1. Physics of Anti-matter Lecture 5
N. Tuning
Niels Tuning (1)

2. Plan Mon 3 Feb: Anti-matter + SM
Wed 5 Feb: CKM matrix + Unitarity Triangle
Mon 10 Feb: Mixing + Master eqs. + B0J/ψKs
Wed 12 Feb: CP violation in B(s) decays (I)
Mon 17 Feb: CP violation in B(s) decays (II)
Wed 19 Feb: CP violation in K decays + Overview
Mon 24 Feb: Mini-project (MSc. V. Syropoulos)
Wed 26 Feb: Exam
Final Mark: 2/3*Exam + 1/6*Homework + 1/6*Mini project
In March: 7 Lectures on Flavour Physics by prof.dr. R. Fleischer
Niels Tuning (2)

4. Recap uI W dI u W d,s,b Diagonalize Yukawa matrix Yij Mass terms
Quarks rotate
Off diagonal terms in charged current couplings u
d,s,b W
Replace the derivative with the covariant derivative introducing the force carriers: gluons, weak vector bosons and photon.
The constants g_s, g and g’ are the corresponding coupling constants of the gauge particles.
Niels Tuning (4) 4

5. CKM-matrix: where are the phases?
Possibility 1: simply 3 ‘rotations’, and put phase on smallest:
Possibility 2: parameterize according to magnitude, in O(λ): u
d,s,b W
Niels Tuning (5)

6. This was theory, now comes experiment
We already saw how the moduli |Vij| 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 (6)

7. Some algebra for the decay P0  f
Interference
P0 f
P0P0 f

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

9. Classification of CP Violating effects
Recap CP violation
Classification of CP Violating effects
CP violation in decay
CP violation in mixing
CP violation in interference

10. Im( λf) CP violation in decay CP violation in mixing
Recap CP violation
Im( λf)
CP violation in decay
CP violation in mixing
CP violation in interference
We will investigate λf for various final states f

11. CP violation: type 3
Niels Tuning (11)

12. λf contains information on final state f
Investigate three final states f:
B0J/ψKs
B0sJ/ψφ
B0sDsK
CP violation in interference
Niels Tuning (12)

13. |λf|=1 Final state f : J/ΨKs
Interference between B0→fCP and B0→B0→fCP
For example: B0→J/ΨKs and B0→B0→ J/ΨKs
Lets’ s simplify …
For B0 we have:
Since fCP =fCP we have:
The amplitudes |A( B0→J/ψKs)| and |A(B0→J/ψKs)| are equal:
|λf|=1
B0 d B0
Niels Tuning (13)

14. Relax: B0J/ΨKs simplifies…
ΔΓ=0
Niels Tuning (14)

15. λf for B0 ® J/yK0S c J/y K0 B0 b s d b d s d
|Vcs Vcd|^2 mc^2 = (1*lambda)^2 mc^2 vs. |Vts Vtd|^2 mt^2 = (lambda^2*lambda^3)^2 mt^2  suppressed by lambda^8, enhanced by (mt/mc)^2 << 1 s d
Niels Tuning (15)

16. Time-dependent CP asymmetry
λf for B0 ® J/yK0S
Time-dependent CP asymmetry
Theoretically clean way to measure b
Clean experimental signature
Branching fraction: O(10-4)
“Large” compared to other CP modes!
|Vcs Vcd|^2 mc^2 = (1*lambda)^2 mc^2 vs. |Vts Vtd|^2 mt^2 = (lambda^2*lambda^3)^2 mt^2  suppressed by lambda^8, enhanced by (mt/mc)^2 << 1
Niels Tuning (16)

17. 2 amplitudes 2 phases Remember!
Necessary ingredients for CP violation:
Two (interfering) amplitudes
Phase difference between amplitudes
one CP conserving phase (‘strong’ phase)
one CP violating phase (‘weak’ phase)
2 amplitudes
2 phases
Niels Tuning (17)

18. λf contains information on final state f
Investigate three final states f:
B0J/ψKs
B0sJ/ψφ
B0sDsK
CP violation in interference
Niels Tuning (18)

19. βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S
Replace spectator quark d  s
Niels Tuning (19)

20. βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S
Niels Tuning (20)

21. Remember: The “Bs-triangle”: βs
Replace d by s:
Niels Tuning (21)

22. βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S
Differences: B0
B0s
CKM
Vtd
Vts ΔΓ ~0
~0.1
Final state (spin)
K0 : s=0
φ: s=1
Final state (K)
K0 mixing -
Niels Tuning (22)

