VI. Discrete Symmetries and CP violation

1. Particle Physics I • Introduction, history & overview (2) • Concepts (5): • Units (h=c=1) • Relativistic kinematics • Cross section, lifetime, decay width, … • Symmetries (quark model, …) • Quantum Electro Dynamics: QED (7) • Spin 0 electrodynamics (Klein-Gordon) • Spin ½ electrodynamics (Dirac) • Experimental highlights: “g-2”, ee, … • Particle Physics II • Quantum Chromo Dynamics: QCD (4) • Colour concept and partons • High q2 strong interaction • Structure functions • Experimental highlights: s, ep, … • Quantum Flavour Dynamics: QFD (6) • Low q2 weak interaction • High q2 weak interaction • Experimental highlights: LEP • Origin of matter? (6) • Strange particles • GIM (why does the charm exist?) • K0-K0, oscillations, • CP violation • B0-B0 oscillations • Current CP violation experiment • Origin of mass? (2) • Symmetry breaking • Higgs particle: in ee and in pp File on “paling”: graven/ED_MASTER/master2003.ppt VI. Discrete Symmetries and CP violation Part of the “Particle and Astroparticle Physics” Master’s Curriculum

2. Strange Particles Isospin +1 -1 “Strangeness” -1 +1 Ep threshold (GeV) 0.91 1.5 6.0 Note: long lifetime! In general: more difficult (i.e. higher threshold) to make S=-1 particles then S=+1 when target is either p or n, and beam consists of p+ or p- because for S=+1, need to get an antiquark from somewhere… Quite useful: can make ‘pure’ K0 or K+ sample by running below threshold

3. “V particle”: particles that are produced in pairs and thus leaves a ‘v’ trial in a bubble chamber picture Details: create a new quantum number, “strangeness“ which is conserved by the production process hence pair production by strong force however, the decay must violate “strangeness” if only weak force is “strangeness violating” then it is responsible for the decay process hence (relatively) long lifetime… • Observations: • High production cross-section • Long lifetime • Conclusion: • must always be produced in pairs!

4. Strange Particles Isospin +1 -1 “Strangeness” -1 +1 • mK ~ 494 MeV/c2 • No strange particles lighter than Kaons exist • Decay must violate “strangeness” • Strong force conserves “strangeness” • Decay is a pure weak interaction • Hadronic and leptonic decays: • particle and anti-particle behave the same • Semi-leptonic decays: • particle and anti-particle are distinct from one another! • “DQ=DS rule”

5. Weak decays: K- vs. p-

6. Universality of weak interactions Weak doublets:

7. K0 decays: A problem? the reason there are no FCNC is that VC is unitary: Z0 boson will now couple to uu and d’d’ ... This generates a “FCNC”, (Flavour Changing Neutral Current)… need to do more. Or, to put it the other way around: The absence of FCNC requiresV to be unitary

8. K0 decays: enter the charm To (almost) cancel this diagram, lets introduce another up-type quark, and have it interact through a W with the orthogonal combination of (d,s) This new ’c’ quark causes an additional diagram that (almost) cancels the one above… If mumc, then the cancellation would be complete! This is called “GIM suppression” leads to a prediction of the charm mass of 1.5—2 GeV, prior to the discovery of J/y

9. In general: the weak eigenstates are not the mass eigenstates! If all quarks were the same mass, this could not happen as we could take any linear combination of quarks as the mass eigenstates… And as long as V is unitary, there will be no FCNC! note: can (and will) extend this to 3 families later Q: what happens if VC=1 (i.e. qC=0)? A: the s quark (and thus all S0 particles) would be stable!!! Q: how many independent parameters does V have when there are 2 generations (i.e. is qC all there is?). How about 3 generations? A: 2*22-22-(2*2-1)=1; 2*32-32-(2*3-1)=4

10. Intermezzo: Discovery of the J/y Brookhaven: J SLAC: y(3105) By studying the decay of strange particles, the existence of the charm and its properties (eg. mass, weak couplings) were predicted before its discovery – but nobody believed it! Sam Ting and Burt Richter got the 1976 Nobel prize for their discovery

11. Back to K0 decays… • Known: • K0 can decay to p+p- • Hypothesized: • K0 has a distinct anti-particle K0 • Claims: • K0 (K0) is a “particle mixture” with two distinct lifetimes • Each lifetime has its own set of decay modes • No more than 50% of K0 (K0) will decay to p+p- Phys. Rev. 97, 1387 (1955)

12. K0 and CP symmetry Known decay: Assuming CP symmetry, this should be possible as well: Assuming the reverse reaction is allowed, particle can “mix” into anti-particle, and vice-versa… How does this system evolve in time? (ignore decays for the time being) Mixing causes tiny off-diagonal element: With completely different eigenstates!

13. K0 decay and CP: K1 and K2 Phys Rev 103,1901 (1956) CP: +1 -1 K1 and K2 are their own antiparticle, but one is CP even, the other CP odd: Only the CP even state (K1) can decay into 2 pions (which are CP even) The odd K2 state will decay into 3 particles instead (ppp,pmn, pen,…). There is a huge difference between K0pp and K0 ppp in phasespace (~600x!). So the CP even state will decay much faster

14. 2 vs. 3 particle phase space

15. More on time evolution Tag K0 and K0 decay by semileptonic decay (remember the DS=DQ rule?) K1 decays K2 decays

16. Testing CP conservation q K2p+p- Effect is tiny: about 2/1000 Easy to create a pure K2 beam: just “wait” until the K1 component has decayed… If CP conserved, should not see the decay to 2 pions in this K2 beam This is exactely what was tested by Cronin & Fitch in 1957… Main background: p+p- p0 … and for this experiment they got the Nobel price in 1980…

