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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• Physik

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• Publié par: johannes_gutenberg-universitat_mainz
• Publié le: 01 janvier 2006
• Nombre de lectures: 10
• Langue: English
• Poids de l'ouvrage: 10 Mo

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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