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: C hris P arkes CP Violation Part I Introductory concepts Slides available on my web page Slides available on my web page

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2/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

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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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6 Adding Relativity to QM See Advanced QM II Free particleApply QM prescription Get Schrödinger Equation Missing phenomena: Anti-particles, pair production, spin Or non relativistic Whereas relativistically Klein-Gordon Equation Applying QM prescription again gives: 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 Chris Parkes 7 predicted 1931

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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. Dirac E mc 2 etc.. positron -mc 2 electron positron

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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 particle in chamber Incoming particle (high momentum / low curvature) Outgoing particle (low momentum / high curvature) Cosmic rays with a cloud camber

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10/Chris Parkes Discovery of the positron (2/2) 4 years later Anderson confirmed this with e + e - in lead plate using from a radioactive source

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Dirac equation: for every (spin ½) particle there is an antiparticle Chris Parkes 11 Dirac: predicted 1931 Positron observed 1932 Antiproton observed 1959 Bevatron Anti-deuteron 1965 PS CERN / AGS Brookhaven Anti-Hydrogen 1995 CERN LEAR Spectroscopy starts 2011 CERN 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 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, (2011) Will Bertsche

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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 !

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17/Chris Parkes 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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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 !

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22/Chris Parkes How measured? Nucleosynthesis – abundance of light elements depends on Nbaryons/Nphotons

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23/Chris Parkes Proton decay so far unobserved in experiment, limit is lifetime > 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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24/Chris Parkes Dynamic Generation of Baryon Asymmetry in Universe CP Violation & Baryon Number Asymmetry

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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

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Symmetries and conservation laws

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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

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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

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29/Chris Parkes P operator acts on a state | (r, t)> as 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)Y l m ( , ) P Y l m ( , ) Y l m ( - , + ) =(-1) l Y l m ( , ) So atomic s,d +ve, p,f –ve P Hence, electric dipole transition l=1 P =- 1 Parity - spatial inversion (1/2)

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30/Chris Parkes Parity multiplicative: | > = | a > | b >, P=P a P b Proton Convention P p =+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. J P = 0 +, 0 -, 1 -, 1 + -, o,K -,K o all 0 -, photon 1 - Parity - spatial inversion (2/2)

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31/Chris Parkes Left-handed=spin anti-parallel to momentum Right-handed= spin parallel to momentum

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37/Chris Parkes Spin in direction of momentum Spin in opposite direction of momentum

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43/Chris Parkes Charge conjugation C operator acts on a state | (x, t)> as 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 >

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49 Measuring Helicity of the Neutrino Goldhaber et. al Electron capture K shell, l=0 photon emission Consider the following decay: Eu at rest Select photons in Sm* dir n Neutrino, Sm In opposite dirns e-e- Momenta, p spin OR S=+ ½ S=- ½ Left-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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50 Neutrino Helicity Experiment Tricky bit: identify forward γ Use resonant scattering! Measure γ polarisation with different B-field orientations magnetic field Pb NaI PMT 152 Sm 152 Eu γ γ 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 electron opposite. Forward photons, (opposite p to neutrino), Have slightly higher p than backward and cause resonant scattering Only left-handed neutrinos exist

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51 C P CPCP Parity Inversion Spatial mirror Charge Inversion Particle-antiparticle mirror

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52/Chris Parkes left-handed right-handed Parity left-handed right-handed Charge & Parity Massless approximation (Goldhaber et al., Phys Rev (1958) Neutrino helicity ✗

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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

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55/Chris Parkes CPT invariance CPT THEOREM Any Lorentz-invariant local quantum field theory is invariant under the combination of C, P and T 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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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)

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