Rare B meson decays - mathieu trocmé

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II- Physical Background 7 II- PHYSICAL BACKGROUND II.1- Symmetries in Particle Physics: In Particle Physics, there are three fundamental discrete symmetry operations that can be performed on a particle to look at its behaviour. The first one is the charge conjugation operation ‘C’ which inverts all the signs of all the internal quantum numbers of a particle, leaving its mass, energy, momentum p r , spin s r r r and helicity (or ‘handedness’) h ≡ s . p unchanged: r C r r C r p ⎯ ⎯→ p , s ⎯⎯→ s , C h ⎯⎯→ h The second one is the parity operation ‘P’ which reverses all the space coordinates of a particle. Therefore, all its real vectors like its position r and its momentum are reversed, whereas all its axial or pseudo vectors like its spin are not. This implies that its helicity must change. r P r r P r r P r P r ⎯ ⎯→ −r , p ⎯⎯→ − p , s ⎯⎯→ s , h ⎯⎯→ −h As mentioned in the introduction, it is the combined operation CP (or PC) that changes a particle into its antiparticle. The third and last one is the time reversal operation ‘T’ which converts all the properties of a particle into those of the same particle running backwards in time, that is, moving and ‘spinning’ in the opposite direction, leaving its handedness unchanged. r T r r T r p ⎯ ⎯→ − p , s ⎯⎯→ −s , T h ⎯⎯→ h
II- Physical Background 8 These three symmetry transformations were originally thought to be exact symmetries, that is, one could not differentiate between: - a particle observed in a matter universe from its ‘antiparticle’ observed in the same antimatter universe (C conservation) - a ‘mirror-particle’ observed in a mirror universe (P conservation) - a particle moving backwards in time in a universe evolving equally backwards in time (T conservation) However, it turned out that these symmetries can all be broken or violated in weak decays. In 1956, Lee and Yang discovered that parity was not conserved via weak interaction in K mesons systems whereas it was in the electromagnetic and strong ones [5]. This was also successfully corroborated in 1957 by Ms Wu and her team [6]. Soon after, it was found that C was equally violated, especially by examining the spins of − e + + − and e in respectively µ and µ decays [7]. Another example of C violation is the nonexistence of these 2 potential particles that should only be sensitive to the weak interaction, namely the right-handed neutrino ν R ( h > 0 i. e. θ r r ( s , p) < 90° ) and the left-handed antineutrino ν L ( h < 0 i. e. θ r r ( s , p) > 90° ). No experiments have ever observed one or the + − other. For instance, applying C to the decay of a π emitting a ν L should give a π emitting an ν L . But only a ν R is observed. More recently in 1998 and in K meson systems again, the CPLEAR experiment at CERN (CP standing for CP violation and LEAR for Low Energy Anti-proton Ring) observed a case of T violation [8]. Considering the previous example leading to C violation, one can nevertheless see that applying P after C would turn the ν L into ν R which is observed. L ν does not exist => P violation ν R P C ν L C & P ν R C P ν L Figure 1: C and P symmetry operations are violated by the weak interaction. However, the combined CP operation seems to be conserved. ν R does not exist => C violation
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: I- Introduction 6 A way to quantify
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 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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