Momentum reconstruction and Pion production analysis in HADES
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Transcript of Momentum reconstruction and Pion production analysis in HADES
Momentum reconstruction and Pion production analysis in HADESManuel Sánchez García
Index1. Introduction to HADES@GSI
2. The HYDRA framework
3. Vertex reconstruction
4. Momentum reconstruction1. Kick plane algorithm
2. Reference trajectories algorithm
3. Track matching
5. Pion production analysis
6. Conclusions
1. The HADES experiment Motivation
Study the high density phase produced in the early stages of heavy ion collisions at SIS energies Partial restoration of chiral symmetry expected
Procedure Study in medium modifications to properties of
vector mesons produced in heavy ion collisions Need for short lived vector mesons: , ,
Study decay of the vector mesons in lepton pairs No nuclear interaction in the final state implies the lepton
pair retains memory of its originating particle mass
xy
z
1. The HADES spectrometerTolerates high count rates (106 s-1)Selective triggerDilepton acceptance: 40%
Mass resolution 1% in the regionLow mass materials to reduce multiple scattering
High granularity
Rejection of hadronic and EM backgroundFlat acceptance in m, mT
Small branching ratio for dileptonic decays (10-5)High invariant mass resolution (to resolve the meson)Need to measure heavy systems implies high multiplicitiesReject hadronic and EM background ( Dalitz …)
1. The RICH detector Threshold Cherenkov detector
Identifies leptons Off and online for 2nd level trigger
Threshold =18.2
The Magnet (ILSE) Superconducting magnet
Compact field Toroidal field geometry
Field only between the MDC Inhomogeneous field
Momentum kick ranging from 40 to 120 MeV
Matches angular momentum distribution of particles
Bends charged particles allowing p determination Positively charged particles bent
towards the beam pipe
The MDC chambers 24 drift chambers
4 chambers per sector Six layers per chamber
Butterfly geometry Sizes ranging from 88x80
cm to 280x230 cm Operates on He-Isobutane Position resolution per
layer around 80 m Track particle before and
after the magnet
The TOF detector Wall of scintillating bars
64 bars per sector Each bar read out by two
photomultipliers Measuring particle time of
flight (=100-150 ps) and position (=1.5 - 2.3 cm)
Main tasks Measuring multiplicity for
1st level trigger (centrality) Lepton identification
based on time of flight
The TOFINO detector Wall of scintillating bars
4 bars per sector Covers the lower polar angles
Measures Particle time of flight
Main tasks Measuring multiplicity for 1st trigger
(centrality) Assist SHOWER detector in lepton
identification for low momentum particles
The SHOWER detector One detector per sector
Three streamer chambers with pad readout separated by 2 lead converters of 2 radiation lengths each
Measures charge distribution on each streamer chamber
Main task Lepton identification by
measuring electromagnetic showers in lead
2. HYDRA (Hades sYstem for Data Reduction and Analysis)
User Requirements on the framework Reconstruction of events recorded by HADES
Algorithms applied on some data levels to transform them into more elaborated ones
Ability to reprocess partially reconstructed data Easy access to output for physics analysis Ensure reconstruction parameters consistency
Basic decisions Object oriented approach to facilitate modularity ROOT as a foundation framework
2. Hydra framework: architecture
Hades
+fOutputSizeLimit
+eventLoop()+Hades *instance()+makeTree()+activateTree()
HEvent
+getCategory()+addCategory()+makeBranch()+activateBranch()
HRecEvent
+getHeader()+addPartialEvent()+getPartialEvent()
2
HDataSource
+virtual init()+virtual getNextEvent()
1
HRootSource
+getNextEvent()
HTaskSet
+next()+connect()
*
HMessageMgr
+setDebugLevel()+warning(int level, char *text)
1
HSpectrometer
+addDetector()+getDetector()+init()
1
TFile
HTree
1
1
HDEtector
+setModules()+init()
*
HRuntimeDb
+getContainer()+setFirstInput()+setSecondInput()+setOutput()+initContainers()+writeContainers()
1
3. Vertex reconstruction Vertex defined as the point of closest approach to all
reconstructed tracks Obtained with a Least Squares Method (LSM) where
Has analytical solution if wi and i constant, but i depends on vertex position for each track
Non constant weights wi introduced for robustness
Iterative numerical minimization Assume both wi, i change slowly
In each iteration, use previous vertex to compute new i, wi
N
i i
ivii
N
i i
ii
rrw
dwQ
02
2
02
22
ˆ
3. Treatment of outliers: Tukey weights Outliers: non gaussian background Maximum Likelihood estimator assuming a
probability distribution: Gaussian signal + uniform background For that probability distribution, the LSM is
recovered with non constant weights wi
wi can be approximated by the Tukey weights:
d
tCtCttw TT
with
otherwise0
if/1)(22
3. Vertex reconstruction
C+C Au+Aux(mm) y(mm) z(mm) x(mm) y(mm) z(mm)
