1. Introductory concepts:
CP Violation Part I
Introductory concepts
Slides available on my web page
Chris Parkes

2. THEORETICAL CONCEPTS (with a bit of experiment)
Outline
THEORETICAL CONCEPTS (with a bit of experiment)
Introductory concepts
Matter and antimatter
Symmetries and conservation laws
Discrete symmetries P, C and T
CP Violation in the Standard Model
Kaons and discovery of CP violation
Mixing in neutral mesons
Cabibbo theory and GIM mechanism
The CKM matrix and the Unitarity Triangle
Types of CP violation

3. Matter and antimatter

5. Matter antimatter Symmetry
“Surely something is wanting in our conception of the universe... positive and negative electricity, north and south magnetism…”
Matter antimatter Symmetry
“matter and antimatter may further co-exist in bodies of small mass”
Particle Antiparticle Oscillations
Prof. Physics, Manchester – physics building named after

6. Adding Relativity to QM
See Advanced QM II
Free particle
Apply QM prescription
Get Schrödinger Equation
Missing phenomena:
Anti-particles, pair production, spin
Or non relativistic
Whereas relativistically
Applying QM prescription again gives:
Klein-Gordon Equation
Quadratic equation  2 solutions
One for particle, one for anti-particle
Dirac Equation  4 solutions
particle, anti-particle each with spin up +1/2, spin down -1/2

7. Anti-particles: Dirac
Combine quantum mechanics and special relativity, linear in δt
Half of the solutions have negative energy
Or positive energy anti-particles
Same mass/spin… opposite charge
predicted 1931
Chris Parkes

8. Antiparticles – Interpretation of negative energy solutions
- Dirac: in terms of ‘holes’ like in semiconductors
- Feynman & Stückelberg: as particles traveling backwards in time, equivalent to antiparticles traveling forward in time
 both lead to the prediction of antiparticles !
Paul A.M. Dirac E
mc2
etc..
positron
-mc2
electron
positron
Westminster Abbey

9. Discovery of the positron (1/2)
1932 discovery by Carl Anderson of a positively-charged particle “just like the electron”. Named the “positron”
First experimental confirmation of existence of antimatter!
Cosmic rays with a cloud camber
Outgoing particle (low momentum / high curvature)
Lead plate to slow down particle in chamber
Incoming particle (high momentum / low curvature)

10. Discovery of the positron (2/2)
4 years later Anderson confirmed this with g  e+e- in lead plate using g from a radioactive source

11. Dirac equation: for every (spin ½) particle there is an antiparticle
predicted 1931
Antiproton observed 1959
Bevatron
Positron observed 1932
Spectroscopy
starts 2011
CERN LEAR (ALPHA)
Anti-deuteron 1965
PS CERN / AGS Brookhaven
Anti-Hydrogen 1995
CERN LEAR
Chris Parkes

12. Antihydrogen Production
Will Bertsche
Fixed Target Experiments (too hot, few!)
First anti-hydrogen
< 100 atoms CERN (1995), Fermilab
Anti-protons on atomic target
‘Cold’ ingredients (Antiproton Decelerator)
ATHENA (2002), ATRAP, ALPHA, ASACUSA
Hundreds of Millions produced since 2002.
G.Bauer et al. (1996) Phys. Lett. B 368 (3)
M. Amoretti et al. (2002). Nature 419 (6906): 456
ALPHA Experiment

13. Antihydrogen Trapping
Will Bertsche
Nature 468, 355 (2010). Nature Physics, 7, (2011)
Antihydrogen:
How do you trap something electrically neutral ?
Atomic Magnetic moment in minimum-B trap
T < 0.5 K!
Quench magnets and detect annihilation
ALPHA Traps hundreds of atoms for up to 1000 seconds!
Hence can start spectroscopy studies

15. Matter and antimatter Differences in matter and antimatter
Do they behave differently ? Yes – the subject of these lectures
We see they are different: our universe is matter dominated
Equal amounts
of matter &
antimatter (?)
Matter Dominates !

17. Tracker: measure deflection R=pc/|Z|e, direction gives Z sign
Time of Flight: measure velocity beta
Tracker/TOF: energy loss (see Frontiers 1) measure |Z|

18. Search for anti-nuclei in space
AMS experiment:
A particle physics experiment in space
Search of anti-helium in cosmic rays
AMS-01 put in space in June 1998 with Discovery shuttle
Lots of He found
No anti-He found !

