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CP Violation Part I
Introductory concepts
Slides available on my web page
http://www.hep.manchester.ac.uk/u/parkes/
Chris Parkes
Outline
THEORETICAL CONCEPTS (with a bit of experiment)
I.
Introductory concepts
Matter and antimatter
Symmetries and conservation laws
Discrete symmetries P, C and T
II.
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
Chris Parkes
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Matter and antimatter
Chris Parkes
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“Surely something is wanting in our conception of the
universe... positive and negative electricity, north an
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
Adding Relativity to QM

p2
Apply QM prescription
E
2m
2 2


   i
Get Schrödinger Equation
2m
dt
Missing phenomena:
Anti-particles, pair production, spin
Free particle
Or non relativistic
Whereas relativistically
See Advanced QM II
p  i
1
p2
2
E  mv 
2
2m
E 2  p 2c 2  m2c 4
Applying QM prescription again gives:
Klein-Gordon Equation

1 
 mc 
2






2
2
c dt
  
2
2
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
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Anti-particles: Dirac

Combine quantum mechanics and
special relativity, linear in δt

Half of the solutions have negative
energy
predicted 1931
Or positive energy anti-particles
 Same mass/spin… opposite charge

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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
etc..
electron
mc2
-mc2
positron
etc..
Westminster Abbey
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positron
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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)
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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
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Dirac equation: for every (spin ½) particle there is an antiparticle
Dirac:
predicted 1931
Antiproton observed 1959
Bevatron
Positron observed 1932
Anti-deuteron 1965
PS CERN / AGS Brookhaven
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Anti-Hydrogen 1995
Spectroscopy
starts 2011
CERN LEAR
CERN LEAR (ALPHA)
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Antihydrogen Production

Will Bertsche
Fixed Target Experiments (too hot, few!)
– First anti-hydrogen G.Bauer et al. (1996) Phys. Lett. B 368 (3)
– < 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.
M. Amoretti et al. (2002). Nature 419 (6906): 456
ALPHA Experiment
Antihydrogen Trapping & Spectroscopy
Nature 468, 355 (2010). Nature Physics, 7, 558-564 (2011).
Nature 541, 506–510 (2017).



Will Bertsche
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!
– Have performed first spectroscopy studies, agreement with hydrogen
– Observation of 1S-2S transition stimulated with laser
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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 !
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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|
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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 !
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How measured?
Nucleosynthesis – abundance of light elements depends on Nbaryons/Nphotons
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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
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Dynamic Generation of Baryon Asymmetry in Universe
CP Violation & Baryon Number Asymmetry
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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
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Symmetries
and conservation laws
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
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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


but
L=xpL
Charge Conjugation, C
– Charge conjugation turns a particle into its antiparticle


x  -x , p  -p


e+  e- , K -  K +
Time Reversal, T
– Changes, for example, the direction of motion of particles

Chris Parkes
t  -t
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Parity - spatial inversion (1/2)
P operator acts on a state |(r, t)> as
P  (r, t )   P (r, t )
P  (r, t )   (r, t )
2
Hence eigenstates P=±1
|(r, t)>= cos x has P=+1, even
|(r, t)>= sin x has P=-1, odd
|(r, t)>= cos x + sin x, no eigenvalue
Chris Parkes
Hence, electric dipole
transition l=1Pg=- 1
e.g. hydrogen atom wavefn
|(r,, )>=(r)Ylm(,)
m
m
P Yl (,)  Yl (-,+)
=(-1)l Ylm(,)
So atomic s,d +ve, p,f –ve P
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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
scalar, pseudo-scalar, vector, axial(pseudo)-vector, etc.
JP = 0+, 0-, 1-, 1+
-,o,K-,Ko all 0- , photon 1-
 Conserved in strong & electromagnetic interactions
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Left-handed=spin anti-parallel to momentum
Right-handed= spin parallel to momentum
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Spin in direction of momentum
Spin in opposite direction of momentum
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Charge conjugation
Particle to antiparticle transformation
C operator acts on a state |(x, t)> as
C (r, t )   C (r, t )
C 2 (r, t )  (r, t )
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|g> = -1
o  g + g
(BR~99%)
Thus, C|o> =(-1)2 |o> = +1 |o>
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(Demonstrated Parity, Charge Conjugation
Violated. Experiment did not determine Helicity of neutrino)
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Measuring Helicity of the Neutrino
Goldhaber et. al. 1958
Consider the following decay:
Electron capture
K shell, l=0
See textbook
photon emission
•Momenta, p
Eu at rest
Neutrino, Sm
In opposite dirns
•spin
e-

Select photons
in Sm* dirn
Sm*  152 Sm  g
J= 1
0 1
152
g
S=+ ½
S=+ 1
OR
right-handed
right-handed
S=- ½
S=- 1
Left-handed
Left-handed
•Helicities of forward photon and neutrino same
49 helicity
•Measure photon helicity, find neutrino
Neutrino Helicity Experiment


Tricky bit: identify forward γ
Use resonant scattering!
g  152 Sm  152 Sm*  152 Sm  g

Measure γ polarisation with different B-field orientations
152Eu
magnetic field
Fe
γ
Pb
γ
Vary magnetic field to vary photon
absorbtion.
Photons absorbed by e- in iron
only if spins of photon and electron
opposite.
S g  S e  S 'e
1
1
(1)  ( )  ( )
2
2
1
1
(1)  ( )  ( )
2
2
Forward photons,
NaI
(opposite p to neutrino),
152Sm
152Sm
Have slightly higher p than backward
PMT
and cause resonant scattering
Only left-handed
neutrinos exist
50
Similar experiment with Hg carried out for anti-neutrinos
Charge Inversion
Particle-antiparticle
mirror
C
P
Parity
Inversion
Spatial
mirror
CP
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Neutrino helicity
• Massless approximation
Parity
Charge & Parity
Chris Parkes
(Goldhaber et al., Phys Rev 109 1015 (1958)
 left-handed

 right-handed
✗
 left-handed

 right-handed

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T - time reversal
 Inversion 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
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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:
(mK 0  mK 0 ) mK 0  ~ 10 18
(see PDG review on “CPT invariance Tests in Neutral Kaon decays”)
 Non-CPT-invariant theories have been formulated,
but are not satisfactory
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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)
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