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Measurement of the {K_1hn± → π_1hn+π_1hn-e_1hn±v_1hn(_1hn-_1hn)_1tne [K ± pi + pi - e + - (-) v e] form factors and of the ππ [pi pi] scattering length a_1hn0_1tn0 [Elektronische Ressource] / Lucia Masetti

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Measurement of the(—)± + − ±K →π π e ν form factorse0and of the ππ scattering length a0Dissertationzur Erlangung des Grades“Doktor der Naturwissenschaften”am Fachbereich Physik derJohannes Gutenberg-Universitat¨ MainzLucia Masettigeboren in Ravenna (Italien)Mainz 2006D77 (Diss. Universit¨at Mainz)IIAbstractThequarkcondensateisafundamentalfreeparameterofChiralPerturbationTheory(χPT),sinceitdeterminestherelativesizeofthemassandmomentumtermsinthepowerexpansion.In order to confirm or contradict the assumption of a large quark condensate, on whichχPT0is based, experimental tests are needed. In particular, the S-wave ππ scattering lengths a02and a can be predicted precisely within χPT as a function of this parameter and can be0(—)± + − ±measured very cleanly in the decay K →π π e ν (K ).e e4About one third of the data collected in 2003 and 2004 by the NA48/2 experiment were(—)± + − ±analysed and 342,859 K → π π e ν (K ) candidates were selected. The backgrounde e4contamination in the sample could be reduced down to 0.3% and it could be estimateddirectly from the data, by selecting events with the same signature as K , but requiring fore4the electron the opposite charge with respect to the kaon, the so-called “wrong sign” events.This is a clean background sample, since the kaon decay with ΔS =−ΔQ, that would be theonly source of signal, can only take place through two weak decays and is therefore stronglysuppressed.

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Published 01 January 2006
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Measurement of the
(—)± + − ±K →π π e ν form factorse
0and of the ππ scattering length a0
Dissertation
zur Erlangung des Grades
“Doktor der Naturwissenschaften”
am Fachbereich Physik der
Johannes Gutenberg-Universitat¨ Mainz
Lucia Masetti
geboren in Ravenna (Italien)
Mainz 2006
D77 (Diss. Universit¨at Mainz)IIAbstract
ThequarkcondensateisafundamentalfreeparameterofChiralPerturbationTheory(χPT),
sinceitdeterminestherelativesizeofthemassandmomentumtermsinthepowerexpansion.
In order to confirm or contradict the assumption of a large quark condensate, on whichχPT
0is based, experimental tests are needed. In particular, the S-wave ππ scattering lengths a0
2and a can be predicted precisely within χPT as a function of this parameter and can be0
(—)± + − ±measured very cleanly in the decay K →π π e ν (K ).e e4
About one third of the data collected in 2003 and 2004 by the NA48/2 experiment were
(—)± + − ±analysed and 342,859 K → π π e ν (K ) candidates were selected. The backgrounde e4
contamination in the sample could be reduced down to 0.3% and it could be estimated
directly from the data, by selecting events with the same signature as K , but requiring fore4
the electron the opposite charge with respect to the kaon, the so-called “wrong sign” events.
This is a clean background sample, since the kaon decay with ΔS =−ΔQ, that would be the
only source of signal, can only take place through two weak decays and is therefore strongly
suppressed.
The Cabibbo-Maksymowicz variables, used to describe the kinematics of the decay, were
computed under the assumption of a fixed kaon momentum of 60 GeV/c along the z axis,
so that the neutrino momentum could be obtained without ambiguity. The measurement
0of the form factors and of the ππ scattering length a was performed in a single step by0
comparing the five-dimensional distributions of data and MC in the kinematic variables.
