1. University of Gaziantep Department of Engineering Physics April 2007 Page 1 Ph.D. Thesis in Engineering Physics University of Gaziantep Supervisor: Assoc. Prof. Dr. Ayda BEDDALL Co-supervisor: Assist. Prof. Dr. Andrew BEDDALL By Ahmet BİNGÜL April 2007

2. University of Gaziantep Department of Engineering Physics April 2007 Page 2 Introduction High energy collisions of sub-atomic particles can result in events containing a high multiplicity of hadronic particles. An example was the production of Z 0 Bosons at LEP an e + e − collider with E CM = 91.2 GeV (≈ 1.5 x 10 −8 Joules) Chapter 1-2

3. University of Gaziantep Department of Engineering Physics April 2007 Page 3 Chapter 1-2

4. University of Gaziantep Department of Engineering Physics April 2007 Page 4 The Standard Model Chapter 1-2

5. University of Gaziantep Department of Engineering Physics April 2007 Page 5 The transition: quarks and gluons  hadrons can only be described by phenomenological models. The measurement of inclusive particle production cross sections of resonant states (e.g: ω or ρ ) improves the description of the hadronization process. LEP was ideal for studying hadronization. Chapter 1-2

6. University of Gaziantep Department of Engineering Physics April 2007 Page 6 This study describes the ALEPH measurement of  the production rate and  the differential cross section of the meson in hadronic decays of the Z boson. candidates are reconstructed from the decay channel: The results are compared with:  JETSET 7.4 (a Monte Carlo event generator software)  OPAL measurement (unique at LEP) Chapter 1-2

7. University of Gaziantep Department of Engineering Physics April 2007 Page 7 The Large Electron-Positron Collider (LEP)  Circumference 27 km (largest e + e − collider)  Located in an underground at a depth about 100 m  Operated between 1989 – 1995; E CM = 91.2 GeV for Z between 1995 – 2000; E CM = 160–190 GeV for W + W – for ALEPH, DELPHI, OPAL and L3 experiments Chapter 3

8. University of Gaziantep Department of Engineering Physics April 2007 Page 8 Particle Detectors Detectors employed in HEP experiments record position, arrival time, momentum, energy and identity of particles. Charged particles ( ) can be detected through their ionisation in tracking chambers * a measure of the curvature of the track in a magnetic field gives a measure of its momentum * a measure of the rate of ionisation loss (dE/dx) can be used to determine its type Neutral particles ( ) are detected via calorimeters, where their position and energy are measured. Chapter 3

9. University of Gaziantep Department of Engineering Physics April 2007 Page 9 Different particle types interact differently with matter e.g. photons do not feel a magnetic field We need different types of detectectors to measure different types of particles. Chapter 3

10. University of Gaziantep Department of Engineering Physics April 2007 Page 10 The ALEPH Detector Chapter 3

11. University of Gaziantep Department of Engineering Physics April 2007 Page 11 Chapter 3

12. University of Gaziantep Department of Engineering Physics April 2007 Page 12 Tracking Chambers DetectorResolutionPhoto Vertex Detector (VDET) Inner Tracking Chamber (ITC) Time Projection Chamber (TPC) Chapter 3

13. University of Gaziantep Department of Engineering Physics April 2007 Page 13 Electromagnetic Calorimeter (ECAL) For electrons and photons of high energy, a dramatic result of the combined phenomena of bramsstrahlung and pair production is the occurance of cascade showers. A parent electron will radiate photons, which converts to pairs, which radiate and produce fresh pairs in turn, the number of particles increasing exponentially with depth in the medium. Chapter 3

14. University of Gaziantep Department of Engineering Physics April 2007 Page 14 Chapter 3

15. University of Gaziantep Department of Engineering Physics April 2007 Page 15 Energy resolution Spatial resolution Chapter 3

16. University of Gaziantep Department of Engineering Physics April 2007 Page 16 Event Reconstruction and Simulation Chapter 4

17. University of Gaziantep Department of Engineering Physics April 2007 Page 17 Event Selection Chapter 5 The ALEPH detector recorded a variety of events  events  most of decays of Z boson to its various modes In addition, there are small number of background: − beam-gas interaction − beam electrons − cosmic rays

18. University of Gaziantep Department of Engineering Physics April 2007 Page 18 Chapter 5

19. University of Gaziantep Department of Engineering Physics April 2007 Page 19 To remove events which suffer from a low geometric acceptance, a cut applied on the polar angle, θ, of the event axis as defined by sphericity. Events are accepted if 35 o < θ < 145 o (|cos θ|<0.82)

