Rare B meson decays - mathieu trocmé

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III- Analysis Method 35 The final number of signal in the SR is therefore given by: real N sig = ntot _ SR − nbg _ SR where ntot _ SR is the total number of events falling down the SR as counted once all the cuts have been applied and nbg _ SR the estimated number of combinatoric background defined from what has been said above by: nbg _ SR = R × nbg _ GSB = R × ntot _ GSB where nbg _ GSB is the number of combinatoric background in the GSB, that is simply the number of events counted in the GSB once all the cuts have been applied ntot _ GSB . real So finally, = n − ( R × n ) N sig tot _ SR tot _ GSB The systematical error on ntot _ SR and ntot _ GSB is zero (these are just counters) as well as the statistical one on R. The systematical error on this is also obtained by playing with the different parameters offered by the fit function of ROOT. The value of R is taken as the best fit value with an error equal to the half of the maximum deviation to this value: Concerning N , With, real sig 1 ⎧ = Rbest _ fit ± MAX ⎨ Rbest _ fit − Rmax_ fit , Rbest _ fit − R fit 2 ⎩ R min_ stat stat 2 stat 2 σ real = ( σ ) + ( σ ) = n n SR + n ( σ N sig tot _ SR bg _ SR nbg _ SR syst syst 2 syst 2 σ real = σ ) + ( σ ) = n n ( σ syst n N sig SR bg _ SR bg _ SR σ stat n bg_SR = n bg_SR × ⎛ σ ⎜ ⎝ R stat R ⎞ ⎟ ⎠ 2 ⎛ σ + ⎜ ⎜ n ⎝ stat n tot _ GSB tot _ GSB ⎞ ⎟ ⎟ ⎠ 2 stat = ) 2 n n bg_SR tot _ GSB = R n tot _ GSB syst 2 syst 2 syst ⎛σ ⎞ ⎛ σ ⎞ R n R n ⎜ ⎛ tot GSB σ ⎞ _ = ⎟ bg _ SR × ⎜ + = nbg SR × = ntot GSB R ⎟ n ⎜ tot GSB R ⎟ ⎜ ⎟ _ _ _ syst σ × σ nbg _ SR ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎫ ⎬ ⎭ syst R
III- Analysis Method 36 III.3.4- Errors on the branching ratio: As previously seen, the calculation of the branching ratio requires the following stages: ⎛ BR = ⎜ N ⎜ ⎝ real sig Hence, the errors on that branching ratio are such that: σ σ stat BR = BR × ⎛σ ⎜ N ⎜ N ⎝ ⎝ stat real sig real sig ⎞ ⎟ ⎟ ⎠ ⎠ 2 ⎛ σ + ⎜ ⎜ ε ⎝ ⎝ × stat ε MC , corr MC, corr 1 ⎞ ⎟ ⎠ N 0 real B ε MC, corr ⎞ ⎟ ⎟ ⎠ ⎠ 2 ⎛σ ⎜ + ⎜ ⎜ N ⎝ ⎛ σ ⎝ stat real N B 0 real 0 B 2 2 syst syst syst real ⎛σ ⎞ ⎛ σ ⎞ ⎜ N 0 ⎜ N B syst sig ⎟ ⎜ ε MC , corr = × + ⎟ BR BR ⎜ ⎟ + ⎜ ⎟ ⎜ real N sig ε MC, corr ⎜ N 0 B ( since 2 ⎞ ⎟ ⎟ ⎟ ⎠ 2 ⎞ ⎟ ⎟ ⎟ ⎠ = BR × real N 0 = 61 600 000 ± 0 ± 680 000 given ) B ⎛σ ⎜ N ⎜ N ⎝ stat sig sig ⎞ ⎟ ⎟ ⎠ 2 ⎛ σ + ⎜ ⎜ ε ⎝ stat ε MC , corr MC, corr Where all the intermediate calculations to arrive to the final results can be found in looking at the previous parts. It is nonetheless worth noting that the statistical error comes from ntot _ SR and ntot _ GSB whereas the systematical one comes from the background charaterisation ratio R and the corrective factor for the MC Efficiency k corr (and to a lesser extent from real N 0 ). B real N sig = ntot _ SR − nbg _ SR nbg _ SR = R × ntot _ GSB ε = MC, corr kcorrε MC ε MC N = N MC sig MC 0 B ⎞ ⎟ ⎟ ⎠ 2
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 and 32: III- Analysis Method 30 III.3.2- MC
Page 33 and 34: III- Analysis Method 32 With, MC Ns
Page 35: III- Analysis Method 34 By integrat
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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