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Introductory concepts

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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)

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