23. βs: Bs0 ® J/yφ A║ A┴ A0 B0 B0s CKM Vtd Vts ΔΓ ~0 ~0.1
Vts large, oscilations fast,
need good vertex detector A║ A0 A┴
l=2
l=1
l=0
3 amplitudes B0
B0s
CKM
Vtd
Vts ΔΓ ~0
~0.1
Final state (spin)
K0 : s=0
φ: s=1
Final state (K)
K0 mixing -
Niels Tuning (23)

24. “Recent” excitement (5 March 2008)
Niels Tuning (24)

25. Bs  J/ψФ : Bs equivalent of B J/ψKs !
The mixing phase (Vtd): φd=2β
B0  f
B0  B0  f
Wolfenstein parametrization to O(λ5):
Niels Tuning (25)

26. Bs  J/ψФ : Bs equivalent of B J/ψKs !
The mixing phase (Vts): φs=-2βs
B0  f
B0  B0  f
Vts - s Ф Bs Bs Ф s s s
Vts
Wolfenstein parametrization to O(λ5):
Niels Tuning (26)

27. Bs  J/ψФ : Bs equivalent of B J/ψKs !
The mixing phase (Vts): φs=-2βs
B0  f
B0  B0  f
Vts - s Ф Bs Bs Ф s s s
Vts
Niels Tuning (27)

28. Next: γ
Niels Tuning (28)

29. CKM Angle measurements from Bd,u decays
Sources of phases in Bd,u amplitudes*
The standard techniques for the angles:
bu
Amplitude
Rel. Magnitude
Weak phase
bc
Dominant
bu
Suppressed γ
td (x2, mixing)
Time dependent 2β
*In Wolfenstein phase convention.
td
B0 mixing + single bu decay
B0 mixing + single bc decay
Interfere bc and bu in B± decay.
Niels Tuning (29)

30. Determining the angle g
From unitarity we have:
Must interfere b  u (cd) and b c(ud)
Expect b  u (cs) and b c(us) to have the same phase, with more interference (but less events) g l3 l l2 1 l3 1 l2 l
Niels Tuning (30)

31. Measure γ: B0s  DsK-/+ : both λf and λf2 +
Γ(Bf)= 2 +
Γ(Bf )=
NB: In addition B s  DsK-/+ : both λ f and λf
Niels Tuning (31)

32. Break
Niels Tuning (32)

33. Measure γ: Bs  DsK-/+ first one f: Ds+K-
This time | Af||Af|, so |λ|1 !
In fact, not only magnitude, but also phase difference:
Niels Tuning (33)

34. Measure γ: Bs  DsK-/+ B0s  Ds-K+ has phase difference ( - ):
Need B0s  Ds+K- to disentangle  and :
Niels Tuning (34)

35. Measure γ: Bs  DsK-/+: in practice!
1) Signal & Backgrounds
Time fit
 m
2) Acceptance
 t
3) Decay time resolution
Expect  with ~ 280 precision
Improve with 2012 data
LHCb average now: 670  120
 Δt
4) Flavour Tagging

36. Zoom Measure γ 1) Backgrounds (from mass fit) Time fit
2) Acceptance vs decay time
3) Decay time resolution
4) Flavour Tagging

37. Measure γ
Time fit
2) Acceptance vs decay time S D C γ Im Re

38. Basics The basics you know now!
CP violation from complex phase in CKM matrix
Need 2 interfering amplitudes (B-oscillations come in handy!)
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 (38)

39. Next
Niels Tuning (39)

40. Next CP violation in decay CP violation in mixing
CP violation in interference

41. CP violation in Decay? (also known as: “direct CPV”)
First observation of Direct CPV in B decays (2004):
BABAR
hep-ex/
Phys.Rev.Lett.93:131801,2004
4.2s
BABAR
HFAG:
ACP = ± 0.012
Niels Tuning (41)

42. CP violation in Decay? (also known as: “direct CPV”)
First observation of Direct CPV in B decays at LHC (2011):
LHCb
LHCb-CONF
LHCb
Niels Tuning (42)

43. 2 amplitudes 2 phases Remember!
Necessary ingredients for CP violation:
Two (interfering) amplitudes
Phase difference between amplitudes
one CP conserving phase (‘strong’ phase)
one CP violating phase (‘weak’ phase)
2 amplitudes
2 phases
Niels Tuning (43)

