: c hris p arkes cp violation part i introductory concepts slides available on my web page slides...
TRANSCRIPT
:
Chris Parkes
CP Violation Part IIntroductory concepts
Slides available on my web pagehttp://www.hep.manchester.ac.uk/u/parkes/
Slides available on my web pagehttp://www.hep.manchester.ac.uk/u/parkes/
2/Chris Parkes
Outline
THEORETICAL CONCEPTS (with a bit of experiment)
I. Introductory conceptsMatter and antimatter
Symmetries and conservation laws
Discrete symmetries P, C and T
II. CP Violation in the Standard ModelKaons 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
Matter and antimatter
4/Chris Parkes
“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 Em
2
2p Apply QM prescription ip
Get Schrödinger Equationdt
im
22
2Missing phenomena:Anti-particles, pair production, spin
Or non relativisticWhereas relativistically
m
pmvE
22
1 22
42222 cmcE p
22
2
2
2
1
mc
dtcKlein-Gordon Equation
Applying QM prescription again gives:
Quadratic equation 2 solutionsOne for particle, one for anti-particleDirac Equation 4 solutionsparticle, anti-particle each with spin up +1/2, spin down -1/2
Anti-particles: Dirac
Combine quantum mechanics and special relativity, linear in δt
Half of the solutions have negative energy
Or positive energy anti-particlesSame mass/spin… opposite charge
Chris Parkes
7
predicted 1931
8/Chris Parkes
Antiparticles – Interpretation of negative energy solutions
Westminster Abbey
- 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. DiracE
mc2
etc..
etc..
positron
-mc2
electron
positron
9/Chris Parkes
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!
Lead plate to slow down particlein chamber
Incoming particle (high momentum / low curvature)
Outgoing particle (low momentum / high curvature)
Cosmic rays with a cloud camber
10/Chris Parkes
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
Dirac equation: for every (spin ½) particle there is an antiparticle
Chris Parkes
11
Dirac: predicted 1931
Positron observed 1932
Antiproton observed 1959Bevatron
Anti-deuteron 1965PS CERN / AGS Brookhaven
Anti-Hydrogen 1995CERN LEAR
Spectroscopystarts 2011CERN LEAR (ALPHA)
Antihydrogen Production
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.
ALPHA Experiment
Will Bertsche
G.Bauer et al. (1996) Phys. Lett. B 368 (3)
M. Amoretti et al. (2002). Nature 419 (6906): 456
Antihydrogen Trapping
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
Nature 468, 355 (2010). Nature Physics, 7, 558-564 (2011) Will Bertsche
14/Chris Parkes
15/Chris Parkes
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 !
16/Chris Parkes
17/Chris Parkes
Tracker: measure deflection R=pc/|Z|e, direction gives Z signTime of Flight: measure velocity betaTracker/TOF: energy loss (see Frontiers 1) measure |Z|
18/Chris Parkes
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 !
19/Chris Parkes
20/Chris Parkes
21/Chris Parkes
22/Chris Parkes
How measured?Nucleosynthesis – abundance of light elements depends on Nbaryons/Nphotons
23/Chris Parkes
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/Chris Parkes
Dynamic Generation of Baryon Asymmetry in Universe
CP Violation & Baryon Number Asymmetry
25/Chris Parkes
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
Symmetries
and conservation laws
27/Chris Parkes
Symmetries and conservation laws
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
Fundamental discrete symmetries we will study- Parity (P) – spatial inversion- Charge conjugation (C) – particle antiparticle transformation- Time reversal (T)- CP, CPT
Emmy Noether
28/Chris Parkes
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/Chris Parkes
P operator acts on a state |y(r, t)> as
),(),(
),(),(
2 ttP
ttP P
rr
rr
Hence 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
e.g. hydrogen atom wavefn
|y(r,, )>=(r)Ylm(,)
P Ylm(,) Yl
m(-,+)
=(-1)l Ylm(,)
So atomic s,d +ve, p,f –ve P
Hence, electric dipole transition l=1P=- 1
Parity - spatial inversion (1/2)
30/Chris Parkes
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-
Parity - spatial inversion (2/2)
31/Chris Parkes
Left-handed=spin anti-parallel to momentumRight-handed= spin parallel to momentum
32/Chris Parkes
33/Chris Parkes
34/Chris Parkes
35/Chris Parkes
36/Chris Parkes
37/Chris Parkes
Spin in direction of momentum
Spin in opposite direction of momentum
38/Chris Parkes
39/Chris Parkes
40/Chris Parkes
41/Chris Parkes
42/Chris Parkes
43/Chris Parkes
Charge conjugation
C operator acts on a state |y(x, t)> as),(),(
),(),(
2 ttC
ttC C
rr
rr
Particle to antiparticle transformation
Only a particle that is its own antiparticle can be eigenstate of C !
e.g. C |o> = ±1 |o>
o + (BR~99%)
EM sources change sign under C,hence C|> = -1
Thus, C|o> =(-1)2 |o> = +1 |o>
44/Chris Parkes
45/Chris Parkes
46/Chris Parkes
47/Chris Parkes
48/Chris Parkes
49
Measuring Helicity of the Neutrino
152 * 152Sm Sm
J= 1 0 1
Goldhaber et. al. 1958
Electron captureK shell, l=0
photon emission
Consider the following decay:
Eu at restSelect photons in Sm* dirn
Neutrino, SmIn opposite dirns
e-
• Momenta, p
• spin
OR
S=+ ½
S=- ½Left-handed
S=+ 1
S=- 1
right-handed
Left-handed
right-handed
• Helicities of forward photon and neutrino same• Measure photon helicity, find neutrino helicity
See textbook
50
Neutrino Helicity Experiment Tricky bit: identify forward γ Use resonant scattering!
Measure γ polarisation with different B-field orientations
152 152 * 152Sm Sm Sm
magnetic field
Pb
NaI
PMT
152Sm152Sm
152Eu
γγ
Fe
Similar experiment with Hg carried out for anti-neutrinos
Vary magnetic field to vary photon absorbtion.Photons absorbed by e- in iron only if spins of photon and electronopposite.
)2
1()
2
1()1(
)2
1()
2
1()1(
'
ee SSS
Forward photons,(opposite p to neutrino),Have slightly higher p than backwardand cause resonant scattering
Only left-handed neutrinos exist
51
C P
CPParity InversionSpatialmirror
Charge InversionParticle-antiparticlemirror
52/Chris Parkes
left-handed
right-handed
Parity
left-handed
right-handed
Charge & Parity
• Massless approximation (Goldhaber et al., Phys Rev 109 1015 (1958)
Neutrino helicity
✗
53/Chris Parkes
T - time reversal
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
54/Chris Parkes
55/Chris Parkes
CPT invariance
CPT THEOREMAny Lorentz-invariant local quantum field theoryis invariant under the combination of C, P and T
CPT THEOREMAny Lorentz-invariant local quantum field theoryis 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
1810~)( 000
KKKmmm
(see PDG review on “CPT invariance Tests in Neutral Kaon decays”)
56/Chris Parkes
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)