The MC distributions were corrected in order to properly take into account the trigger and
selection efficiencies of the data and the background contamination, The following parameter
2values were obtained from a binned maximum likelihood fit, where a was expressed as a0
0function of a according to the prediction of chiral perturbation theory:0
0f /f = 0.133±0.013(stat)±0.026(syst),ss
00
f /f = −0.041±0.013(stat)±0.020(syst),ss
f /f = 0.221±0.051(stat)±0.105(syst),e s
0
f /f = −0.459±0.170(stat)±0.316(syst),se
˜f /f = −0.112±0.013(stat)±0.023(syst),p s
g /f = 0.892±0.012(stat)±0.025(syst),p s
0g /f = 0.114±0.015(stat)±0.022(syst),sp
h /f = −0.380±0.028(stat)±0.050(syst),p s
0a = 0.246±0.009(stat)±0.012(syst)±0.002(theor),0
where the statistical uncertainty only includes the effect of the data statistics and the theo-
2retical uncertainty is due to the width of the allowed band for a .0Contents
1. Introduction 1
2. Theoretical predictions and previous results 3
2.1. The Standard Model of particle physics . . . . . . . . . . . . . . . . . . . . . 3
2.1.1. Particles, interactions and symmetries . . . . . . . . . . . . . . . . . . 3
2.1.2. The strong interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.3. The electroweak interaction . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2. Chiral Perturbation Theory (χPT) . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1. The chiral symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2. Spontaneous Chiral Symmetry Breaking (SCSB) . . . . . . . . . . . . 11
2.2.3. The quark condensate . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.4. The lowest order chiral Lagrangian . . . . . . . . . . . . . . . . . . . . 12
2.3. The ππ scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
0 22.3.1. Predictions for the scattering lengths a and a . . . . . . . . . . . . . 150 0
2.4. The K decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17e4
2.4.1. The Cabibbo-Maksymowicz variables . . . . . . . . . . . . . . . . . . . 19
2.4.2. Matrix element and decay rate . . . . . . . . . . . . . . . . . . . . . . 19
2.4.3. The Form Factors (FF) . . . . . . . . . . . . . . . . . . . . . . . . . . 20
− + − −2.4.4. The K →π π e ν decay . . . . . . . . . . . . . . . . . . . . . . . 22e
ΔS=−ΔQ
2.4.5. The K decay . . . . . . . . . . . . . . . . . . . . . . . . . . . 23e4
2.5. Previous experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5.1. ππ scattering lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5.2. K form factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25e4
2.5.3. Limits on ΔS =−ΔQ . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3. Experimental apparatus 27
3.1. The Super Proton Synchrotron (SPS) accelerator at CERN . . . . . . . . . . 27
3.2. The NA48/2 beam line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1. The vacuum tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3. The NA48/2 detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1. The KAon BEam Spectrometer (KABES) . . . . . . . . . . . . . . . . 31
3.3.2. The magnetic spectrometer . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.3. The Charged HODoscope (CHOD) . . . . . . . . . . . . . . . . . . . . 37
3.3.4. The Liquid Krypton electromagnetic calorimeter (LKr) . . . . . . . . 38
3.3.5. The Neutral HODoscope (NHOD) . . . . . . . . . . . . . . . . . . . . 43
3.3.6. The HAdron Calorimeter (HAC) . . . . . . . . . . . . . . . . . . . . . 44
3.3.7. The MUon Veto (MUV) . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.8. The photon anti-counters (AKL) . . . . . . . . . . . . . . . . . . . . . 45
VContents
3.3.9. The beam position monitor . . . . . . . . . . . . . . . . . . . . . . . . 46
4. Trigger and data acquisition 49
4.1. The Level 1 trigger (L1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2. The Level 2 trigger (L2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.1. The NeUtral Trigger (NUT) . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.2. The MassBoX (MBX) . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.3. The Trigger Supervisor (TS) . . . . . . . . . . . . . . . . . . . . . . . 54
4.3. The Data AcQuisition (DAQ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.1. The PC-Farm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.2. The Central Data Recording (CDR) . . . . . . . . . . . . . . . . . . . 58
4.4. The Level 3 trigger (L3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5. Reconstruction 61
5.1. The physical objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.1.1. Decoding, reconstruction and COmPACT output . . . . . . . . . . . . 61
5.1.2. Track reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.1.3. LKr cluster reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.1.4. MUV hits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2. The COmPACT reader program . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2.1. Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2.2. Vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2.3. Muon reconstr . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2.4. SuperCOmPACT production and filtering . . . . . . . . . . . . . . . . 66
6. Monte Carlo simulation 69
6.1. Kaon beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2. Kaon decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2.1. The K generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71e4
6.2.2. Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2.3. Radiative corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.2.4. Coulombtion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.3. Tracking in the detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.3.1. Electromagnetic showers . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.3.2. Pion decay in flight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.4. Reconstruction and corrections . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.4.1. The generated four-momenta in SuperCOmPACT . . . . . . . . . . . 75
7. Event selection and reconstruction 77
7.1. Data and MC samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.2. Selection criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.2.1. Pre-selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.2.2. Vertex selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7.2.3. Particle identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.2.4. Differences in the MC selection . . . . . . . . . . . . . . . . . . . . . . 82
