c hris p arkes
DESCRIPTION
:. CP Violation Part I Introductory concepts. Slides available on my web page http:// www.hep.manchester.ac.uk /u/ parkes /. C hris P arkes. Outline. THEORETICAL CONCEPTS (with a bit of experiment) Introductory concepts Matter and antimatter Symmetries and conservation laws - PowerPoint PPT PresentationTRANSCRIPT
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:
Chris Parkes
CP Violation Part IIntroductory concepts
Slides available on my web pagehttp://www.hep.manchester.ac.uk/u/parkes/
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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
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Matter and antimatter
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“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
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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
mpmvE22
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
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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
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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
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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!
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
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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
Chris Parkes
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Dirac: predicted 1931
Positron observed 1932
Antiproton observed 1959Bevatron
Anti-deuteron 1965PS CERN / AGS Brookhaven
Anti-Hydrogen 1995CERN LEAR
Spectroscopystarts 2011CERN LEAR (ALPHA)
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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
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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
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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 signTime of Flight: measure velocity betaTracker/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 foundNo 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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Symmetriesand conservation laws
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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
Emmy Noether
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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
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
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P operator acts on a state |(r, t)> as
),(),(
),(),(2 ttP
ttP P
rr
rr
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
e.g. hydrogen atom wavefn
|(r,, )>=(r)Ylm(,)
P Ylm(,) Yl
m(-,+)
=(-1)l Ylm(,)
So atomic s,d +ve, p,f –ve PHence, electric dipole transition l=1Pg=- 1
Parity - spatial inversion (1/2)
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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)
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Left-handed=spin anti-parallel to momentumRight-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
C operator acts on a state |(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 g + g (BR~99%)
EM sources change sign under C,hence C|g> = -1
Thus, C|o> =(-1)2 |o> = +1 |o>
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Measuring Helicity of the Neutrino
152 * 152Sm SmJ= 1 0 1
g
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
gS=+ 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
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Neutrino Helicity Experiment Tricky bit: identify forward γ Use resonant scattering!
Measure γ polarisation with different B-field orientations
152 152 * 152Sm Sm Smg g
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.
)21()
21()1(
)21()
21()1(
'
ee SSSg
Forward photons,(opposite p to neutrino),Have slightly higher p than backwardand cause resonant scattering
Only left-handed neutrinos exist
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C P
CPParity InversionSpatialmirror
Charge InversionParticle-antiparticlemirror
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left-handed
right-handed
Parity
left-handed
right-handed
Charge & Parity
• Massless approximation (Goldhaber et al., Phys Rev 109 1015 (1958)
Neutrino helicity
✗
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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
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CPT invariance
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”)
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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)