconstruction quality. Energy reconstruction quality. Cluster with 2 maximumsCluster with 2 maximums

► Reconstructed Reconstructed energy energy distribution for distribution for both photons is both photons is OkOk

► But for each of But for each of them…them…

Energy reconstruction quality. Energy reconstruction quality. Cluster with 2 maximumsCluster with 2 maximums

Reconstruction algorithm tends to increase asymmetry in energy of photons(also by PHENIX experience)

AuAu 25 GeV UrQMD eventsAuAu 25 GeV UrQMD events

► 730 photons in event730 photons in event► 299 photons in 299 photons in

calorimeter calorimeter acceptanceacceptance 131 with energy > 0.7 131 with energy > 0.7

GeVGeV

► 35% reconstruction 35% reconstruction efficiencyefficiency

► 91% for isolated 91% for isolated photonsphotons rises with increasing rises with increasing

isolation isolation

AuAu 25 GeV UrQMD eventsAuAu 25 GeV UrQMD events

► 35% 35% reconstruction reconstruction efficiencyefficiency

► Boundaries Boundaries between between calorimeter calorimeter regionsregions occupancyoccupancy

Reconstruction efficiency vs. θ and energy

MatchingMatching

► Matching between MC and Matching between MC and reconstructed particlesreconstructed particles not only MC photonsnot only MC photons

► Why?Why? check origin of clustercheck origin of cluster

misidentificationmisidentification

► neutronneutron► ……

physics processesphysics processes► ππ00 and and ηη decays decays► prompt photonsprompt photons► ……

RequirementsRequirements► Matching for many Matching for many

maximums clustersmaximums clusters► Correct matching with Correct matching with

converted converted γγ and brem e and brem e

Available informationAvailable information► Energy deposition in each Energy deposition in each

cell of cluster by each MC cell of cluster by each MC particleparticle CbmEcalStructureCbmEcalStructure

► Shower shape for each Shower shape for each reconstructed particlereconstructed particle CbmEcalShowerLibCbmEcalShowerLib

CbmEcalMatching. At SVN

Matching. Multimaximum Matching. Multimaximum clustercluster

► Idea: use shape of Idea: use shape of reconstructed photonsreconstructed photons

► For each For each MC/reconstructed MC/reconstructed particle compute:particle compute:

only cells with energy only cells with energy deposition of current deposition of current particle are in playparticle are in play

match with MC particle match with MC particle with Pwith Pii>0.6>0.6

cells

jcluster

jco

jSumj

Sum

jcoi

MCi EEP

P

EEP Re

Re ,

► Clusters with 2 Clusters with 2 maximums: 99.97% maximums: 99.97% efficiencyefficiency

Matching (Numerous Matching (Numerous converted converted γγ))

► Idea: for Idea: for γγ((ee±±)) look at mother look at mother ee±±((γγ)), grandmother, …, grandmother, … for each for each γγ and e and e±± MCTrack: MCTrack:

P=PP=Pthisthis++ΣΣPPdaughterdaughter

► Several realizations availableSeveral realizations available Choose Choose γγ/e/e±± with maximum P with maximum P Choose parent eChoose parent e± ± if daughter if daughter γγ

have P>const*Phave P>const*Pγγ

…… Exact algorithm/constants are Exact algorithm/constants are

defined in configuration filedefined in configuration file►still under developmentstill under development

γ

e+e-

γReco

Conclusions and next stepsConclusions and next steps

► Reconstruction algorithms are completed and Reconstruction algorithms are completed and testedtested 35% reconstruction efficiency35% reconstruction efficiency

►occupancy!occupancy!

► Calorimeter geometry optimizationCalorimeter geometry optimization costcost physical observables sensitivityphysical observables sensitivity

► reconstruction efficiencyreconstruction efficiency

►Digitization and response nonuniformity impactDigitization and response nonuniformity impact moving towards final and realistic geometrymoving towards final and realistic geometry

Fitting the clusterFitting the cluster

►first approximationfirst approximation see simple reconstruction for detailssee simple reconstruction for details

►χχ22 minimizationminimization

►FitterFitter TFitterMinuitTFitterMinuit

►shower shape Eshower shape Epredpred

shower library (CbmEcalShowerLib)shower library (CbmEcalShowerLib)►σσ22 formula formula

cells cell

predcell

meascell EE

2

22 )(

Cluster finder performanceCluster finder performancebefore and after before and after

bug correction.bug correction.Cluster size under control.Cluster size under control.

χχ22 distributions distributions

χχ22 does not depend on impact angle! does not depend on impact angle!

E=1 GeV. Middle ECAL region

E=16 GeV. Middle ECAL region

Other calorimeter region

χχ22 distributions distributions

Shape is different, but 95% of Shape is different, but 95% of γγ have have χχ22<2<2

E=1 GeV. Middle ECAL region

E=16 GeV. Middle ECAL region

σσ22 formula. Free parameters formula. Free parameters

► Idea:Idea: find cfind c00 and c and c1 1 which which

minimize difference in minimize difference in χχ22 cut for different cut for different energiesenergies►calculate calculate χχ22

cutcut for each for each energyenergy

►find among them find among them χχ22minmin

►choose cchoose c00 and c and c11 which which minimize minimize ΣΣ((χχ22

cutcut//χχ22minmin-1)-1)22

for each calorimeter for each calorimeter regionregion

► Two variablesTwo variables one constraintone constraint one free parameterone free parameter

Minimum

Inner calorimeter region

σσ22 formula. Different regions formula. Different regions

Middle calorimeter regionOuter calorimeter region

Optimal C0 and C1 is different for each region!

σσ22 formula. Tuning the formula. Tuning the parametersparameters

Dependency can be fitted with pol1

For each C0 find C1 which minimizes Σ(χ2

cut/χ2min-1)2 Middle calorimeter region

σσ22 formula. Tuning the formula. Tuning the parametersparameters

► Idea: chose a Idea: chose a different (not 95%) different (not 95%) efficiency and look at efficiency and look at CC11 vs C vs C00 dependency dependency They does not They does not

intersect!!!intersect!!!►Shape of Shape of χχ22 is different is different

for each energy!for each energy!

► Idea (TODO): two Idea (TODO): two photon separation photon separation power vs. Cpower vs. C00 and C and C11

Middle calorimeter region

χχ22 reconstruction quality. Cluster reconstruction quality. Cluster with 2 maximumswith 2 maximums

Middle calorimeter region. 1 cluster

Middle calorimeter region. 2 clusters

χχ22 is a little bit different is a little bit different

Separation vs. CSeparation vs. C00

► Separation power Separation power depends weakly depends weakly on Con C00

33σσ cut cut can be enhanced can be enhanced

by tighten cutsby tighten cuts►45% for 245% for 2σσ cut cut

Fitter requirementsFitter requirements

► Robust reconstruction Robust reconstruction of single photonsof single photons

► Two close photons Two close photons case:case: robust reconstruction of robust reconstruction of

parameters in case two parameters in case two separate maximumsseparate maximums

separation one/two separation one/two photons in case of one photons in case of one maximummaximum► χχ22 criteria criteria►all analyzed approaches all analyzed approaches

have failed to have failed to reconstruct photons reconstruct photons energy/position correctlyenergy/position correctly

► χχ22 shape should not shape should not depend on photon’s depend on photon’s energyenergy same value for same value for

efficiency cutefficiency cut► separation power of separation power of

one/two photons in one/two photons in case of one maximum case of one maximum as a criteriaas a criteria example: with 95% example: with 95%

efficiency for clusters efficiency for clusters formed by single formed by single photonphoton