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Dirac Equation → 4 Solutions Particle, Anti-Particle Each with Spin up +1/2, Spin Down -1/2 6 Anti-Particles: Dirac

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Dirac Equation → 4 Solutions Particle, Anti-Particle Each with Spin up +1/2, Spin Down -1/2 6 Anti-Particles: Dirac : CP Violation Part I Introductory concepts Slides available on my web page http://www.hep.manchester.ac.uk/u/parkes/ 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 Chris Parkes 2/ Matter and antimatter Chris Parkes 4/ “Surely something is wanting in our conception of the universe... positive and negative electricity, north and south magnetism…” èMatter antimatter Symmetry “matter and antimatter may further co-exist in bodies of small mass” èParticle Antiparticle Oscillations Prof. Physics, Manchester – physics building named after Adding Relativity to QM l See Advanced QM II Free particle p2 Apply QM prescription p i = E → −! ∇ 2m 2 ! 2 ∂ψ Get Schrödinger Equation − ∇ Ψ = i! 2m dt Missing phenomena: Anti-particles, pair production, spin 2 1 2 p Or non relativistic E = mv = 2 2m Whereas relativistically E 2 −p2c2 = m2c4 Applying QM prescription again gives: 2 2 Klein-Gordon Equation 1 ∂ ψ 2 ⎛ mc ⎞ − 2 2 + ∇ ψ = ⎜ ⎟ ψ c dt ⎝ ! ⎠ 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 6 Anti-particles: Dirac l Combine quantum mechanics and special relativity, linear in δt l Half of the solutions have negative predicted 1931 energy l Or positive energy anti-particles l Same mass/spin… opposite charge Chris Parkes 7 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 etc.. E electron mc2 -mc2 positron etc.. positron Chris WestminsterParkes Abbey 8/ 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) Chris Parkes 9/ Discovery of the positron (2/2) 4 years later Anderson confirmed this with γ à e+e- in lead plate using γ from a radioactive source Chris Parkes 10/ Dirac equation: for every (spin ½) particle there is an antiparticle Dirac: Antiproton observed 1959 predicted 1931 Bevatron Positron observed 1932 Spectroscopy Anti-deuteron 1965 Anti-Hydrogen 1995 starts 2011 PS CERN / AGS Brookhaven CERN LEAR CERN LEAR (ALPHA) Chris Parkes 11 Antihydrogen Production Will Bertsche l Fixed Target Experiments (too hot, few!) – First anti-hydrogen G.Bauer et al. (1996) Phys. Lett. B 368 (3) – < 100 atoms CERN (1995), Fermilab – Anti-protons on atomic target l ‘Cold’ ingredients (Antiproton Decelerator) – ATHENA (2002), ATRAP, ALPHA, ASACUSA – Hundreds of Millions produced since 2002. M. Amoretti et al. (2002). Nature 419 (6906): 456 ALPHA Experiment Antihydrogen Trapping & Spectroscopy Nature 468, 355 (2010). Nature Physics, 7, 558-564 (2011). Nature 541, 506–510 (2017). Will Bertsche l Antihydrogen: l How do you trap something electrically neutral ? l Atomic Magnetic moment in minimum-B trap – T < 0.5 K! l Quench magnets and detect annihilation l ALPHA Traps hundreds of atoms for up to 1000 seconds! – Have performed first spectroscopy studies, agreement with hydrogen – Observation of 1S-2S transition stimulated with laser Chris Parkes 14/ Matter and antimatter Ø 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 ! Chris Parkes 15/ Chris Parkes 16/ 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| Chris Parkes 17/ Search for anti-nuclei in space AMS experiment: q A particle physics experiment in space q Search of anti-helium in cosmic rays q AMS-01 put in space in June 1998 with Discovery shuttle Lots of He found No anti-He found ! Chris Parkes 18/ Chris Parkes 19/ Chris Parkes 20/ Chris Parkes 21/ How measured? Nucleosynthesis – abundance of light elements depends on Nbaryons/Nphotons Chris Parkes 22/ 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 Chris Parkes 23/ Dynamic Generation of Baryon Asymmetry in Universe CP Violation & Baryon Number Asymmetry Chris Parkes 24/ 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 Chris Parkes 25/ Symmetries and conservation laws Symmetries and conservation laws Emmy Noether Role of symmetries in Physics: q Conservation laws greatly simplify building of theories Well-known examples (of continuous symmetries): q translational ⇒ momentum conservation q rotational ⇒ angular momentum conservation q time ⇒ energy conservation Fundamental discrete symmetries we will study - Parity (P) – spatial inversion - Charge conjugation (C) – particle ⇔ antiparticle transformation - Time reversal (T) - CP, CPT Chris Parkes 27/ The 3 discrete symmetries q 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 q Charge Conjugation, C – Charge conjugation turns a particle into its antiparticle + - + - - + § e → e , K → K q Time Reversal, T – Changes, for example, the direction of motion of particles § t → -t Chris Parkes 28/ Parity - spatial inversion (1/2) P operator acts on a state |ψ(r, t)> as P Ψ(r,t) = Ψ P (−r,t) P2 Ψ(r,t) = Ψ(r,t) Hence eigenstates P=±1 |ψ(r, t)>= cos x has P=+1, even e.g. hydrogen atom wavefn |ψ(r, t)>= sin x has P=-1, odd m |ψ(r,θ,φ )>=χ(r)Yl (θ,φ) m m |ψ(r, t)>= cos x + sin x, no eigenvalue P Yl (θ,φ) ⇒ Yl (π-θ,π+φ) =(-1)l Y m(θ,φ) Hence, electric dipole l transition Δl=1∴Pγ=- 1 So atomic s,d +ve, p,f –ve P Chris Parkes 29/ Parity - spatial inversion (2/2) q Parity multiplicative: |φ> = |φa> |φb> , P=PaPb q Proton q Convention Pp=+1 q Quantum Field Theory q Parity of fermion → opposite parity of anti-fermion q Parity of boson → same parity as anti-particle q Angular momentum q Use intrinsic parity with GROUND STATES q Also multiply spatial config. term (-1) l scalar, pseudo-scalar, vector, axial(pseudo)-vector, etc. JP = 0+, 0-, 1-, 1+ π-,πo,K-,Ko all 0- , photon 1- q Conserved in strong & electromagnetic interactions Chris Parkes 30/ Left-handed=spin anti-parallel to momentum Right-handed= spin parallel to momentum Chris Parkes 31/ Chris Parkes 32/ Chris Parkes 33/ Chris Parkes 34/ Chris Parkes 35/ Chris Parkes 36/ Spin in direction of momentum Spin in opposite direction of momentum Chris Parkes 37/ Chris Parkes 38/ Chris Parkes 39/ Chris Parkes 40/ Chris Parkes 41/ Chris Parkes 42/ Charge conjugation Particle to antiparticle transformation C Ψ(r,t) = ΨC (r,t) C operator acts on a state |ψ(x, t)> as C 2 Ψ(r,t) = Ψ(r,t) Only a particle that is its own antiparticle can be eigenstate of C ! e.g. C |πo> = ±1 |πo> EM sources change sign under C, hence C|γ> = -1 πo à γ + γ (BR~99%) Thus, C|πo> =(-1)2 |πo> = +1 |πo> Chris Parkes 43/ (Demonstrated Parity, Charge Conjugation Violated. Experiment did not determine Helicity of neutrino) Chris Parkes 44/ Chris Parkes 45/ Chris Parkes 46/ Chris Parkes 47/ Chris Parkes 48/ Measuring Helicity of the Neutrino Goldhaber et. al. 1958 Consider the following decay: See textbook 152 e- 152 * 152 Eu "" → Sm + ν → Sm + γ (960 KeV) Electron capture e photon emission K shell, l=0 J = 0 1 1 2 0 1 • Momenta, p Eu at rest Neutrino, Sm Select photons 152 * 152 Sm→ Sm +γ In opposite dirns in Sm* dirn • spin J= 1 0 1 e- ν γ € S=+ ½ S=+ 1 OR right-handed right-handed S=- ½ S=- 1 Left-handed Left-handed • Helicities of forward photon and neutrino same • Measure photon helicity, find neutrino49 helicity Neutrino Helicity Experiment l Tricky bit: identify forward γ l Use resonant scattering! 152 152 * 152 γγ+Sm→ Sm → Sm + l Measure γ polarisation with different B-field orientations 152Eu Vary magnetic field to vary photon magnetic field Fe absorbtion. Photons absorbed by e- in iron only if spins of photon and electron opposite. S + S = S' γ γ γ e e Pb 1 1 (−1) + (+ ) = (− ) 2 2 Forward photons, 1 1 NaI (opposite p to neutrino), (+1) + (+ ) ≠ (± ) 152Sm 152Sm 2 2 Have slightly higher p than backward PMT and cause resonant scattering Only left-handed50 neutrinos exist Similar experiment with Hg carried out for anti-neutrinos Charge Inversion C P Particle-antiparticle mirror Parity CP Inversion Spatial mirror 51 Neutrino helicity • Massless approximation (Goldhaber et al., Phys Rev 109 1015 (1958) ν left-handed ü Parity ν right-handed ✗ ν left-handed ü Charge & Parity ν right-handed ü Chris Parkes 52/ T - time reversal q Inversion of the time coordinate: t → -t – Changes, for example, the direction of motion of particles q Invariance checks: detailed balances q a + b → c + d becomes under T q c + d → a + b q Conserved in strong & electromagnetic interactions Chris Parkes 53/ Chris Parkes 54/ CPT invariance CPT THEOREM Any Lorentz-invariant local quantum field theory is invariant under the combination of C, P and T G.
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