17. Interference KL and KS are no longer orthogonal:

18. T violation in mixing CPLEAR, Phys.Rep. 374(2003) 165-270 t t=0 CP • Note: • This measurement allows one to make an ABSOLUTE distinction between matter and anti-matter • Don’t need to know the specific value of • decay amplitudes; only need:

19. (2x)2 ways to decay… Amplitude t=0 t CP

20. 3 ways to break CP CP violation in decay CP violation in mixing CP violation in the interference between mixing and decay

21. 3 Ways to break CP

22. The Final Result… CP A(KS) A(KS) K0(t=0) K0(t=0) p+p-(t) p+p-(t) • If CP were conserved, KL wouldn’t decay to p+p-, and there would be no interference… A(KL) -A(KL) If h+-=0: only “KS” like decays If h+-0: not only “KL” like decays, down by |h+-|2, but also interference contribution, down by |h+-| The interference term has a sign difference for K0 and K0bar!

23. CPLEAR Detector@CERN Use the strangeness conservation of the strong interactions to perform Tagged K0 and K0 production: • At t=0, events with a • K+ are a pure K0bar sample • K- are a pure K0 sample

24. CPLEAR

25. Results: CP in Interference (K0-K0)/(K0+K0) CPLEAR, PLB 1999 Mainly KSp+p-decays Mainly KLp+p decays K0bar K0 Approx equal KSp+p-and KLp+p- rate: Maximal interference! Interference maximal: Note: rates are normalized to each other in the range (,) decaytime / tS

26. Details…

27. CP violation: when? • Introduce A, Abar into the picture • CP violation seems to occurs in interference • What kinds of interference can we have? • Mixing • Decay • Mixing vs. Decay Pbar P f

28. Basic Equations: Neutral Meson Mixing In general, want to know the time evolution of: • If • At t=0, only a(t) and b(t) are non-zero • We are only interested in a(t) and b(t), and not ci(t) • t is large compared to the strong-interaction scale • Then one can make an approximation (Wigner-Weisskopf) which considerably simplifies things:

29. Basic Equations: Neutral Meson Mixing Virtual Intermediate States L is not Hermitian: otherwise mesons would only oscillate, and never decay… instead: Real Intermediate States

30. Basic Equations: Neutral Meson Mixing L is not Hermitian: otherwise mesons would only oscillate, and never decay… instead: M describes oscillations, G decays

31. Phase conventions Because of the requirement of phase independence, R has only 7 (physical) parameters CPT invariance: T invariance: CP invariance: Requiring CPT reduces this to X parameters (SHOW!)

32. Solving the master equations

33. Computing Dm and DG in K0 mixing Or: why is kaon mixing so different from B mixing And why is D mixing different again??? Actually, why is the B lifetime so large? as expected, the D lifetime is much less than the K0S one Show that mixing vanishes if all quark masses are equal Okun p88? Cahn-Goldhaber, chapter 15

34. Solution (CP violating case) Nobel Lecture Val Fitch http://www.nobel.se/physics/laureates/1980/

35. Intermezzo: KS regeneration i.e. why the helium bag? Or: another way to measure dm

36. Enter the B meson… Third generation -> VCKM Long lifetime! -> Vcb must be tiny! It mixes! -> top must be VERY heavy

37. And then there were 3…The CKM matrix Unexpected long B lifetime! => Vcb must be small! Eg. B+ to mu+ not observed, only limits

38. Mixing of neutral mesons

39. D0 mixing vs. Bd mixing Mixing dominated by Vtd Must have heavy (>100 GeV) top! As VtdVtb**2 isn’t very large (0.2**6) Not yet observed! Experimental limit goes here How do we measure mixing?? Compute Vtd from the measured dm values

40. Bd mixing vs. Bs mixing Mixing Dominated by Vtd Mixing Dominated by Vts Some other effects of O(30%) lead to the SM expectation of ~18 Not yet observed! Experimental limit goes here Lifetime difference dominated by Vcd: tiny Lifetime difference dominated by Vcs: Expect 10-20%

41. CP violation in mixing Why small? Experimental results Kaons, Bd mesons

42. Is P a good symmetry? B q e-  More electrons emitted opposite the J direction. Parity violation! • Sketch and photograph of apparatus used to study beta decay in polarized cobalt-60 nuclei. The specimen, a cerium magnesium nitrate crystal containing a thin surface layer of radioactive cobalt-60, was supported in a cerium magnesium nitrate housing within an evacuated glass vessel (lower half of photograph). An anthracene crystal about 2 cm above the cobalt-60 source served as a scintillation counter for beta-ray detection. Lucite rod (upper half of photograph) transmitted flashes from the counter to a photomultiplier (not shown). Magnet on either side of the specimen was used to cool it to approximately 0.003 K by adiabatic demagnetization. Inductance coil is part of a magnetic thermometer for determining specimen temperature. Parity violation observed in 60Co experiment in 1956. e- q Parity transformation Magnetic field   J J 60Co 60Co I(q) = 1 + a (v/c) cos q with a = -1 Observed C. Yang and T. Lee, 1956 C. S. Wu, 1957 Parity violation 2010 1950 ‘60 ‘70 ‘80 ‘90 2000

43. Intermezzo: CP

44. Exercise: Show CP |pi+pi-> = + | pi+pi-> CP |pi+pi-pi0> = - |pi+pi-pi0>

46. More details about Mixing: regeneration How do we make sure KL -> p+p- is really the same final state As KS->pipi ? maybe we’re missing a particle that takes away very little momentum? NOTE: beta decay spectrum was ‘solved’ by introducing a new particle (the neutrino) Let them interfere! Q: why does eg. K*0 not mix? It has the same quark content… A: it decays to K+pi-, a strong decay – it just isn’t stable enough! A2: it is a vector particle…

47. Trace Theorems