1. Particle Physics II – CP violation (also known as “Physics of Anti-matter”) Lecture 4
N. Tuning
Niels Tuning (1)

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
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. Neutral Meson Oscillations (1)
Start with Schrodinger equation:
Find eigenvalue:
Solve eigenstates:
Eigenstates have diagonal Hamiltonian: mass eigenstates!
(2-component state in
P0 and P0 subspace)
Niels Tuning (7)

8. Neutral Meson Oscillations (2)
Two mass eigenstates
Time evolution:
Probability for |P0>  |P0> !
Express in M=mH+mL and Δm=mH-mL  Δm dependence

9. Meson Decays Formalism of meson oscillations: Subsequent: decay
Niels Tuning (9)

10. Notation: Define Af and λf
Niels Tuning (10)

11. Some algebra for the decay P0  f
Interference
P0 f
P0P0 f
Niels Tuning (11)

12. Some algebra for the decay P0  f
Niels Tuning (12)

13. The ‘master equations’
(‘direct’) Decay
Interference
Niels Tuning (13)

14. The ‘master equations’
(‘direct’) Decay
Interference
Niels Tuning (14)

15. Classification of CP Violating effects
CP violation in decay
CP violation in mixing
CP violation in interference
Niels Tuning (15)

16. Meson Decays Formalism of meson oscillations: Subsequent: decay P0 f
Interference
P0 f
P0P0 f
Interference
(‘direct’) Decay

17. Classification of CP Violating effects
CP violation in decay
CP violation in mixing
CP violation in interference
Niels Tuning (17)

18. Now: Im( λf) CP violation in decay CP violation in mixing
CP violation in interference
We will investigate λf for various final states f

19. CP violation: type 3
Niels Tuning (19)

20. Classification of CP Violating effects - Nr. 3:
Consider f=f :
If one amplitude dominates the decay, then Af = Af
CP violation in interference
Niels Tuning (20)

21. CP violation: a famous example
The golden decay B0→J/ΨKs
DESY
KEK
SLAC
Niels Tuning (21)

22. |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 (22)

23. Relax: B0J/ΨKs simplifies…
ΔΓ=0
Niels Tuning (23)

24. 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 (24)

25. 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 (25)

26. Remember: C and P eigenvalue
C and P are good symmetries (not involving the weak interaction)
Can associate a conserved value with them (Noether Theorem)
Each hadron has a conserved P and C quantum number
What are the values of the quantum numbers
Evaluate the eigenvalue of the P and C operators on each hadron P|y> = p|y>
What values of C and P are possible for hadrons?
Symmetry operation squared gives unity so eigenvalue squared must be 1
Possible C and P values are +1 and -1.
Meaning of P quantum number
If P=1 then P|y> = +1|y> (wave function symmetric in space) if P=-1 then P|y> = -1 |y> (wave function anti-symmetric in space)
Niels Tuning (26)

27. Remember: P eigenvalues for hadrons
The p+ meson
Quark and anti-quark composite: intrinsic P = (1)*(-1) = -1
Orbital ground state  no extra term
P(p+)=-1
The neutron
Three quark composite: intrinsic P = (1)*(1)*(1) = 1
P(n) = +1
The K1(1270)
Quark anti-quark composite: intrinsic P = (1)*(-1) = -1
Orbital excitation with L=1  extra term (-1)1
P(K1) = +1
Meaning: P|p+> = -1|p+>
Niels Tuning (27)

28. Intermezzo: CP eigenvalue
Remember:
P2 = 1 (x  -x  x)
C2 = 1 (ψ  ψ  ψ )
 CP2 =1
CP | f > =  | f >
Knowing this we can evaluate the effect of CP on the K0
CP|K0> = -1|K0>
CP| K0> = -1|K0 >
K0 is not CP eigenstate, but flavour eigenstate (sd) !
Mass eigenstates:
|KS> = p| K0> +q|K0>
|KL> = p| K0> - q|K0>
|Ks> (CP=+1) → p p (CP= (-1)(-1)(-1)l= =+1)
|KL> (CP=-1) → p p p (CP = (-1)(-1)(-1)(-1)l=0 = -1)
( S(K)=0  L(ππ)=0 )
Niels Tuning (28)

29. CP eigenvalue of final state J/yK0S
CP |J/y> = +1 |J/y>
CP |K0S> = +1 |K0S>
CP |J/yK0S> = (-1)l |J/yK0S>
( S(J/y)=1 )
( S(B)=0  L(J/yK0S)=1 )
Relative minus-sign between
state and CP-conjugated state:
|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 (29)

