1. Particle Physics II – CP violation (also known as “Physics of Anti-matter”) Lecture 6
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
N328!
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. Why bother with all this?
CKM matrix has origin in LYukawa
Intricately related to quark massed…
Both quark masses and CKM elements show intriguing hierarchy
There is a whole industry of theorist trying to postdict the CKM matrix based on arguments on the mass matrix in LYukawa…
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6. 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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7. 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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8. Meson Decays Formalism of meson oscillations: Subsequent: decay P0 f
Interference
P0 f
P0P0 f
Interference
(‘direct’) Decay

9. Classification of CP Violating effects
CP violation in decay
CP violation in mixing
CP violation in interference
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10. Classification of CP Violating effects
CP violation in decay
Example:
CP violation in mixing
CP violation in interference
B0→J/ψKs
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11. 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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12. Remember!
2 amplitudes
2 phases
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13. 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.
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14. Classification of CP Violating effects
CP violation in decay
CP violation in mixing
CP violation in interference
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15. Next… Something completely different? No, just K
CP violation in decay
CP violation in mixing
CP violation in interference

16. 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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17. Neutral kaons – 60 years of history
1947 : First K0 observation in cloud chamber (“V particle”)
1955 : Introduction of Strangeness (Gell-Mann & Nishijima)
K0,K0 are two distinct particles (Gell-Mann & Pais)
1956 : Parity violation observation of long lived KL (BNL Cosmotron)
1960 : Dm = mL-mS measured from regeneration
1964 : Discovery of CP violation (Cronin & Fitch)
1970 : Suppression of FCNC, KLmm - GIM mechanism/charm hypothesis
1972 : 6-quark model; CP violation explained in SM (Kobayashi & Maskawa)
: K0,K0 time evolution, decays, asymmetries (CPLear)
: Direct CP violation measured: e’/e ≠ 0 (KTeV and NA48)
… the θ0 must be considered as a "particle mixture" exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes, and that no more than half of all θ0's undergo the familiar decay into two pions.
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From G.Capon

18. 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 >
CP 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 )
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19. Decays of neutral kaons
Neutral kaons is the lightest strange particle  it must decay through the weak interaction
If weak force conserves CP then
decay products of K1 can only be a CP=+1 state, i.e. |K1> (CP=+1) → p p (CP= (-1)(-1)(-1)l= =+1)
decay products of K2 can only be a CP=-1 state, i.e. |K2> (CP=-1) → p p p (CP = (-1)(-1)(-1)(-1)l=0 = -1)
You can use neutral kaons to precisely test that the weak force preserves CP (or not)
If you (somehow) have a pure CP=-1 K2 state and you observe it decaying into 2 pions (with CP=+1) then you know that the weak decay violates CP…
( S(K)=0  L(ππ)=0 )
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20. Designing a CP violation experiment
How do you obtain a pure ‘beam’ of K2 particles?
It turns out that you can do that through clever use of kinematics
Exploit that decay of K into two pions is much faster than decay of K into three pions
Related to fact that energy of pions are large in 2-body decay
t1 = 0.89 x sec
t2 = 5.2 x 10-8 sec (~600 times larger!)
Beam of neutral Kaons automatically becomes beam of |K2> as all |K1> decay very early on…
K1 decay early (into pp)
Pure K2 beam after a while! (all decaying into πππ) !
Initial K0 beam
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21. The Cronin & Fitch experiment
Essential idea: Look for (CP violating) K2  pp decays 20 meters away from K0 production point
Decay of K2 into 3 pions
Incoming K2 beam
If you detect two of the three pions of a K2  ppp decay they will generally not point along the beam line
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22. The Cronin & Fitch experiment
Essential idea: Look for K2  pp decays 20 meters away from K0 production point
Decay pions
Incoming K2 beam
If K2 decays into two pions instead of three both the reconstructed direction should be exactly along the beamline (conservation of momentum in K2  pp decay)
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23. The Cronin & Fitch experiment
Essential idea: Look for K2  pp decays 20 meters away from K0 production point
Decay pions
K2  pp decays (CP Violation!)
Incoming K2 beam
K2  ppp decays
Result: an excess of events at Q=0 degrees!
CP violation, because K2 (CP=-1) changed into K1 (CP=+1)
Note scale: 99.99% of K ppp decays are left of plot boundary
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24. Nobel Prize 1980
"for the discovery of violations of fundamental symmetry principles in the decay of neutral K mesons"
The discovery emphasizes, once again, that even almost self evident principles in science cannot be regarded fully valid until they have been critically examined in precise experiments.
James Watson Cronin  
1/2 of the prize  
University of Chicago Chicago, IL, USA
b. 1931
Val Logsdon Fitch  
1/2 of the prize  
Princeton University Princeton, NJ, USA
b. 1923
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25. Cronin & Fitch – Discovery of CP violation
Conclusion: weak decay violates CP (as well as C and P)
But effect is tiny! (~0.05%)
Maximal (100%) violation of P symmetry easily follows from absence of right-handed neutrino, but how would you construct a physics law that violates a symmetry just a tiny little bit?
Results also provides us with convention-free definition of matter vs anti-matter.
If there is no CP violation, the K2 decays in equal amounts to p+ e- ne (a) p- e+ ne (b)
Just like CPV introduces K2  ππ decays, it also introduces a slight asymmetry in the above decays (b) happens more often than (a)
“Positive charge is the charged carried by the lepton preferentially produced in the decay of the long-lived neutral K meson”
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26. Intermezzo: Regeneration
Different cross section for σ(p K0) than σ(pK0)
Elastic scattering: same
Charge exchange : same
Hyperon production: more for K0 !
What happens when KL-beam hits a wall ??
Then admixture changes…: |KL> = p| K0> - q|K0>
Regeneration of KS !
Could fake CP violation due to KS→π+π-…
strong interactions:
must conserve strangeness
leave little free energy – unlikely!
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27. KS and KL KL and KS are not orthogonal:
Usual (historical) notation in kaon physics:
Modern notation used in B physics:
Regardless of notation:
KL and KS are
not orthogonal:
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28. Three ways to break CP; e.g. in K0→ π+π-
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29. Classification of CP Violating effects
CP violation in decay
CP violation in mixing
CP violation in interference
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30. Time evolution
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31. B-system 2. CP violation in mixing K-system
CPLEAR, Phys.Rep. 374(2003)
BaBar, (2002)
CPLear (2003)

