1. Niels Tuning (1) CP violation Lecture 5 N. Tuning

3. Diagonalize Yukawa matrix Y ij –Mass terms –Quarks rotate –Off diagonal terms in charged current couplings Niels Tuning (3) Recap uIuI dIdI W u d,s,b W

4. Niels Tuning (4) CKM-matrix: where are the phases? u d,s,b W Possibility 1: simply 3 ‘rotations’, and put phase on smallest: Possibility 2: parameterize according to magnitude, in O( λ):

5. This was theory, now comes experiment We already saw how the moduli |V ij | are determined Now we will work towards the measurement of the imaginary part –Parameter: η –Equivalent: angles α, β, γ. To measure this, we need the formalism of neutral meson oscillations… Niels Tuning (5)

6. Some algebra for the decay P 0  f Interference P0 fP0 fP 0  P 0  f

7. Meson Decays Formalism of meson oscillations: Subsequent: decay Interference(‘direct’) Decay Recap osc + decays

8. Classification of CP Violating effects 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference Recap CP violation

9. Im( λ f ) 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference We will investigate λ f for various final states f Recap CP violation

10. Niels Tuning (10) CP eigenvalue of final state J/K 0 S CP |J/> = +1 |J/> CP |K 0 S > = +1 |K 0 S > CP |J/K 0 S > = (-1) l |J/K 0 S > ( S( B )=0  L(J/K 0 S )=1 ) Relative minus-sign between state and CP-conjugated state: ( S(J/)=1 )

11. λ f contains information on final state f Niels Tuning (11) Recap CP in B Investigated three final states f B 0  J/ψK s B 0 s  J/ψφ B 0 s  D s K 3.CP violation in interference

12. λ f contains information on final state f Niels Tuning (12) B 0 s  J/ψφ 3.CP violation in interference Recap CP in B

13. β s : B s 0 J/φ : B s 0 analogue of B 0 J/K 0 S Niels Tuning (13) Recap CP in B

14. Remember! Necessary ingredients for CP violation: 1)Two (interfering) amplitudes 2)Phase difference between amplitudes –one CP conserving phase (‘strong’ phase) –one CP violating phase (‘weak’ phase) Niels Tuning (14)

15. Remember! Niels Tuning (15)

16. Basics The basics you know now! 1.CP violation from complex phase in CKM matrix 2.Need 2 interfering amplitudes (B-oscillations come in handy!) 3.Higher order diagrams sensitive to New Physics Next: (Direct) CP violation in decay CP violation in mixing (we already saw this with the kaons: ε≠0, or |q/p|≠1 ) Penguins The unitarity triangle Niels Tuning (16)

17. Next: γ Niels Tuning (17)

18. Niels Tuning (18) CKM Angle measurements from B d,u decays Sources of phases in B d,u amplitudes* The standard techniques for the angles: *In Wolfenstein phase convention. AmplitudeRel. MagnitudeWeak phase bcbcDominant0 bubuSuppressed γ t  d ( x2, mixing)Time dependent 2β2β B 0 mixing + single b  c decay B 0 mixing + single b  u decay Interfere b  c and b  u in B ± decay. bubu tdtd

19. Niels Tuning (19) Determining the angle  From unitarity we have: Must interfere b  u ( c d) and b  c( u d) Expect b  u ( c s) and b  c( u s) to have the same phase, with more interference (but less events)  3 2 3 2  

20. Measure γ : B 0 s  D s  K -/+ : both λ f and λ  f Niels Tuning (20) NB: In addition  B s  D s  K -/+ : both  λ f and  λ  f + Γ( B  f)= + Γ( B  f )= 2 2

21. Niels Tuning (21) Measure γ : B s  D s  K -/+ --- first one f : D s + K - This time | A f ||A f |, so | λ|  1 ! In fact, not only magnitude, but also phase difference:

22. Measure γ : B s  D s  K -/+ Niels Tuning (22) Need B 0 s  D s + K - to disentangle  and : B 0 s  D s - K + has phase difference ( - ):

23. Next 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference

24. Niels Tuning (24) B A B AR CP violation in Decay? (also known as: “direct CPV”) HFAG: hep-ex/0407057 Phys.Rev.Lett.93:131801,2004 4.2  B A B AR First observation of Direct CPV in B decays (2004): A CP = -0.098 ± 0.012

25. Niels Tuning (25) LHCbLHCb CP violation in Decay? (also known as: “direct CPV”) LHCb-CONF-2011-011LHCbLHCb First observation of Direct CPV in B decays at LHC (2011):

26. Niels Tuning (26) Direct CP violation: Γ( B 0  f) ≠ Γ(B 0  f ) Only different if both δ and γ are ≠0 !  Γ( B 0  f) ≠ Γ(B 0  f ) CP violation if Γ( B 0  f) ≠ Γ(B 0  f ) But: need 2 amplitudes  interference Amplitude 1 + Amplitude 2

27. Niels Tuning (27) Hint for new physics? B 0  Kπ and B   K  π 0 Average 3.6  Average Redo the experiment with B  instead of B 0 … d or u spectator quark: what’s the difference ?? B0KπB0Kπ B+KπB+Kπ

28. Hint for new physics? B 0  Kπ and B   K  π 0 Niels Tuning (28)

29. Hint for new physics? B 0  Kπ and B   K  π 0 Niels Tuning (29) T (tree) C (color suppressed) P (penguin) B0→K+π-B0→K+π- B+→K+π0B+→K+π0

30. Next 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference

31. Niels Tuning (31) CP violation in Mixing? (also known as: “indirect CPV”: ε≠0 in K-system) gV cb * gV cb t=0 t ? Look for like-sign lepton pairs: Decay

32. Niels Tuning (32) (limit on) CP violation in B 0 mixing Look for a like-sign asymmetry: As expected, no asymmetry is observed…

33. CP violation in B s 0 Mixing?? Niels Tuning (33) D0 Coll., Phys.Rev.D82:032001, 2010. arXiv:1005.2757 b s s b “Box” diagram: ΔB=2 φ s SM ~ 0.004 φ s SM M ~ 0.04

34. CP violation from Semi-leptonic decays SM: P(B 0 s →  B 0 s ) = P(B 0 s ←  B 0 s ) DØ: P(B 0 s →  B 0 s ) ≠ P(B 0 s ←  B 0 s ) b → Xμ - ν, b → Xμ + ν b → b → Xμ + ν, b → b → Xμ - ν  Compare events with like-sign μμ  Two methods:  Measure asymmetry of events with 1 muon  Measure asymmetry of events with 2 muons ? Switching magnet polarity helps in reducing systematics But…:  Decays in flight, e.g. K→μ  K + /K - asymmetry

35. CP violation from Semi-leptonic decays SM: P(B 0 s →  B 0 s ) = P(B 0 s ←  B 0 s ) DØ: P(B 0 s →  B 0 s ) ≠ P(B 0 s ←  B 0 s ) ? B 0 s → D s ± X 0 μν

36. More β… Niels Tuning (36)