Momentum reconstruction and Pion production analysis in HADES

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Momentum reconstruction and Pion production
analysis in HADES

• Manuel Sánchez García

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Index

• Introduction to HADES_at_GSI
• The HYDRA framework
• Vertex reconstruction
• Momentum reconstruction
• Kick plane algorithm
• Reference trajectories algorithm
• Track matching
• Pion production analysis
• Conclusions

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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 r, w, j
• 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

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1. The HADES spectrometer

• Mass resolution 1 in the w region
• Low mass materials to reduce multiple scattering

• Tolerates high count rates (106 s-1)
• Selective trigger
• Dilepton acceptance 40

?

• Rejection of hadronic and EM background
• Flat acceptance in m, mT

• High granularity

Small branching ratio for dileptonic decays (10-5)
High invariant mass resolution (to resolve the w
meson)
Need to measure heavy systems implies high
multiplicities
Reject hadronic and EM background (h Dalitz )
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1. The RICH detector

• Threshold Cherenkov detector
• Identifies leptons
• Off and online for 2nd level trigger
• Threshold g18.2

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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

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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 mm
• Track particle before and after the magnet

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The TOF detector

• Wall of scintillating bars
• 64 bars per sector
• Each bar read out by two photomultipliers
• Measuring particle time of flight (s100-150 ps)
  and position (s1.5 - 2.3 cm)
• Main tasks
• Measuring multiplicity for 1st level trigger
  (centrality)
• Lepton identification based on time of flight

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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

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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

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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

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2. Hydra framework architecture
1

Hades
fOutputSizeLimit
1
1
eventLoop()
Hades instance()
makeTree()
activateTree()

1
2
1
1
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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 si constant,
  but
• si depends on vertex position for each track
• Non constant weights wi introduced for robustness
• Iterative numerical minimization
• Assume both wi, si change slowly
• In each iteration, use previous vertex to compute
  new si, wi

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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

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3. Vertex reconstruction
CC CC CC AuAu AuAu AuAu
x(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
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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

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4. Experimental scenarios
Two chambers
Four chambers
Three chambers
Setup
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4. Kick plane algorithm

• Momentum from deflection

Maxwell
A,B and C do not depend on momentum they depend
on position in the kick plane
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4. Kick surface Parameterization

• HGEANT used to get points on the Kick surface
• No Multiple Scattering
• LSM fit to a model
• Q2 Syi - f(xi, zi)2
• Sector symmetry
• f(x,z) f(-x, z)
• Fast ray tracing
• Simple models

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4. Kick plane parameterization/1

• Kick surface divided in 8400 bins in q and j
• A,B and C are constant in each bin
• Several hundred tracks are simulated per bin
• A,B and C extracted from p versus x fit

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4. Kick plane parameterization/2

• Problem of outliers in the fit
• Low momentum tracks which curl in the magnet
• Typical momentum threshold is the magnets
  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

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4. Kick plane resolution with TOF
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4. Kick plane resolution with SHOWER
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4. Matching 2 chambers META

• 6 coordinates 5 track parameters 1 constraint
• Correlation between polar and azimuthal
  deflections

• Same equation as for momentum reconstruction,
  modified to eliminate singularity at j0 due to
  sector symmetry (Dj0 for all p)
• A, B and C extracted from fits of p versus Dj

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4. Matching xPull distribution /1
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4. Matching with 2 MDC Efficiency
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Setup with 3 MDC
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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

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4. Setup with 3 MDC kick surface
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4. Setup with 3 MDC resolution (no MS)
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4. Setup with 3 MDC resolution (MS)
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4. Matching MDC12 with MDC3
dKick

• 3 possible constraints (8-5)
• Correlation between polar and azimuthal
  deflection (Dj)
• 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
Dj
Ideal tracking Realistic tracking
Efficiency 98 98
Noise level 1.5 8.6
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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
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Setup with 4 MDCs
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4. Momentum fit Reference trajectories

• Fitting measurements xm(x1,y1,...,x4,y4) to a
  track model F(p) with p(1/p,r,z,q,j)
• 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 pk1e pke (AT W A)-1 AT W
  (xm - F(pke))
• F(p) encapsulated in HRtFunctional
• Easy to change track models

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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, r, z, q, j)
• 311040 bins 2tables 8measurements
  4bytes20MB
• 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

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4. Resolution without MS
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4. Resolution with MS
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5. Pion production analysis

• Data from CC 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

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5. Correction Energy loss

• Mainly in the Target and Rich detector
• Reconstructed momentum is systematically lower
  than the original
• Ad-hoc correction

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5. Pion Mass

• Determined from 1/mass plot (mass is not Gaussian)

mp1401 MeV
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5. Particle Identification

• Two dimensional cut in Momentum vs Beta
• Different cuts for TOF and SHOWER due to their
  different resolutions

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5. PID improvement with 3 chambers
Two MDC chambers
Three MDC chambers
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5. Resolution comparison with 3 chambers
Two MDC chambers
Three MDC chambers
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5. Kick plane efficiency (e)

• 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

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5. xPull probability distribution for TOF
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5. xPull distribution for SHOWER
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5. p p- 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 0.70.02 1.170.02 0.930.02 -
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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

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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 D decays
• Fit to two thermal distributions temperatures
  correlated

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5. Pion transverse momentum spectrum
T2413 T1862
KaoS collaboration T2403 T1862
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Pion transverse momentum
T2502 T1942
Reduced range T2413 T1862
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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

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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
  CC data
• Efficiency, Energy loss and Acceptance
  corrections have been derived
• Good agreement with previous measurements from
  other collaborations

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The Endfor now
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Outliers in the parameterization
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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 HRuntimeDbgetContainer()

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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 connectedarbitrarily via
  return codes
• New algorithm in most cases only need to
• Inherit new class from HReconstructor
• Override init(),reinit(),finalize() and execute()

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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 ROOTs TClonesArray
• Different implementations for different needs
• Creates a ROOTs TTree according to its structure
  for I/O

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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

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4. Matching xPull distributions /2