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**Introductory concepts**

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

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**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

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Matter and antimatter

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**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

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**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

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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-particles Same mass/spin… opposite charge predicted 1931 Chris Parkes

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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 mc2 etc.. positron -mc2 electron positron Westminster Abbey

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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**

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

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**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

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**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

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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

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**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 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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**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=1P=- 1

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**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-

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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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**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>

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**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

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**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

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

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** ✗ Neutrino helicity**

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

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**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

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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: Non-CPT-invariant theories have been formulated, but are not satisfactory (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)

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