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