20. University of Gaziantep Department of Engineering Physics April 2007 Page 20 Hadronic Event Selection Hadronic events are selected on the basis of the total charged multiplicity and energy within an event. For this, cuts are applied to select ‘good charged tracks’. Track Cuts removes same badly reconstructed tracks. A good charged track must have:  at least 4 TPC hits  a polar angle 20 o < θ < 160 o  a transverse impact parameter |d 0 |<2 cm  a longitudinal impact parameter |z 0 |< 5cm  a transverse momentum p t > 200 MeV/c Chapter 5

21. University of Gaziantep Department of Engineering Physics April 2007 Page 21 Chapter 5

22. University of Gaziantep Department of Engineering Physics April 2007 Page 22 With these cuts a total 3,239,746 hadronic events are selected with efficiency: ε = 95.0 % purity : P = 99.6 % from data recorded by ALEPH from 1991 to 1995 running periods. Chapter 5 Event Cuts 1. a minimum of 5 ‘good’ tracks 2. a minimum of 15 GeV total ‘good’ charged energy

23. University of Gaziantep Department of Engineering Physics April 2007 Page 23 Flow chart of hadronic event selection: Chapter 5

24. University of Gaziantep Department of Engineering Physics April 2007 Page 24 Track Selection candidates are reconstructed from the decay channel: selection is relatively trivial, while selection and reconstruction is more complicated. All selection performances are determined from the Monte Carlo with the aim to maximise both purity and efficiency. Chapter 6

25. University of Gaziantep Department of Engineering Physics April 2007 Page 25 Charged Track Selection All good tracks originating from IP are considered as pions. The following cuts select with ε = 95% and P = 43% Chapter 6 a transverse impact parameter |d 0 |<0.5 cm longitudinal impact parameter |z 0 |< 3.0 cm a transverse momentum p t > 250 MeV/c if available, −2 < χ(dE/dx) < 3 (with pion hypothesis)

26. University of Gaziantep Department of Engineering Physics April 2007 Page 26 Tight cuts on the impact parameters are introduced to increase the reconstruction purity of mesons from. Chapter 6

27. University of Gaziantep Department of Engineering Physics April 2007 Page 27 Charged particle identification is performed by the measurement of ionisation energy loss, dE/dx. The deviation from an assumed hypothesis expressed as: Chapter 6

28. University of Gaziantep Department of Engineering Physics April 2007 Page 28 Neutral Pion Selection Selection: Neutral pions are built from the decay Invariant mass spectra is built up by the equation: Following cuts are applied: Each photon energy E γ > 1 GeV Pion energy E π < 18 GeV Invariant mass of two photon M(γ 1,γ 2 ), should be within ±2σ mass window around pion signal. σ is defined as HWHM. Poor purity of the pions are improved by a ‘Ranking’ Method. Chapter 6

29. University of Gaziantep Department of Engineering Physics April 2007 Page 29 The topology of reconstructed is found to be important. Geometric representation of four possible topologies are given right. Chapter 6 Photon pairs taken from: topology 1: one ECAL cluster, within which two subclusters are resolved topology 2: one ECAL cluster, within which more than two subclusters are resolved topology 3: two ECAL clusters, within each of which no subclusters are resolved topology 4: two ECAL clusters, within one or both of which more than one subcluster is resolved

30. University of Gaziantep Department of Engineering Physics April 2007 Page 30 Mass Constraint Uncertainties in the reconstructed momentum vector of a are introduced due to the finite ECAL spatial and energy resolution. To improve the momentum resolution of the pion the reconstructed mass can be constrained to the nominal pion mass of 135 MeV/c 2. This is done by modifying the photon energies (E 1 and E 2 ) and opening angle (θ) between photons until the required mass is obtained. These parameters can be found by minimising the chi- square form: with mass constraint: Chapter 6

31. University of Gaziantep Department of Engineering Physics April 2007 Page 31 Neutral Pion Calibration Selecting candidates from a mass window around the peak provides initial rejection of most of the combinatorial background. It is found that: peak mass and width of the signal depend on both energy and topology. So, we need to calibrate two functions: Chapter 7

32. University of Gaziantep Department of Engineering Physics April 2007 Page 32 The calibration procedure is as follows: 1.The mass spectra is plotted for the matched pion signal (for each topology in 1 GeV energy intervals) 2.The peak (signal) is fitted with a Gaussian from which positions a and b, taken at half height, are measured 3.Half width at half maximum HWHM and the center of the mass window are evaluated Chapter 7

33. University of Gaziantep Department of Engineering Physics April 2007 Page 33 Chapter 7

34. University of Gaziantep Department of Engineering Physics April 2007 Page 34 An example to show the performance of the calibration for each topology for pion energy between The calibration functions give a correct selection of peak.