44. Direct CP violation: Γ( B0 f) ≠ Γ(B0f )
CP violation if Γ( B0 f) ≠ Γ(B0f )
But: need 2 amplitudes  interference
Amplitude 1
Amplitude 2 +
Only different if both δ and γ are ≠0 !
 Γ( B0 f) ≠ Γ(B0f )
Niels Tuning (44)

45. Hint for new physics? B0Kπ and BKπ0
Redo the experiment with B instead of B0…
d or u spectator quark: what’s the difference ??
B0Kπ
Average
3.6s ?
B+Kπ
Average
Niels Tuning (45)

46. Hint for new physics? B0Kπ and BKπ0
Niels Tuning (46)

47. Hint for new physics? B0Kπ and BKπ0
T (tree)
C (color suppressed)
P (penguin)
B0→K+π-
B+→K+π0
Niels Tuning (47)

48. First CP violation in Bs0 system Bs0→K+π−
Historical?
History:
1964: Discovery of CPV with K0 (Prize 1980)
2001: Discovery of CPV with B0 (Prize 2008)
2013: Discovery of CPV with B0s
Bs0→K+π−
Bs0→K−π+

49. Next CP violation in decay CP violation in mixing
CP violation in interference

50. CP violation in Mixing? (also known as: “indirect CPV”: ε≠0 in K-system)
Look for like-sign
lepton pairs:
t=0 t
Decay
gVcb*
gVcb
Niels Tuning (50)

51. (limit on) CP violation in B0 mixing
Look for a like-sign
asymmetry:
As expected, no
asymmetry is observed…
Niels Tuning (51)

52. 2 amplitudes 2 phases Remember!
Necessary ingredients for CP violation:
Two (interfering) amplitudes
Phase difference between amplitudes
one CP conserving phase (‘strong’ phase)
one CP violating phase (‘weak’ phase)
2 amplitudes
2 phases
Niels Tuning (52)

53. CP violation in Bs0 Mixing??
D0 Coll.,
Phys.Rev.D82:032001,2010.
arXiv:
CP violation in Bs0 Mixing?? b s
“Box” diagram: ΔB=2
φsSM ~ 0.004
φsSMM ~ 0.04
Niels Tuning (53)

54. CP violation from Semi-leptonic decays
SM: P(B0s→B0s) = P(B0s←B0s)
DØ: P(B0s→B0s) ≠ P(B0s←B0s) ?
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

55. CP violation from Semi-leptonic decays
SM: P(B0s→B0s) = P(B0s←B0s)
DØ: P(B0s→B0s) ≠ P(B0s←B0s) ?
B0s→Ds±X0μν

56. More β…
Time?
Niels Tuning (56)

57. Other ways of measuring sin2β
Need interference of bc transition and B0 –B0 mixing
Let’s look at other bc decays to CP eigenstates:
All these decay amplitudes have the same phase
(in the Wolfenstein parameterization)
so they (should) measure the same CP violation
Niels Tuning (57)

58. CP in interference with BφKs
Same as B0J/ψKs :
Interference between B0→fCP and B0→B0→fCP
For example: B0→J/ΨKs and B0→B0→ J/ΨKs
For example: B0→φKs and B0→B0→ φKs
Amplitude 1
Amplitude 2 +
e-iφ
Niels Tuning (58)

59. CP in interference with BφKs: what is different??
Same as B0J/ψKs :
Interference between B0→fCP and B0→B0→fCP
For example: B0→J/ΨKs and B0→B0→ J/ΨKs
For example: B0→φKs and B0→B0→ φKs
Amplitude 1
Amplitude 2 +
e-iφ
Niels Tuning (59)

60. Penguin diagrams
Nucl. Phys. B131:
Niels Tuning (60)

61. Penguins?? The original penguin: A real penguin: Our penguin:
Niels Tuning (61)

62. Funny Flying Penguin Dead Penguin Penguin T-shirt: Super Penguin:
Niels Tuning (62)

63.  The “b-s penguin” Asymmetry in SM B0J/ψKS B0φKS b sμ
“Penguin” diagram: ΔB=1
… unless there is new physics!
New particles (also heavy) can show up in loops:
Can affect the branching ratio
And can introduce additional phase and affect the asymmetry
Niels Tuning (63)

64. ? Hint for new physics?? B J/ψ Ks φ Ks B sin2β sin2βpeng g,b,…? ~~d c s φ Ks B s b d t ?
g,b,…? ~~
sin2βbccs = ± 0.03
sin2βpeng = ± 0.05
sin2β
sin2βpeng
Niels Tuning (64)
S.T’Jampens, CKM fitter, Beauty2006