22. How measured?
Nucleosynthesis – abundance of light elements depends on Nbaryons/Nphotons

23. Proton decay so far unobserved in experiment, limit is lifetime > 1032 years
Observed BUT magnitude (as we will discuss later) is too small
In thermal equilibrium N(Baryons) = N(anti-Baryons) since in equilibrium

24. Dynamic Generation of Baryon Asymmetry in Universe
CP Violation & Baryon Number Asymmetry

25. Key Points So Far
Existence of anti-matter is predicted by the combination of
Relativity and Quantum Mechanics
No ‘primordial’ anti-matter observed
Need CP symmetry breaking to explain the absence of antimatter

26. Symmetries
and conservation laws

27. Symmetries and conservation laws
Emmy Noether
Role of symmetries in Physics:
Conservation laws greatly simplify building of theories
Well-known examples (of continuous symmetries):
translational  momentum conservation
rotational  angular momentum conservation
time  energy conservation
Fundamental discrete symmetries we will study
Parity (P) – spatial inversion
Charge conjugation (C) – particle  antiparticle transformation
Time reversal (T)
CP, CPT

28. The 3 discrete symmetries
Parity, P
Parity reflects a system through the origin. Converts right-handed coordinate systems to left-handed ones.
Vectors change sign but axial vectors remain unchanged
x  -x , p  -p but L = x  p  L
Charge Conjugation, C
Charge conjugation turns a particle into its antiparticle
e+  e- , K-  K+
Time Reversal, T
Changes, for example, the direction of motion of particles
t  -t + 

29. Parity - spatial inversion (1/2)
P operator acts on a state |y(r, t)> as
Hence eigenstates P=±1
|y(r, t)>= cos x has P=+1, even
e.g. hydrogen atom wavefn
|y(r,, )>=(r)Ylm(,)
P Ylm(,)  Ylm(-,+)
=(-1)l Ylm(,)
So atomic s,d +ve, p,f –ve P
|y(r, t)>= sin x has P=-1, odd
|y(r, t)>= cos x + sin x, no eigenvalue
Hence, electric dipole transition l=1P=- 1

30. scalar, pseudo-scalar, vector, axial(pseudo)-vector, etc.
Parity - spatial inversion (2/2)
Parity multiplicative: |> = |a> |b> , P=PaPb
Proton
Convention Pp=+1
Quantum Field Theory
Parity of fermion  opposite parity of anti-fermion
Parity of boson  same parity as anti-particle
Angular momentum
Use intrinsic parity with GROUND STATES
Also multiply spatial config. term (-1) l
Conserved in strong & electromagnetic interactions
scalar, pseudo-scalar, vector, axial(pseudo)-vector, etc.
JP = 0+, 0-, 1-, 1+
-,o,K-,Ko all 0- , photon 1-

31. Left-handed=spin anti-parallel to momentum
Right-handed= spin parallel to momentum

37. Spin in direction of momentum
Spin in opposite direction of momentum

43. o   +  (BR~99%) Charge conjugation
Particle to antiparticle transformation
C operator acts on a state |y(x, t)> as
Only a particle that is its own antiparticle can be eigenstate of C !
e.g. C |o> = ±1 |o>
EM sources change sign under C,
hence C|> = -1
o   +  (BR~99%)
Thus, C|o> =(-1)2 |o> = +1 |o>

49. Measuring Helicity of the Neutrino
Goldhaber et. al. 1958
See textbook
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

50. 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

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

52.  ✗   Neutrino helicity
Massless approximation (Goldhaber et al., Phys Rev (1958) 
 left-handed
Parity ✗
 right-handed 
 left-handed
Charge & Parity 
 right-handed

53. T - time reversal Conserved in strong & electromagnetic interactions
Invertion of the time coordinate: t  -t
Changes, for example, the direction of motion of particles
Invariance checks: detailed balances
a + b  c + d
becomes under T
c + d  a + b
Conserved in strong & electromagnetic interactions

55. CPT invariance CPT THEOREM
Any Lorentz-invariant local quantum field theory
is invariant under the combination of C, P and T
G. Lűders, W. Pauli, J. Schwinger (1954)
Consequences: particles / antiparticles have
Opposite quantum numbers
Equal mass and lifetime
Equal magnetic moments of opposite sign
Fields with Integer spins commute, half-integer spins anti-commute (Pauli exclusion principle)
Tests:
Best experimental test of CPT invariance:
Non-CPT-invariant theories have been formulated,
but are not satisfactory
(see PDG review on “CPT invariance Tests in Neutral Kaon decays”)

56. Key Points So Far
Existence of anti-matter is predicted by the combination of
Relativity and Quantum Mechanics
No ‘primordial’ anti-matter observed
Need CP symmetry breaking to explain the absence of antimatter
Three Fundamental discrete symmetries: C, P , T
C, P, and CP are conserved in strong and electromagnetic interactions
C, P completely broken in weak interactions, but initially CP looks OK
CPT is a very good symmetry
(if CP is broken, therefore T is broken)