35. University of Gaziantep Department of Engineering Physics April 2007 Page 35 The Ranking Method Consider n photons taken from the ECAL. We can form candidates by building photon pairs as follows: Chapter 8 Number of combinations: we have candidates forming S+B but only of them are true forming S. Signal-to-background ratio:

36. University of Gaziantep Department of Engineering Physics April 2007 Page 36 Purity and Efficiency In this study, we define the neutral pion purity ( ) and efficiency ( ) as follows: where: S is the number of signal, and B is the number of background for the given mass window and S 0 is the total number of signal within mass window Chapter 8

37. University of Gaziantep Department of Engineering Physics April 2007 Page 37 The Standard Method Chapter 8

38. University of Gaziantep Department of Engineering Physics April 2007 Page 38 Chapter 8

39. University of Gaziantep Department of Engineering Physics April 2007 Page 39 Chapter 8

40. University of Gaziantep Department of Engineering Physics April 2007 Page 40 Chapter 8

41. University of Gaziantep Department of Engineering Physics April 2007 Page 41 Chapter 8

42. University of Gaziantep Department of Engineering Physics April 2007 Page 42 Chapter 8

43. University of Gaziantep Department of Engineering Physics April 2007 Page 43 Chapter 8

44. University of Gaziantep Department of Engineering Physics April 2007 Page 44 Estimators An estimator, based on kinematics of, can be used to discriminate signal and background. Following distributions define our estimators: Solid curve has the form: Chapter 8

45. University of Gaziantep Department of Engineering Physics April 2007 Page 45 Ranking Method After the initial mass window selection, additional improvement can be achived by applying the estimator indirectly with a ‘Ranking’ method. The algorithm is as follows: 1.Pion estimator values are calculated for each pion in an event 2.Pions candidates are ranked according to their estimator values 3.A scan is then made through the list for pairs of pions which share photons. When such a pair exist, one or both candidates must be false; the candidate with largest estimator value is removed Chapter 8

46. University of Gaziantep Department of Engineering Physics April 2007 Page 46 Example of applying Ranking method: SELECTED CANDIDATES BEFORE RANKING Pion Photon Truth # est. 1 2 info. A 0.05 A1 A2 TRUE B 0.12 B1 B2 TRUE X 0.19 D1 E1 FALSE C 0.28 C1 C2 TRUE Y 0.45 A1 B2 FALSE D 0.63 D1 D2 TRUE Z 0.87 C2 E2 FALSE SELECTED CANDIDATES AFTER RANKING Pion Photon Truth # est. 1 2 info. A 0.05 A1 A2 TRUE B 0.12 B1 B2 TRUE X 0.19 D1 E1 FALSE C 0.28 C1 C2 TRUE Chapter 8 To investigate performance of the Ranking method, the mass window, and pion energy is varied. The results are compared with the standard method. Performance is measured in terms of the product:

47. University of Gaziantep Department of Engineering Physics April 2007 Page 47 Performance of the Ranking Method Mass window Energy Chapter 8

48. University of Gaziantep Department of Engineering Physics April 2007 Page 48 Example Applications Chapter 8

49. University of Gaziantep Department of Engineering Physics April 2007 Page 49 Extraction of the Signal The rate and cross section of the meson are extracted from the invariant mass distribution of its daughter pions, by fitting the invariant mass to a sum of signal and background functions. Extraction of yield is complicated by:  the large with resonance  the reflection of other mesons (especially )  the partially reconstructed signal  the large combinatorial background  the residual Bose-Einstein correlations that affects both signal and background shape Chapter 9

50. University of Gaziantep Department of Engineering Physics April 2007 Page 50 Two-pion Invaiant Mass Charged and Neutral pions are selected as described in Chapter 6. Invariant mass of two pions is defined as: where with Chapter 9