Ideal tracking 1.1 1.1 1.9 0.3 0.3 0.5
4. Momentum reconstruction Two alternative methods:
Kick Plane For each track, the deflection occurs at one point
The set of all such points defines the kick surface Deflection angle in the kick surface gives the track
momentum Reference Trajectories
A data base with simulated tracks covering the full acceptance of the HADES has been created
Comparison between real tracks and simulated tracks allows the momentum determination and covariance matrix computation
4. Experimental scenarios
Alg
orith
m
Kick Plane Reference Trajectories
Setu
p Four chambersThree chambersTwo chambers
Match
ing
Inner chambers with Meta
Inner with outer chambersMdc system with Meta
4. Kick plane algorithm
META
Kick plane
pin
pout
p
Momentum from deflection
Maxwell
CBA
p
)2/sin()2/sin(
2sin
2sin
2sin 32
12
Ocba
2
1
)( 12
KBdp
A,B and C do not depend on momentum;they depend on position in the kick plane
)2/sin(2
p
p
pin=pout
4. Kick surface Parameterization HGEANT used to get points on the Kick surface No Multiple Scattering
LSM fit to a model Q2 = yi - f(xi, zi)]2
Sector symmetry f(x,z) = f(-x, z)
Fast ray tracing Simple models
cbzaxy 2
866.0
71.3
14604
c
b
a
4. Kick plane parameterization/1 Kick surface divided in 8400 bins in and
A,B and C are constant in each bin Several hundred tracks are simulated per bin A,B and C extracted from p versus fit
4. Kick plane parameterization/2
Problem of outliers in the fit Low momentum tracks which curl in the magnet
Typical momentum threshold is the magnet’s momentum kick (parameter A)
Solution Reject tracks with momentum below 200 MeV
Good estimation of A because it depends essentially on the larger momenta
Second fit rejecting tracks with momentum below the momentum kick: better B and C estimates
Iterative robust fit with Tukey weights
4. Kick plane: resolution with TOF
4. Kick plane: resolution with SHOWER
MDC
META
Kick plane
4. Matching: 2 chambers + META 6 coordinates – 5 track parameters = 1 constraint
Correlation between polar and azimuthal deflections
cm xx
cmc
xxxPullxp
CBA
p
)2/sin()2/sin(
)2/sin(')2/(sin'')2/sin( 2 CBAp
))(tan( 1 kmkc zzxx
Same equation as for momentum reconstruction, modified to eliminate singularity at =0 due to sector symmetry (=0 for all p)
A’, B’ and C’ extracted from fits of p versus
),,( kkk zyx
cx
1
mx
4. Matching: xPull distribution /1
Correlated noise:
4. Matching with 2 MDC: Efficiency
Setup with 3 MDC
4. Setup with 3 MDC: Momentum Kick plane algorithm as for 2 MDC setup New ways to measure deflection angle
Direction from MDC3 Tails and/or systematic errors in MDC3 slope
Straight line from points in MDC3 and Meta Low resolution
Straight line from points in MDC3 and kick plane Kick surface parameterization quality is more important MDC3 inside field makes kick surface change with
respect to the previous case
All possibilities provided as options
4. Setup with 3 MDC: kick surface
14.1,821.0,1290,138.0,6428.0
1100
1100400
400
1100)(400)(
400)(
edcba
z
z
z
cdedaxbaz
cdaxbaz
cxbaz
y
4. Setup with 3 MDC: resolution (no MS)
4. Setup with 3 MDC: resolution (MS)
4. Matching: MDC12 with MDC3 3 possible constraints (8-5) Correlation between polar and
azimuthal deflection () d: Distance between inner and outer segments dKick: Distance from cross point of inner and
outer segments to the kick surface Non square cuts needed due to tails in MDC3
slope reconstruction
d
dK
ick
Ideal tracking Realistic tracking
Efficiency 98% 98%
Noise level 1.5% 8.6%
4. Matching: 3MDCs with META Position in META (2 measurements) allows
two more constraints xPull as in the low resolution kick plane Extrapolation of the track from MDC3 to META
Problem: Residual field prevents straight extrapolation Solution: Use as matching variable the normalized
difference in reconstructed momentum with Mdc3 and Meta Automatically takes into account the residual field
Ideal tracking Realistic tracking
Efficiency 90% 90%
Noise level 3.5% 4.7%
Setup with 4 MDCs
4. Momentum fit: Reference trajectories Fitting measurements xm=(x1,y1,...,x4,y4) to a
track model F(p) with p=(1/p,,z,,) F(p) = F(p0) + A (p-p0) + O((p-p0)2) with
Minimize Q2 = (F(p0) + A(p-p0) – xm)t W (F(p0) + A(p-p0) – xm)
Minimum at: pe = p0 + (AT W A)-1 AT W (xm - F(p0))
W is the inverse of the covariance matrix
Iterative method: pk+1e = pk
e + (AT W A)-1 AT W (xm - F(pke))
F(p) encapsulated in HRtFunctional Easy to change track models
j
iij p
FA
)(p
4. Track model: Table of simulated tracks F(p) is numerically computed with HGeant and the results stored in a table for fast lookup Binning 166151812 (1/p, , z, , )
311040 bins 2tables 8measurements 4bytes Finer binning improves resolution at the cost of memory
F(p) partial derivatives calculated using Savitzky-Golay filters on each table point pk
Fits tabulated values in the neighborhood of pk to a polynomial, evaluating the derivative from the coefficients