32. B-system 2. CP violation in mixing K-system
BaBar, (2002)
NA48, (2001)
L(e) = (3.317   0.072)  10-3
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33. B0→J/ψKs B-system 3.Time-dependent CP asymmetry BaBar (2002)
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BaBar (2002)

34. B0→J/ψKs K0→π-π+ B-system 3.Time-dependent CP asymmetry K-system
~50/50 decay as Ks and KL
+ interference! K0 _ K0
p+p- rate asymmetry
BaBar (2002)
CPLear (PLB 1999)

35. The Quest for Direct CP Violation
Indirect CP violation in the mixing: 
Direct CP violation in the decay: ’
A fascinating 30-year long enterprise: “Is CP violation a peculiarity of kaons? Is it induced by a new superweak interaction?”
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36. B system 1. Direct CP violation K system
B0→K+π-
B0→K-π+
K0→π-π+
K0→π-π+
K0→π0π0
K0→π0π0
Different CP violation for the two decays 
Some CP violation in the decay!
ε’≠ 0
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37. Niels Tuning (37)

38. Hints for new physics? Ks B φ ~~ g,b,…? 1) sin2β≠sin2β ? s b d t
2) ACP (B0K+π-)≠ACP (B+K+π0) ?
4th generation, t’ ?
3) βs≠0.04 ?
4) P(B0s→B0s) ≠ P(B0s←B0s)
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39. Present knowledge of unitarity triangle
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40. “The” Unitarity triangle
We can visualize the CKM-constraints in (r,h) plane

41. Present knowledge of unitarity triangle

42. I) sin 2β

43. I) sin 2β

44. II) ε and the unitarity triangle: box diagram
CP violation in mixing

45. II) ε and the unitarity triangle: box diagram

46. II) ε and the unitarity triangle: box diagram
Im(z2)=Im( (Rez+iImz)2)=2RezImz

47. II) ε and the unitarity triangleρ
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48. III.) |Vub| / |Vcb| Measurement of Vub
Compare decay rates of B0  D*-l+n and B0  p-l+n
Ratio proportional to (Vub/Vcb)2
|Vub/Vcb| = ± 0.025
Vub is of order sin(qc)3 [= 0.01]

