Rare B meson decays - mathieu trocmé

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III- Analysis Method 31 The corrected MC Efficiency ε MC, corr is given by: ε = MC, corr kcorrε MC where the correction k corr depends on many other factors that are associated with the cuts applied : k k k k k k × k corr = evtShp × PID × trk × 0 × K ∆ S The k evtShp factor is a correction on the event shape modelling process, the k PID one on the 0 PID process, the k trk one on the tracking process, the k 0 one on the K K S selection and the k∆ E S and the km ones on the ∆ E and m ES ES calculations. Except for k trk which must be calculated from the data used, all the other correction factors have been previously calculated, especially by N. Chevalier [18]. Two kinds of error therefore come from the corrected MC efficiency: a statistical one MC due to the counting method used to calculate ε MC ( N sig is just a counter) and a systematical one due to the above corrections (the error on the k factors being only systematical) used to calculate the ‘real’ MC Efficiency (the corrected one). This mathematically leads to the following errors: σ σ = ε ε = MC, corr kcorrε MC × ⎛σ ⎜ k ⎜ ⎝ stat corr ⎞ ⎟ ⎟ ⎠ 2 ⎛σ + ⎜ ⎜ ε ⎝ stat ε MC ⎞ ⎟ ⎟ ⎠ E = ε m ES ⎛σ × ⎜ ⎜ ⎝ stat ε stat corr MC MC ε MC , corr MC, corr k MC, corr ε syst ε MC , corr = ε MC, corr × ⎛σ ⎜ k ⎜ k ⎝ syst corr corr ⎞ ⎟ ⎟ ⎠ 2 ⎛σ ⎜ ε + ⎜ ε ⎝ syst MC MC ⎞ ⎟ ⎟ ⎠ 2 2 = ε MC, corr ⎛σ ⎜ k × ⎜ k ⎝ stat Since as aforementioned σ kcorr = 0. 0 and since MC B O N being fixed by the MC programmer ( N syst = 50 , 000 ± 0 ± 0 ), σ = 0. 0 (since MC N = ε / N ) B O ε MC MC MC syst corr corr sig ⎟ ⎟ ⎞ ⎠ ⎟ ⎟ ⎞ ⎠ MC B O
III- Analysis Method 32 With, MC Nsig 1) ε = ⇒ MC MC N 0 B stat σ ε MC = ε MC × stat stat 2 MC ⎛σ MC ⎞ ⎛σ ⎞ N N ⎜ B 0 ⎜ ⎟ sig ⎟ + ⎜ MC ⎜ MC ⎟ N ⎟ sig ⎜ N 0 ⎝ ⎠ B ⎟ ⎝ ⎠ = MC (since N = 50 , 000 ± 0 ± 0 ) 2) k corr = kevtShp × kPID × ktrk × k 0 × k K ∆E × k S mES ⇒ σ B O 2 2 2 2 syst 2 syst syst ⎛ ⎞ syst syst ⎛ ⎞ syst σ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ 0 ⎜ ⎟ σ σ σ ⎟ ⎜ k ⎜ ⎟ σ σ ⎜ ⎟ ⎜ ⎟ ⎜ k syst kevtShp k K m PID ktrk S k∆E ES = k × + + + ⎜ ⎟ + + k corr ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ corr kevtShp kPID ktrk 0 ⎜ kK ⎟ k∆E S ⎜ k mES ⎝ ⎠ ⎝ III.3.3- Background Characterisation and Subtraction: As previously mentioned, the background events remaining in the whole ∆E - mES plane once all the cuts have been applied, are mainly of a random combinatoric nature, i.e. they are 0 0 in fact B / B candidates reconstructed from completely random particles. Thus, for one real 0 0 B / B , many ⎠ ⎝ 0 0 B / B candidates exist. To avoid multi-counting, a special variable called nevent is used. This is associated with all the same real decay: 0 0 / B ⎠ 2 ⎝ ε N ⎠ MC MC sig ⎝ ⎠ ⎝ 2 ⎞ ⎟ ⎟ ⎟ ⎠ 0 0 B / B candidates assumed to come from the 0 0 B / B candidate # 0 1 2 3 4 5 6 7 8 9 nevent 1 1 2 2 2 2 3 4 5 5 Table 2: To avoid multi-counting, the ‘nevent’ variable is used. 0 0 / B Amongst all these B candidates, only one or zero can be a real B . In order to only keep one candidate and not to underestimate the number of combinatoric background events in the GSB (this will be of great help later), a candidate is usually chosen completely at random.
Page 1 and 2: UNIVERSITY OF BRISTOL DEPARTMENT OF
Page 3 and 4: Acknowledgements 2 ACKNOWLEDGEMENTS
Page 5 and 6: Table of contents 4 III.3.5- Backgr
Page 7 and 8: I- Introduction 6 A way to quantify
Page 9 and 10: II- Physical Background 8 These thr
Page 11 and 12: II- Physical Background 10 s b gWVu
Page 13 and 14: II- Physical Background 12 II.3- B
Page 15 and 16: II- Physical Background 14 To creat
Page 17 and 18: II- Physical Background 16 As a res
Page 19 and 20: III- Analysis Method 18 III- ANALYS
Page 21 and 22: III- Analysis Method 20 Number of e
Page 23 and 24: III- Analysis Method 22 III.2.2.3-
Page 29 and 30: III- Analysis Method 28 0 B ? 0 B ?
Page 31: III- Analysis Method 30 III.3.2- MC
Page 35 and 36: III- Analysis Method 34 By integrat
Page 37 and 38: III- Analysis Method 36 III.3.4- Er
Page 39 and 40: III- Analysis Method 38 All the sel
Page 41 and 42: III- Analysis Method 40 For example
Page 43 and 44: III- Analysis Method 42 III.5- Over
Page 45 and 46: IV- Results 44 IV- RESULTS IV.1- Fi
Page 47 and 48: IV- Results 46 IV.2- MC Efficiency
Page 49 and 50: IV- Results 48 Another common notat
Page 51 and 52: V- Discussion 50 V- DISCUSSION As d
Page 53 and 54: V- Discussion 52 Concerning the opt
Page 55 and 56: Appendix 54 APPENDIX This appendix
Page 57 and 58: References 55 [1] [2] [3] [4] [5] [

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