C hris P arkes

1. : CP Violation Part I Introductory concepts Slides available on my web page • http://www.hep.manchester.ac.uk/u/parkes/ Chris Parkes

2. 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. “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 – physicsbuilding named after

6. See Advanced QM II Adding Relativity to QM 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 negativeenergy 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 ! etc.. Paul A.M. Dirac E electron mc2 -mc2 etc.. positron 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 particlein 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 Dirac: 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. Will Bertsche 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. G.Baueret al. (1996) Phys. Lett. B 368 (3) M. Amoretti et al. (2002). Nature 419 (6906): 456 ALPHA Experiment

13. Antihydrogen Trapping Will Bertsche • 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)

15. Equal amounts of matter & antimatter (?) Matter Dominates ! 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

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. Convertsright-handed coordinate systems to left-handed ones. • Vectors change sign but axial vectors remain unchanged • x  -x , p  -p butL = 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 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)>= cos x has P=+1, even |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. 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 Parity - spatial inversion (2/2) 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. 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 right-handed OR S=- ½ S=- 1 Left-handed Left-handed • Helicities of forward photon and neutrino same • Measure photon helicity, find neutrino helicity

50. Tricky bit: identify forward γ Use resonant scattering! Measure γ polarisation with different B-field orientations Neutrino Helicity Experiment 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