1. Particle Physics II Chris Parkes CP Violation
4th Handout
CP Violation
Parity & Charge conjugation
Helicity of the neutrino
Particle anti-particle oscillations
CP violation measurement in Kaons
CP violation theory in CKM matrix
Predicting b-quark
Distinguishing Matter & Anti-matter
Sakharov conditions
Chris Parkes

2. Matter and anti-matter asymmetry: CP-violation
CP-violation is violation of charge conjugation and parity
distinguishes between matter and antimatter
Not just a naming convention
Responsible for matter-antimatter asymmetry in Universe
Equal amounts of matter & anti-matter in the big bang
Elements
Parity violation
Charge conjugation and parity violation in muon decay, CP conservation
Mixing in the K0 system
CP violation in the K0 system

3. Parity and charge conjugation
Revision
Parity is spatial inversion and reverses vectors r-r; p-p
P operator acts on a state |y(r, t)>
Hence for eigenstates P=±1
|y(r, t)>= cos x has P=+1, even
|y(r, t)>= sin x has P=-1, odd
|y(r, t)>= cos x + sin x, no eigenvalue
Charge conjugation (C)
particles anti-particles
reverses: charge, magnetic moments,
baryon number, strangeness
Only particles that are their own anti-particles are eigenstates of C (e.g. photon, π0, J/ψ…)

4. Parity Violation in weak interactions
Revision
Parity Violation in weak interactions
The “ -” puzzle (1950s)
Two particles
+, (21%) P =+1
++-, (6%) P=-1
found to have same lifetime and mass  same particle? BUT opposite parity
Actually K+  weak decay
Led Lee and Yang to propose that parity may not be conserved in weak interactions

5. Observation of parity violation
Revision
Search for parity violation in b-decay
Need to observe parameter that is sensitive to parity
scalars aa
Vectors p-p
Pseudo-scalar pa.pbpa.pb
Axial-vector L.p-L.p  combination of momentum and spin
Measure <J>.pe = angular distribution of electrons with respect to nuclear spin
Spin parity:
e- (E,-p)
60Co60Ni*+e-+ne
Use g from Ni*Ni to monitor spin alignment J J
B field
Parity
Co60Nuclei
spin aligned
Beta decay to Ni*60
e- (E,p)
Rate ≠ Rate

6. Helicity and the neutrino
In angular momentum we choose the axis of quantisation to be the z axis.
Lets choose this axis along the particle momentum direction.
Helicity is the component of the spin along the momentum direction.
A spin ½ particle can thus have helicity +1 (ms=+ ½) or –1 (ms=- ½ ) p p +1 -1
Right-handed s
Left-handed s
Not so interesting for a massive particle, as not Lorentz invariant,
but consider the neutrino.
Only left-handed neutrinos exist and right-handed anti-
Helicity is a pseudo-scalar
Operating with P on this reverses p, not spin, produces a right-handed neutrino.
Do not observe:
Operating with C on this produces a left-handed anti-neutrino.
Do not observe:
Operating with C and P on this produces a right-handed anti-neutrino.
Do observe!
Weak force violates Parity, but CP OK?

7. Measuring Helicity of the Neutrino
Goldhaber et. al. 1958
Bettini p252
Consider the following decay:
Electron capture
K shell, l=0
photon emission
Momenta, p
Eu at rest
Neutrino, Sm
In opposite dirns
Select photons
in Sm* dirn
spin e-  
S=+ ½
S=+ 1
right-handed OR
right-handed
S=- ½
S=- 1
Left-handed
Left-handed
Helicities of forward photon and neutrino same
Measure photon helicity, find neutrino helicity

8. Neutrino Helicity Experiment
Tricky bit: identify forward γ
Use resonant scattering!
Measure γ polarisation with different B-field orientations
Vary magnetic field to vary photon
absorbtion.
Photons absorbed by e- in iron
only if spins of photon and electron
opposite.
152Eu
magnetic field Fe γ γ Pb
Forward photons,
(opposite p to neutrino),
Have slightly higher p than backward
and cause resonant scattering
NaI
152Sm
152Sm
PMT
Only left-handed neutrinos exist
Similar experiment with Hg carried out for anti-neutrinos

9. Charge Inversion
Particle-antiparticle
mirror P C
Parity Inversion
Spatial
mirror CP

10. Particle anti-particle oscillations
Neutral Mesons can oscillate into
Anti-particles: K0↔ K0, (also B0, B0s, D0)

11. K0-mixing Strangeness is violated in weak decays
K0 and K0 can mix via diagrams

12. CP-violation Observed states are:
Ks0  p+p-, p0p0 Essentially K10 CP=+1
short lifetime 89ps
KL0  p+p-p0, p0p0p0 Essentially K20 CP=-1
long lifetime 51ns (due to available energy)
BUT
KL0 (CP=-1)  p+p- (CP=+1)
is observed CP is violated in weak decays
Observed states are now mixtures of CP=+1 and CP=-1 states
Experimentally |e|=2.3x10-3, so CP violation small effect

13. Charge Inversion
Particle-antiparticle
mirror P C
Parity Inversion
Spatial
mirror CP

14. CPT theorem T is time reversal transformation
A general theorem states that in any relativistic quantum theory in which signals cannot travel faster than the speed of light, CPT must be an invariant
CP is violated  T must also be violated