49. IV.) Δmd and Δms Δm depends on Vtd
Vts constraints hadronic uncertainties

50. Present knowledge of unitarity triangle
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51. Hints for new physics? Ks B φ ~~ g,b,…? 1) sin2β≠sin2β ? s b d t
2) ACP (B0K+π-)≠ACP (B+K+π0) ?
4th generation, t’ ?
3) βs≠0.04 ?
4) P(B0s→B0s) ≠ P(B0s←B0s)
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52. More hints for new physics?
5) εK ?
Treatment of errors…
Input from Lattice QCD BK
Strong dependence on Vcb
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53. More hints for new physics?
6) Vub: 2.9σ ??
BR(B+→τυ)=1.68 ±
Predicted: ±
(If fBd off, then BBd needs to be off too,
to make Δmd agree) ?
|Vub| avg from semi-lep
|Vub| from fit
|Vub| from B→τν
From:
H.Lacker, and A.Buras,
Beauty2011, Amsterdam
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54. A.Buras, Beauty2011:
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55. A.Buras, Beauty2011:
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56. Standard Model: 25 free parameters
Elementary particle masses (MeV):
me 
m 
m 
mu 
mc 
mt 
md 
ms  120
mb  4300
m <
m <
m < 18.2 e  
Electro-weak interaction: u’ d’ s’ = u d s
quark mixing (4)
Vijq
neutrino mixing (4)
e(0)  1/
mW  GeV
mZ  GeV
mH > GeV e   1 2 3
Vijl =
mH > GeV
CMS
LHCb
Strong interaction:
s(mZ) 0.117
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57. The CKM matrix W- b gVub u Couplings of the charged current:
Wolfenstein parametrization: b W- u
gVub
Magnitude:
Complex phases:
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58. The CKM matrix Couplings of the charged current:
Wolfenstein parametrization 1) 2) 3)
Magnitude:
Complex phases:
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59. The CKM matrix Couplings of the charged current:
Wolfenstein parametrization:
Magnitude:
Complex phases:

60. Remember the following:
CP violation is discovered in the K-system
CP violation is naturally included if there are 3 generations or more
3x3 unitary matrix has 1 free complex parameter
CP violation manifests itself as a complex phase in the CKM matrix
The CKM matrix gives the strengths and phases of the weak couplings
CP violation is apparent in experiments/processes with 2 interfering amplitudes with different strong and weak phase
Often using “mixing” to get the 2nd decay process
Flavour physics is powerful for finding new physics in loops!
Complementary to Atlas/CMS
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61. Remember the following:
CP violation is discovered in the K-system
CP violation is naturally included if there are 3 generations or more
3x3 unitary matrix has 1 free complex parameter
CP violation manifests itself as a complex phase in the CKM matrix
The CKM matrix gives the strengths and phases of the weak couplings
CP violation is apparent in experiments/processes with 2 interfering amplitudes with different strong and weak phase
Often using “mixing” to get the 2nd decay process
Flavour physics is powerful for finding new physics in loops!
Complementary to Atlas/CMS
Thank you
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62. Personal impression:
People think it is a complicated part of the Standard Model (me too:-). Why?
Non-intuitive concepts?
Imaginary phase in transition amplitude, T ~ eiφ
Different bases to express quark states, d’=0.97 d s b
Oscillations (mixing) of mesons: |K0> ↔ |K0>
Complicated calculations?
Many decay modes? “Beetopaipaigamma…”
PDG reports 347 decay modes of the B0-meson:
Γ1 l+ νl anything ( ± 0.28 ) × 10−2
Γ347 ν ν γ <4.7 × 10−5 CL=90%
And for one decay there are often more than one decay amplitudes…
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63. Backup
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64. PEP-II accelerator schematic and tunnel view
SLAC: LINAC + PEPII
Linac
PEP-II accelerator schematic and tunnel view
HER
LER

65. Coherent Time Evolution at the (4S)
PEP-2 (SLAC)
B-Flavor Tagging
Exclusive B Meson Reconstruction
Vertexing & Time Difference Determination
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66. LHCb: the Detector pT of B-hadron η of B-hadron High cross section
LHC energy
Bs produced in large quantities
Large acceptance
b’s produced forward
Small multiple scattering
Large boost of b’s
Trigger
↓ Low pT
Leptons + hadrons (MUON, CALO)
Particle identification (RICH)
pT of B-hadron
η of B-hadron

67. Measuring the Quark CouplingsW q’
Vq’q
Measure the CKM triangle to unprecedented precision
Measure very small Branching Ratios
The well known triangle: β
CP phases: γ α γ β
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68. LHCb https://wiki.nikhef.nl/lhcb/Master_student_Projects
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69. LHCb Λb0Dsp Heavy neutrino’s Scintillator Fiber tracker
Never observed
Background to others
Sensitivity to Vub?
Measure factorization
Heavy neutrino’s
Holy grail
Scintillator Fiber tracker
New detector for LHCb
Constructed at Nikhef, to be installed in 2019
Majorana neutrino in Bc+ decays
Hole grail
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