Momentum reconstruction and Pion production analysis in HADES

1. Momentum reconstruction and Pion production analysis in HADES Manuel Sánchez García

2. Index • Introduction to HADES@GSI • The HYDRA framework • Vertex reconstruction • Momentum reconstruction • Kick plane algorithm • Reference trajectories algorithm • Track matching • Pion production analysis • Conclusions

3. 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

4. y x z 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 High invariant mass resolution (to resolve the w meson) Reject hadronic and EM background (h Dalitz …) Need to measure heavy systems implies high multiplicities Small branching ratio for dileptonic decays (10-5)

5. 1. The RICH detector • Threshold Cherenkov detector • Identifies leptons • Off and online for 2nd level trigger • Threshold g=18.2

6. 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 Magnet (ILSE)

7. 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

8. The TOF detector • Wall of scintillating bars • 64 bars per sector • Each bar read out by two photomultipliers • Measuring particle time of flight (s=100-150 ps) and position (s=1.5 - 2.3 cm) • Main tasks • Measuring multiplicity for 1st level trigger (centrality) • Lepton identification based on time of flight

9. 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 TOFINO detector

10. 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

11. 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

12. HTaskSet HMessageMgr HRuntimeDb +next() +setDebugLevel() +getContainer() +connect() +warning(int level, char *text) +setFirstInput() +setSecondInput() +setOutput() +initContainers() HSpectrometer +writeContainers() +addDetector() +getDetector() +init() HDEtector HEvent +setModules() HDataSource TFile +init() +getCategory() +addCategory() +virtual init() +makeBranch() +virtual getNextEvent() +activateBranch() HTree HRootSource HRecEvent +getNextEvent() +getHeader() +addPartialEvent() +getPartialEvent() 2. Hydra framework: architecture 1 * Hades +fOutputSizeLimit 1 1 +eventLoop() +Hades *instance() +makeTree() +activateTree() * 1 2 1 1

13. 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

14. 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:

15. 3. Vertex reconstruction

16. 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

17. KickPlane Reference Trajectories Algorithm • Inner chambers with Meta • Inner with outer chambers • Mdc system with Meta Matching 4. Experimental scenarios Two chambers Four chambers Three chambers Setup

18. META Kick plane pin Dx Dx Dp pout pin=pout 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

19. 4. Kick surface Parameterization • HGEANT used to get points on the Kick surface • No Multiple Scattering • LSM fit to a model • Q2 = S[yi - f(xi, zi)]2 • Sector symmetry • f(x,z) = f(-x, z) • Fast ray tracing • Simple models

20. 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

21. 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

22. 4. Kick plane: resolution with TOF

23. 4. Kick plane: resolution with SHOWER

24. META Kick plane MDC 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 j=0 due to sector symmetry (Dj=0 for all p) • A’, B’ and C’ extracted from fits of p versus Dj

25. Correlated noise: pm+nm 4. Matching: xPull distribution /1

26. 4. Matching with 2 MDC: Efficiency

27. Setup with 3 MDC

28. 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

29. 4. Setup with 3 MDC: kick surface

30. 4. Setup with 3 MDC: resolution (no MS)

31. 4. Setup with 3 MDC: resolution (MS)

32. 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

33. 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

34. Setup with 4 MDCs

35. 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: pk+1e = pke + (AT W A)-1 AT W (xm- F(pke)) • F(p) encapsulated in HRtFunctional • Easy to change track models

36. 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 16´6´15´18´12 (1/p, r, z, q, j) • 311040 bins ´ 2tables ´ 8measurements ´ 4bytes=20MB • 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

37. 4. Resolution without MS

38. 4. Resolution with MS

39. 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

40. 5. Correction: Energy loss • Mainly in the Target and Rich detector • Reconstructed momentum is systematically lower than the original • Ad-hoc correction

41. 5. Pion Mass • Determined from 1/mass plot (mass is not Gaussian) mp=140±1 MeV

42. 5. Particle Identification • Two dimensional cut in Momentum vs Beta • Different cuts for TOF and SHOWER due to their different resolutions

43. 5. PID improvement with 3 chambers Two MDC chambers Three MDC chambers

44. 5. Resolution comparison with 3 chambers Two MDC chambers Three MDC chambers

45. 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:

46. 5. xPull probability distribution for TOF

47. 5. xPull distribution for SHOWER

48. 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

49. 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

50. 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