30. Time dependent CP violation
If final state is CP eigenstate then 2 amplitudes (w/o mixing):
B0f and B0B0f
B0 - B0 oscillation is periodic in time  CP violation time dependent
Amplitude 1
Amplitude 2 +
e-iφ
(i=eiπ/2 δ=90o)
(φ=2β)
Niels Tuning (30)

31. Time dependent CP violation
If final state is CP eigenstate then 2 amplitudes (w/o mixing):
B0f and B0B0f
B0 -B0 oscillation is periodic in time  CP violation time dependent 1 +
e-iφ
(i=eiπ/2 δ=90o)
(φ=2β)
Niels Tuning (31)

32. Sum of 2 amplitudes: sensitivity to phase
What do we know about the relative phases of the diagrams?
B0  f
B0  B0  f
f(strong)=f
Decays are identical
f(strong)=f
K0 mixing exactly cancels Vcs
f(weak)=0
f(weak)=2b
f(mixing)=p/2
There is a phase difference of i between the B0 andB0
Niels Tuning (32)

33. Sum of 2 amplitudes: sensitivity to phase
Now also look at CP-conjugate process
Investigate situation at time t, such that |A1| = |A2| :
Directly observable result (essentially just from counting) measure CKM phase b directly!
N(B0  f)  |A|2  (1-cosf)2+sin2f
= 1 -2cosf+cos2f+sin2f
= 2-2cos(p/2-2b)
 1-sin(2b) + =
Γ(Bf)=
sin(f)
p/2+2b CP
1-cos(f) + =
sin(f)
Γ(Bf)=
p/2-2b
N(B0  f)  (1+cosf)2+sin2f
= 2+2cos(p/2-2b)
 1+sin(2b)
1+cos(f)
Niels Tuning (33)

34. 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 (34)

35. Remember!
2 amplitudes
2 phases
Niels Tuning (35)

36. eiφ e-iφ What do we measure? Γ( B f) = |A1+A2ei(φ+δ)|2
We measure quark couplings
There is a complex phase in couplings!
Visible when there are 2 amplitudes:
matter
anti-matter
Γ( B f) = |A1+A2ei(φ+δ)|2
Γ( B f) = |A1+A2ei(-φ+δ)|2
Proof of existence of complex numbers…
Niels Tuning (36)

37. B0→J/ψKs B-system - Time-dependent CP asymmetry BaBar (2002)
Niels Tuning (37)
BaBar (2002)

38. Consistency with other measurements in (r,h) plane
4-fold ambiguity because we measure sin(2b), not b
Prices measurement of sin(2β) agrees perfectly with other measurements and CKM model assumptions The CKM model of CP violation experimentally confirmed with high precision! 2 1
without sin(2b) h 3 4 r
Method as in Höcker et al, Eur.Phys.J.C21: ,2001
Niels Tuning (38)

39. βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S
Replace spectator quark d  s
Niels Tuning (39)

40. βs: Bs0 ® J/yφ : Bs0 analogue of B0 ® J/yK0S
Niels Tuning (40)

41. Remember: The “Bs-triangle”: βs
Replace d by s:
Niels Tuning (41)

42. 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 (42)

43. 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 (43)

44. “Recent” excitement (5 March 2008)
Niels Tuning (44)

45. 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 (45)

46. 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 (46)

47. 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 (47)

48. 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
Niels Tuning (48)

49. 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 (49)

50. Measure γ: Bs  DsK-/+ B0s  Ds-K+ has phase difference ( - ):
Need B0s  Ds+K- to disentangle  and :
Niels Tuning (50)

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

52. 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)

53. 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)

54. 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)

55. 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)

56. 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-

57. 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”

58. 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

59. 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 (59)

60. 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 (60)

61. 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 (61)

62. 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 (62)

63. 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 (63)

64. Hint for new physics? B0Kπ and BKπ0
Niels Tuning (64)

65. 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 (65)

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

67. 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 (67)

68. (limit on) CP violation in B0 mixing
Look for a like-sign
asymmetry:
As expected, no
asymmetry is observed…
Niels Tuning (68)

69. 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 (69)

70. 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 (70)

71. 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

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

73. More β…
Niels Tuning (73)

74. Time?
Niels Tuning (74)

75. 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 (75)

76. 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 (76)

77. 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 (77)

78. Penguin diagrams
Nucl. Phys. B131:
Niels Tuning (78)

79. Penguins?? The original penguin: A real penguin: Our penguin:
Niels Tuning (79)

80. Funny Flying Penguin Dead Penguin Penguin T-shirt: Super Penguin:
Niels Tuning (80)

81.  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 (81)

82. ? 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 (82)
S.T’Jampens, CKM fitter, Beauty2006