7.3. Event reconstruction and background rejection . . . . . . . . . . . . . . . . . 83
VIContents
7.3.1. K events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83e4
7.3.2. K events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853π
7.3.3. K events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862πD
7.4. Background estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.4.1. “Wrong sign” events . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.4.2. Accidental background . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.4.3. K with π→eν . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903π
7.4.4. K with pion mis-identification . . . . . . . . . . . . . . . . . . . . . 903π
7.4.5. K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 922πD
7.4.6. K 0 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92ππ π
D
7.4.7. Total background estimate with systematic uncertainty . . . . . . . . 93
7.5. Summary of selected events, acceptance and background contamination . . . 94
8. Fit method 97
8.1. Computation of the Cabibbo-Maksymowicz variables . . . . . . . . . . . . . . 97
8.2. Preliminary checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
8.2.1. Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
8.2.2. Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
8.3. Corrections applied to the MC . . . . . . . . . . . . . . . . . . . . . . . . . . 100
8.3.1. Trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8.3.2. Electron identification . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
8.3.3. Pion identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8.3.4. Total weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.4. Fit strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
8.5. Raw result of the first iteration . . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.6. Raw result of the second iteration. . . . . . . . . . . . . . . . . . . . . . . . . 111
9. Corrections and systematic uncertainties 115
9.1. MC tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9.1.1. Corrected result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.2. Systematics of the fit method . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.2.1. Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.2.2. Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
9.2.3. Number of bins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.2.4. MC statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9.3. Systematics from the uncertainty on efficiencies and corrections . . . . . . . . 119
9.3.1. Statistical uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.3.2. Systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.4. Systematics of the MC simulation and event selection . . . . . . . . . . . . . 120
9.4.1. Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
9.4.2. Momentum resolution, kaon spectrum and background expectation . . 122
9.4.3. K reconstructed as K . . . . . . . . . . . . . . . . . . . . . . . . 1232πD e4
9.4.4. Fit of subsamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
9.4.5. Alternative electron identification and computation of the kinematic
variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.4.6. Radiative and Coulomb corrections . . . . . . . . . . . . . . . . . . . . 130
VIIContents
09.5. Theoretical uncertainty and different constraints on a . . . . . . . . . . . . . 1310
2 09.5.1. Uncertainty on the constraint between a and a . . . . . . . . . . . . 1320 0
29.5.2. Universal band and free a . . . . . . . . . . . . . . . . . . . . . . . . 1320
0 19.5.3. δ −δ as a function of s . . . . . . . . . . . . . . . . . . . . . . . . . 133π0 1
9.6. Summary of the systematic and theoretical uncertainties . . . . . . . . . . . . 134
10.Result and discussion 137
10.1.Fit result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.2.Comparison with previous results . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.3.Comp with the theoretical predictions . . . . . . . . . . . . . . . . . . . 140
10.4.Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
11.Summary 143
A. The K matrix element 145e4
B. Additional Figures and Tables to Chapter 8 149
B.1. Efficiency of tight pion ID in data and MC . . . . . . . . . . . . . . . . . . . 149
B.2. K MC distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150e4
B.3. Log-likelihood curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
VIIIList of Tables
2.1. Fermions in the standard model . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2. Interactions and symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3. Charged kaon decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1. Properties of liquid krypton . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1. L1 trigger codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2. Trigger-word . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
7.1. Selected data events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.2. Selected MC events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
8.1. Additional parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
8.2. Raw result of the two iterations . . . . . . . . . . . . . . . . . . . . . . . . . . 111
8.3. Correlation matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.1. Corrected result of the two iterations . . . . . . . . . . . . . . . . . . . . . . . 117
9.2. Systematics of the fit method . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9.3. Uncertainty on the MC corrections . . . . . . . . . . . . . . . . . . . . . . . . 120
9.4. Systematic uncertainty on the acceptance . . . . . . . . . . . . . . . . . . . . 123
9.5. Sys uncertainty on the reconstruction . . . . . . . . . . . . . . . . . . 124
9.6. Systematic uncertainty on the agreement between data and MC . . . . . . . . 127
9.7. Sys uncertainty on the electron ID and kinematic variables . . . . . . 131
9.8. Systematic uncertainty on the radiative and Coulomb corrections . . . . . . . 132
9.9. Summary of the sources of systematic uncertainties . . . . . . . . . . . . . . . 135
10.1.Comparison of the form factor parameters with BNL E865 . . . . . . . . . . . 139
± ± 0 010.2.Comp of the scattering length with BNL E865 and the K → π π π
cusp analysis of NA48/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
IXList of Tables
X