1. Particle Physics II – CP violation (also known as “Physics of Anti-matter”) Lecture 5
N. Tuning
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2. Plan Mon 5 Feb: Anti-matter + SM
Wed 7 Feb: CKM matrix + Unitarity Triangle
Mon 26 Feb: Mixing + Master eqs. + B0J/ψKs
Wed 28 Feb: CP violation in B(s) decays (I)
Mon 12 Mar: CP violation in B(s) and K decays (II)
Wed 14 Mar: Rare decays + Flavour Anomalies
Wed 21 Mar: Exam
Final Mark:
if (mark > 5.5) mark = max(exam, 0.85*exam *homework)
else mark = exam
In parallel: Lectures on Flavour Physics by prof.dr. R. Fleischer
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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.
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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
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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…
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7. Meson Decays Formalism of meson oscillations: Subsequent: decay P0 f
Interference
P0 f
P0P0 f
Interference
(‘direct’) Decay

8. Classification of CP Violating effects
CP violation in decay
CP violation in mixing
CP violation in interference
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9. 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
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10. Remember!
2 amplitudes
2 phases
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11. CP violation: type 3
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12. Classification of CP Violating effects - Nr. 3:
Consider f=f :
If one amplitude dominates the decay, then Af = Af
CP violation in interference
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13. Relax: B0J/ΨKs simplifies…
ΔΓ=0
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14. βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S
Replace spectator quark d  s
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15. βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S
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16. 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 -
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17. 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 -
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18. 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):
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19. 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):
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20. 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
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21. Other angles
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22. Measure γ: B0s  DsK-/+ : both λf and λf2 +
Γ(Bf)= 2 +
Γ(B f )=
NB: In addition B s  DsK-/+ : both λ f and λf
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23. 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:
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24. Measure γ: Bs  DsK-/+ B0s  Ds-K+ has phase difference ( - ):
Need B0s  Ds+K- to disentangle  and :
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25. Next CP violation in decay CP violation in mixing
CP violation in interference

26. γ B - → D0 K- (Time integrated) Bs0 → DsK+- (Time dependent)
( )
B - → D0 K- (Time integrated)
Bs0 → DsK+- (Time dependent)
Necessary ingredients for CP violation:
Two (interfering) amplitudes
Phase difference between amplitudes
one CP conserving phase (‘strong’ phase)
one CP violating phase (‘weak’ phase)

27. γ (GLW) D0K+ fCPK+ B+ GLW: CP eigenstate: D0→ K+K-(ππ) bc favoured
Vub*
Vcb*
( )
B- →D0K-
Relative phase: γ B+
D0K+
fCPK+
bc favoured
bu suppressed
GLW:
CP eigenstate: D0→ K+K-(ππ)

28. γ (GLW) D0K+ fCPK+ B+ GLW: CP eigenstate: D0→ K+K-(ππ) bc favoured
Vub*
Vcb*
( )
B- →D0K-
Relative phase: γ B+
D0K+
fCPK+
bc favoured
bu suppressed
GLW:
CP eigenstate: D0→ K+K-(ππ)

29. γ (GLW) D0K+ fCPK+ B+ GLW: CP eigenstate: D0→ K+K-(ππ) bc favoured
bu suppressed
GLW:
CP eigenstate: D0→ K+K-(ππ)

30. γ (ADS) D0K+ B+ ADS: K-π+K+ B or D Cabibbo favoured: D0→ K+π-
Vub*
Vcb*
( )
B- →D0K-
Relative phase: γ B+
D0K+
bc favoured
bu suppressed
K-π+K+
Cabibbo supp.
Cabibbo allowed.
ADS:
B or D Cabibbo favoured: D0→ K+π-

31. γ (ADS) D0K+ B+ ADS: K-π+K+ B or D Cabibbo favoured: D0→ K+π-
Vub*
Vcb*
( )
B- →D0K-
Relative phase: γ B+
D0K+
bc favoured
bu suppressed
K-π+K+
Cabibbo supp.
Cabibbo allowed.
ADS:
B or D Cabibbo favoured: D0→ K+π-
“Difference in suppression”
“Average suppression”

32. γ (ADS) D0K+ B+ ADS: K-π+K+ B or D Cabibbo favoured: D0→ K+π-
Suppressed mode for the B- is relatively more suppressed than for the B+… B+
D0K+
bc favoured
K-π+K+
Cabibbo supp.
Cabibbo allowed.
bu suppressed
ADS:
B or D Cabibbo favoured: D0→ K+π-
BR~ 2 x 10-7

33. Another example of CP violation in decay
CP violation in mixing
CP violation in interference

34. 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
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35. CP violation in Decay? (also known as: “direct CPV”)
First observation of Direct CPV in B decays at LHC (2011):
LHCb
LHCb-CONF
LHCb
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36. 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
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37. 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 )
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38. 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
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39. Hint for new physics? B0Kπ and BKπ0
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40. Hint for new physics? B0Kπ and BKπ0
T (tree)
C (color suppressed)
P (penguin)
B0→K+π-
B+→K+π0
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41. Next CP violation in decay CP violation in mixing
CP violation in interference

42. 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
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43. (limit on) CP violation in B0 mixing
Look for a like-sign
asymmetry:
As expected, no
asymmetry is observed…
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44. 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 (44)

45. 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
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46. 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

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

48. More β…
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49. 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
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50. 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
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51. 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
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52. Penguin diagrams
Nucl. Phys. B131:
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53. Penguins?? The original penguin: A real penguin: Our penguin:
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54. Funny Flying Penguin Dead Penguin Penguin T-shirt: Super Penguin:
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55.  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
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56. ? 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
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S.T’Jampens, CKM fitter, Beauty2006

58. Kaons… K1, K2, KL, KS, K+, K-, K0 Different notation: confusing!
Smaller CP violating effects
But historically important!
Concepts same as in B-system, so you have a chance to understand…
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