51. University of Gaziantep Department of Engineering Physics April 2007 Page 51 Signal Reconstruction The data is analysed in  six intervals of scaled momentum:  nine intervals of scaled energy: Here (about 45.6 GeV) is the LEP momentum. Note The results of the measurements in x p intervals are compared with those of ALEPH ρ 0 measurement in x E intervals are compared with OPAL ρ ± measurement Chapter 9

52. University of Gaziantep Department of Engineering Physics April 2007 Page 52 Using Monte Carlo, we can study the theoretical shape of the momentum and energy distributions for the generated and reconstructed mesons. The mean efficiency in each interval is used to correct the extracted signal in both Monte Carlo and real data. Chapter 9

53. University of Gaziantep Department of Engineering Physics April 2007 Page 53 Signal Extraction and Fitting Procedure Signal Shape Basic line shape for the signal is a relativistic p-wave BreitWigner: with m is the two-pion invariant mass m 0 is the resonance peak mass is the mass dependent width is the nominal width (FWHM) q is the momentum of the decay products in the rest frame of parent q 0 is the momentum when m = m 0 Monte Carlo ( J ETSET ) uses a non-relativistic Breit-Wigner: ( truncated between 0.3 and 1.3 GeV/c 2 ) Chapter 9

54. University of Gaziantep Department of Engineering Physics April 2007 Page 54 Signal Shape Nominal values are: [PDG 2006] Chapter 9

55. University of Gaziantep Department of Engineering Physics April 2007 Page 55 Partially Reconstructed Signal An important consideration is the effect of partially reconstructed mesons where a is reconstructed from originating from signal and one that is not. Such a combination contains most of the kinematics of the signal for this reason partial signal has similar, but wider shape. Chapter 9

56. University of Gaziantep Department of Engineering Physics April 2007 Page 56 The width ( ) and peak mass ( ) are different from the nominal values due to resolution effects, which is dominated by component. The mass resolution ( ) and peak mass ( ) of the meson are determined from the Monte Carlo. Chapter 9

57. University of Gaziantep Department of Engineering Physics April 2007 Page 57 Summary for the Signal function:  In the fits, nominal values (, ) are replaced by and  The height of the partially reconstructed signal ( H P ) is parameterised as a function of fully reconstructed signal height (H F ), since they are correlated. The ratio r = H F / H P is taken from the Monte Carlo predictions.  Signal function is parametrised as a sum of two RBW functions: p 0 is the normalisation constant. Note that RBW is replaced by BW in the Monte Carlo fits. Chapter 9

58. University of Gaziantep Department of Engineering Physics April 2007 Page 58 Combinatorial Background The combinatorial background is parameterised by a smooth function: where The free parameters p 1 − p 5 are adjusted by the fitting procedure. Reflections mass spectra contain reflections from the decays: Chapter 9

59. University of Gaziantep Department of Engineering Physics April 2007 Page 59 Appropriate functions representing each reflection are selected and fitted to the Monte Carlo. in the Monte Carlo, the height of each reflection is fixed in real data, the height of each reflection (taken from MC) is scaled by a value obtained from the real data measurements. Chapter 9

60. University of Gaziantep Department of Engineering Physics April 2007 Page 60 Bose-Einstein Correlations Bose-Einstein Correlations (BECs) are an apparent attraction in phase-space between identical bosons. Features of BEC:  BEC is relevant if and only if identical bosons (such as pions) are close to each other in phase-space.  Most of the particles generated in hadronic events are pion triplets obeying Bose statistics. As a result, BECs affect the dynamics of the pions in the final state.  BECs are quantum mechanical effect that must appear during the fragmentaion state. Hence, measurement of BECs can help the understanding of QCD studies.  BECs are not implemented in MC programs effectively. Chapter 9

61. University of Gaziantep Department of Engineering Physics April 2007 Page 61 Residual Bose-Einstein Correlations Experimental studies reveal that BECs affect the distribution of effective masses of pairs originating from the IP. The life-time (~10 −24 s) and therefore decay length (~ 1fm) of the meson is sufficiently short that pions from the decay can be considered as coming from the IP. Hence a ‘Residual’ BECs must affect on pions of the meson. Most appearent sign of residual BEC is a distortion in the mass spectra. Chapter 9