Cost per derivative: 5 multiplications, 4 sums, 1 division
4. Resolution without MS
4. Resolution with MS
5. Pion production analysis Data from C+C at 2 AGeV (2001 run)
5 sectors with 2 chambers 1 sector with 3 chambers
Goals of this analysis Show PID capabilities Pion mass and transverse momentum
Corrections for energy loss, efficiency and acceptance Comparison with literature for systematic error checking
Pion production ratio Needs correction for kick plane efficiency Checking for bias in the matching algorithm
5. Correction: Energy loss
Mainly in the Target and Rich detector Reconstructed momentum is systematically lower
than the original Ad-hoc correction
5. Pion Mass
Determined from 1/mass plot (mass is not Gaussian)
m=140±1 MeV
5. Particle Identification
Two dimensional cut in Momentum vs Beta Different cuts for TOF and SHOWER due to their
different resolutions
5. PID improvement with 3 chambersTwo MDC chambers Three MDC chambers
5. Resolution comparison with 3 chambers
Two MDC chambers Three MDC chambers
5. Kick plane efficiency () Method to extract noise and efficiency from
real data needed Let fg, fb be xPull probability distributions for good
and bad track candidates TOF
SHOWER Then for a cut c in xPull:
21
221
2
21 xx
g eCeCf
)erf(122
xdteLxLx
fx t
g
g
c
c g
f
f
c
-c gb
c
-c b
ff
fnoise
noise1
weight
5. xPull probability distribution for TOF
5. xPull distribution for SHOWER
+ - production ratio
Efficiency of PID cut not known Same cut for both pion charges Strong cut to avoid contamination from protons
Different cuts on TOF and SHOWER Unknown relative efficiency implies we cannot
add directly contributions from both detectors
Tof Shower Average Both
Simulation 0.73 1.16 0.94 0.94
Real data 0.7±0.02 1.17±0.02 0.93±0.02 -
5. Additional corrections: Acceptance Acceptance is geometrical efficiency
Determined by comparing the originally uniform distribution in pt - y with the one reconstructed from all kick plane candidates
5. Pion transverse momentum (pt) Described by a thermal model
Around mid rapidity
For charged pions, deviation from a single Boltzmann distribution have been observed Can be attributed to decays Fit to two thermal distributions: temperatures correlated
22with ttT
m
ttt
pEmempdp
d t
22
11 expexp
T
mC
T
mCmp
dp
d tttt
t
5. Pion transverse momentum spectrum
T2=41±3 T1=86±2
KaoS collaboration: T2=40±3 T1=86±2
Pion transverse momentum
T2=50±2 T1=94±2
Reduced range: T2=41±3 T1=86±2
6. Conclusions (1) A software framework for event processing in
HADES has been developed A robust vertex reconstruction algorithm has
been implemented Two algorithms for momentum reconstruction
have been developed, matching HADES completion schedule Kick Plane approach Reference Trajectories method
Conclusions (2) Methods have been derived to match tracks
from the MDC detectors among themselves and the MDC with META
The momentum reconstruction methods have been applied to the analysis of pion production in C+C data Efficiency, Energy loss and Acceptance
corrections have been derived Good agreement with previous measurements
from other collaborations
The Endfor now
Outliers in the parameterization
HRuntimeDb: Runtime Database Repository of reconstruction parameters Geometry, calibration, cuts ...
Provides version management on 2 time axis DAQ time: time in which the data were taken Revision time: People improving parameter sets
Different back ends for parameter I/O ORACLE database: Official repository with history Root File: Contains versions, no history ASCII File: Easy editing, no versions, no history
Simple API: HRuntimeDb::getContainer()
HTaskSet: Task management Modularity at the level of algorithms Composite model
The TaskSet is itself a Task Tree structure for ownership
Non linear execution flow Tasks in the tree connected
arbitrarily via return codes New algorithm in most cases only need to
Inherit new class from HReconstructor Override init(),reinit(),finalize() and execute()
HReconstructor
+execute()+next()
HTask
+next()+virtual init()+virtual reinit()+virtual finalize()
HTaskSet
+next()+connect()
*
HEvent: Data containers HEvent is the repository for event data Organized in data levels (HCategory)
Category: container for objects of the same class Provides matrix-like random access to the data Iteration on data subsets Custom memory management for performance
Implementations based on ROOT’s TClonesArray Different implementations for different needs
Creates a ROOT’s TTree according to its structure for I/O
HDataSource & TTree: Data I/O HDataSource: Data input
Puts data into the event Abstract class with several back ends
ROOT File: simulation or partially reconstructed data From DAQ system: both online or binary file
TTree & TFile: Data output Automatically generated ROOT tree from event
structure used to write the event data The user specifies what data levels to store Output file also contains the analysis configuration
4. Matching: xPull distributions /2