15. CPLEAR- some parameters
Kaon Oscillation d s W-
u, c, t
u, c, t _ _ W+ s d - K0 K0
u, c, t d W- _ _ _ W+ s _ _
u, c, t s d
Rate difference Ko Ko  Ko Ko is T violation
CPLEAR- some parameters
Beam – 106 anti-protons /s into Hydrogen target
Fast online trigger selection of events ~ 103/s
Ability to separate charged pions / kaons using Cherenkov, dE/dx, Time of flight
discriminate in momentum range MeV/c
Can detect and reconstruct Ks vertex to ~ 60 lifetimes c~2.6 cm
Observe events over ~ 4
Magnetic field (0.4T) and tracking leads to particle momentum determination
(~5% accuracy)

16. CPLEAR T invariance test
measure
1) Identify Ko / Ko at production:
produced in association with K+/K-
2) Identify Ko / Ko at decay from charge of lepton:
(S = 0)
(S = 0)
Get positron:
Or electron: ν ν e+ e- W+ W- s u s u Ko
π - Ko π+ d d d d

17. Experiment at LEAR ring at CERN 1990-1996
Pions from kaon decay

18. Discovery of T violation
CPLEAR,1998
Currently the only direct observation of T violation
Measure asymmetry in rates
Number of lifetimes
T, or equivalently CP, violated by this tiny amount

19. CP violation in SM - - How do we include CP violation CKM matrix ? K0
One diagram only for simplicity - d s W- K0 K0 c t _ _ W+ s d _ _ d s - W+ K0 K0 c t W- s d
Hence difference in rates:
CP violation introduced by making CKM matrix terms complex

20. Number of Parameters in CKM
n x n complex matrix,
2n2 parameters
Unitarity n2 constraints
n2 parameters
Phases of quark fields can be rotated freely
(n-1)2 parameters (remove one per row)
Real parameters, rotation (Euler) angles
n(n-1)/2 real
Phases
(n-1)(n-2)/2 phases
n=2, 1 real, 0 phase
n=3, 3 real, 1 phase

21. K&M Predict 3 famillies (Prog. Theor. Phys. 49, 652(1973) )
Only 3 quarks discovered
Charm predicted by GIM mechanism
CP violation discovered
Hence predict three (or more) famillies!
Discovery of b quark
p+(Cu,Pt)Υ (upsilon) +X
Similar to J/ψ discovery. At Fermilab 1977
Precision measurements in e+e-
Again narrow resonances
Υ (1s), Υ (2s), Υ (3s),
b bbar
3S1 states of bottom ‘atom’
Cornell

22. CKM – Unitarity Triangle
Three complex numbers, which sum to zero
Divide by so that the middle element is 1 (and real)
Plot as vectors on an Argand diagram
If all numbers real – triangle has no area – No CP violation
Hence, get a triangle
‘Unitarity’ or ‘CKM triangle’
Triangle if SM is correct.
Otherwise triangle will not close,
Angles won’t add to 180o
Imaginary
Real

23. Unitarity conditions j=1,3 No phase info. j,k =1,3 jk
hence 6 triangles in complex plane
db:
sb:
ds:
ut:
ct:
uc:

24. CKM Triangle - Experiment
Find particle decays that are sensitive to measuring the angles (phase difference) and sides (probabilities) of the triangles
Measurements constrain the apex of the triangle
Measurements are consistent
CKM model works,
2008 Nobel prize

25. Rate depends on top quark mass
B-mixing
Mixing also possible in the neutral B/D-systems
B0d
B0s (discovered 2006)
D0 (discovered 2007)
B-system is best laboratory for
CP violation studies
heavy system allows calculations
‘long lifetime’
CP violation observed in B-system
Babar/Belle (2000)
LHCb: New physics in loops
Rate depends on top quark mass
C. Parkes, P.Soler - s b
u,c,t

26. CP Violation: Why is it interesting ?
Fundamental: The Martian test
C violation does not distinguish between matter/anti-matter. LH/RH are conventions
CP distinguishes matter from anti-matter
CP says preferred decay KLe+ve-
Least Understood: CP Violation is ‘add-on’ in SM
Parity violation naturally imbedded in coupling structure
CP requires a complex phase in 3 generation CKM matrix, allowed but not natural

27. CP: Why ? cont. Problem Powerful: delicately broken symmetry
Very sensitive to New Physics models
Historical: Predicted 3rd generation !
Baryogenesis: there is more matter !
N(antibaryon) << N(baryon) << N(photons)
Fortunately! : 109
Sakharov (1968) Conditions
Baryon number violation
CP violation
Not in thermal equilibrium
Problem
Not enough CP violation in CKM !
Assuming not initial conditions, but dynamic.
Cannot allow all inverse reactions to have happened

28. backup

29. Muon decay e± m± m± Consider muon decay P e± Experimental results q
P-q e±
By C-invariance cannot distinguish between particle and anti-particle
 identical lifetimes
 identical decay distributions
P-invariance  the rate should be the same for q and –q
Results show both C and P invariance are violated
BUT
Lifetimes are the same
 C respected for this
Experimental results

30. Muon decay Results show both C and P invariance are violated BUT m+
Lifetimes are the same  C respected for this
Solution:
CP is conserved (almost!) in weak interactions
Under C m+  m-
Under P q  p-q m+ m-