62. University of Gaziantep Department of Engineering Physics April 2007 Page 62 The distortion in real data can be described by interference effect, believed to originate from residual BECs, between the amplitudes of and coherent (non-resonant) background. A successful parameterisation is performed by Söding Model used before in the and analysis. To include the interference effect, the fit function is extended by adding the term: where C is the strength of the interference, and is determined from data fits. Chapter 9

63. University of Gaziantep Department of Engineering Physics April 2007 Page 63 The interference term is a model to describe the distortion affecting both signal and background. This can be shown by removing the interference term from the real data mass distribution. Chapter 9 C = 0.00  original distribution C = 0.30  close to its fitted value of 0.28

64. University of Gaziantep Department of Engineering Physics April 2007 Page 64 Total Fit Function Total fit function is built by adding six model functions as follows: Note that is omitted for the Monte Carlo Chapter 9

65. University of Gaziantep Department of Engineering Physics April 2007 Page 65 Rates & Cross Sections Production Rate: N : number of selected hadronic events S : number of (fitted) signal : width of the energy interval ε : reconstruction efficiency defined as: ε = = number of reconstructed rho-mesons in MC number of generated rho-mesons in MC n rec n gen Differential Cross Section: Chapter 9

66. University of Gaziantep Department of Engineering Physics April 2007 Page 66 Systematic Error Analysis Statistical errors originate from counting (statistical) uncertainties that result in measured values being randomly high or low. Systematic errors originate from detector effects, uncertainties in models, measurement procedures resulting in measured values being systematically high or low. Possible source of systematic errors:  track selection cuts  fitting procedure  reflection models  signal function  efficiency correction  uncertainty in the extrapolation to full x p and x E ranges Chapter 10

67. University of Gaziantep Department of Engineering Physics April 2007 Page 67 Chapter 10

68. University of Gaziantep Department of Engineering Physics April 2007 Page 68 Chapter 10

69. University of Gaziantep Department of Engineering Physics April 2007 Page 69 Results Chapter 11

70. University of Gaziantep Department of Engineering Physics April 2007 Page 70 Chapter 11

71. University of Gaziantep Department of Engineering Physics April 2007 Page 71 Chapter 11

72. University of Gaziantep Department of Engineering Physics April 2007 Page 72 Chapter 11

73. University of Gaziantep Department of Engineering Physics April 2007 Page 73 Chapter 11

74. University of Gaziantep Department of Engineering Physics April 2007 Page 74 Summary of the Analysis

75. University of Gaziantep Department of Engineering Physics April 2007 Page 75 Conclusion  Inclusive production of the mesons in hadronic Z decays has been observed with the ALEPH detector.  Measured rate and differential cross-section are in good agreement with OPAL measurements within the error bars.  Monte Carlo rates obtained from J ETSET and P YTHIA are consistent with the real data measurements of two independent experiments.  The model for BEC used in our study is same as the OPAL. This model successfully describes distortion in two-pion invariant mass. Chapter 11

76. University of Gaziantep Department of Engineering Physics April 2007 Page 76 Future Work Experiences gained in this study can be applied to future work in a number of possible areas:  Particle production involving decay products  A measurement of  Much work needs to be done to implement BECs in the MC models, since BECs are not implemented in MC correctly. This is important for LEP and LHC.  Work on the ATLAS Experiment. Chapter 11

77. University of Gaziantep Department of Engineering Physics April 2007 Page 77 Publications  A. Beddall, A. Beddall, A. Bingül, Y. Durmaz A Comparison of Multi-Variate PDE Methods in Neutral Pion Discrimination, Acta Physica Polonica B, 38 187-195 (2007).  A. Beddall, A. Beddall, A. Bingül, Y. Durmaz Smoothed multi-variate histogrammed PDEs, and $chi^2$ optimisation, Computer Physics Communications, 175 700-707 (2006).  A. Beddall, A. Beddall, A. Bingül Reducing systematic errors in the selection of signals from two- photon mass spectra, Nuclear Inst. and Methods in Phy. Res A, 554 469-473 (2005).  A. Beddall, A. Beddall, A. Bingül A Ranking Method for Neural Pion Selection in High Multiplicity Hadronic Events, Nuclear Inst. and Methods in Phy. Res A 482, 520- 527 (2002). * A Ranking Method for Neutral Pion and Eta Selection in Hadronic Events, TFD 22 (2004) * Inclusive Production of rho+- mesons in Hadronic Z Decays, AIP 899 (2007)

78. University of Gaziantep Department of Engineering Physics April 2007 Page 78 QUESTIONS ?