Elementary Particle Physics Part 5 Symmetries Manfred Jeitler WS 2007/2008

1. Elementary Particle PhysicsPart 5SymmetriesManfred JeitlerWS 2007/2008

2. SYMMETRIES

3. symmetries in physics • certain transformations do not change the laws of nature • translation in space • translation in time • for each continuous symmetry transformation, there is a conservation law (Noether theorem, 1918) • translation in space: conservation of momentum • translation in time: conservation of energy

4. discrete symmetries • Fundamental symmetry operations in particle physics: • parity transformation (spatial inversion P) • particle-antiparticle conjugation (charge conjugation C) • timeinversion (T) p+ p- According to the kind of interaction, the result of such a transformation may describe a physical state occurring with the same probability (“the symmetry is conserved”) or not (“the symmetry is broken” or “violated”).

5. Looking at particles more closely Do particles behave just like balls in a game of billiards? Is there room for an asymmetry in time? K p e

6. intrinsic parity of the negative pion π- • consider pion capture: π- + d --> n + n • total angular momentum J = 1 • sd = 1, sπ = 0, capture occurs in S-state (L=0) • J = L + S = 1 • L=0,S=1 or L=1,S=0 or L=1,S=1 or L=2,S=1 • symmetry under neutron exchange: (-1)L+S+1 • must be negative (neutrons are fermions --> Fermi-Dirac statistics) --> L+S must be even ! • orbital momentum L: even-numbered states are symmetric • spin: S=1 (“triplet”) is symmetric, S=0 (“singlet”) is antisymmetric • --> L=1, S=1 • parity = (-1)L = -1 is negative • proton and neutron have intrinsic parity +1 • --> deuteron has positive parity • pion (π-) has negative parity !

7. triplet and singlet spin states

10. parity violation • most physicists had thought that fundamental symmetries were never violated • this had not been proved, however, for Weak interactions • C.N.Yang and T.D.Lee conjectured that parity might not be conserved in Weak interactions • K+ --> 2π (positive parity) and • K+ --> 3π (negative parity): “τ-θ puzzle” • experiment made by C.S.Wu • β-decay of 60Cobalt • --> the world’s mirror image differs from the world itself

11. parity violation C.S.Wu C.N.Yang and T.D.Lee

12. parity violation: Wu’s experiment • polarized matter • 60Co at 0.01 Kelvin inside solenoid • high proportion of nuclei aligned • 60Co (J=5) --> 60Ni* (J=4) • “Gamow-Teller transition”: lepton spin = 1 • electron spin σ points in direction of 60Co spin J • conservation of angular momentum • degree of 60Co alignment determined from observation of 60Ni* γ-rays • observed electron intensity: • θ: angle between electron (p) and spin (J) • σ.p is pseudoscalar • mirror flips p but not σ

13. parity violation

14. helicity • electrons have a “helicity”: H = -v/c • “left-handed” • the faster they are, the more the spin is aligned antiparallel to the momentum • positrons have opposite helicity: H = +v/c • “right-handed” • photons occur right-handed and left-handed with equal probability • --> parity is conserved in electromagnetic interactions • what about the neutrino? • it is very light and therefore flies very fast most of the time (v/c ~ 1) • it is a lepton -- the “neutral sibling” of the electron • what should we expect?

15. the helicity of the neutrino

16. the helicity of the neutrino • experiment carried out by Goldhaber et al., 1958 • result: helicity of neutrino is negative • H = -1 for massless neutrino • ν has same lepton number (Le) as e-

17. neutrinos P

18. neutrinos and antineutrinos P C CP

19. Parity CP Charge spinning neutrinos and antineutrinos left-handed neutrino right-handed neutrino X Parity CP Charge particle-antiparticle conjugation In weak interactions P and C are “maximally violated” while the combined symmetry under CP is mostly conserved: right-handed antineutrino

20. the neutral kaon system • kaons are mesons that contain 1 light quark (u, d,`u ,`d) and 1 strange-type quark (i.e., strange or anti-strange) • quark model allows us to build to neutral kaons: • K0 = d `s `K0 = s `d • however, the physical particles we find are linear combinations of these two: • KL ~ K0 - `K0KS ~ K0 + `K0 • these are the eigenstates under Weak interaction, through which these particles decay (only Weak interactions can transform quarks of different generations into one another) • when a K0 or `K0 is formed by Strong interactions, these particles “oscillate” (transform into one another)

21. “oscillation” of neutral kaons due to transitions via virtual 2π and 3π states

22. box and penguin graphs

23. p K0L p p CP = -1 CP = -1 K0S p p CP = +1 CP = +1 CP-eigenvalue • particles can be attributed a “CP-eigenvalue” • like charge, mass, parity • this eigenvalue is multiplicative: • CP () = -1 • CP () = +1 • there are 2 kinds of “neutral K-mesons” • the (long-lived) K0L decays into 3 -mesons • the (short-lived) K0S decays into 2 -mesons • K0L andK0S differ by their CP-eigenvalue ! • CP(K0L) = -1 CP(K0S) = +1

24. p K0L p p K0S p p CP-violation 1964: sometimes (0.3 percent) also CP = -1 p K0L CP = -1 p CP = -1 CP = +1 CP = +1 CP = +1

25. CP-violation: the first experiment Christenson, Cronin, Fitch and Turlay: Brookhaven 1964 Nobel prize 1980

26. simple setup (by present standards): • spark chambers • scintillators • Cerenkov detectors the first signal: K0L p+p-

27. CP and the decay of neutral kaons CP eigenstates: CP ( K1 ) = + K1 CP ( K2 ) = - K2 but the physical states areKL and KS: KL  K2 + e K1 KS  K1 + e K2 CP-conserving: KL (CP  -1)  ppp (CP = -1) CP-violating: KL (CP  -1)  pp (CP = +1)

28. Indirect and direct CP-violation KL (CP  -1)= K2 (CP = -1)+ e K1 (CP = +1)  pp (CP = +1) indirect CP-violation (through mixing) direct CP-violation (in the decay) indirect CP-violation: must be same for p0p0 and for p+p- direct CP-violation: may be different for p0p0 and for p+p-

29. p0 p0 p0 p0 KS KL p+ p+ p- p- KL KS NA48: measuring the double ratio R R  1: direct CP-violation exists ”frequent“ ”rare“ /

30. Indirect and direct CP-violation only indirect CP-violation: explanation by “superweak model” possible (introducing a “5th interaction”) direct CP-violation: explanation only through “Standard Model” experimental results (NA48@CERN, KTeV@Fermilab): R  1  superweak model excluded

31. Layout of the NA48 experiment at CERN:the measurement of “direct CP-violation”

32. muon ring anti hadron calorimeter ring anti DCH DCH magnet DCH DCH The detector of the NA48 experiment at CERN • muon detector and anti-counters for background suppression • electromagnetic liquid-krypton calorimeter for measuring p0p0-decays • hodoscope for exact timing • spectrometer (consisting of 4 drift chambers and a magnet) and hadron calorimeter for measuring p+p--decays

33. the tagging detector • distinguish KS- and KL-decays by “tagging” the protons directed at the “KS-target” • beam is “split up” onto several individual scintillators to reach good double-pulse resolution in spite of high rate (up to 30 MHz) • very fast flash-ADC (digitisation electronics) developed at HEPHY, Vienna

34. the Cabibbo-Kobayashi-Maskawa matrix • the coupling between “up-type” and “down-type” quarks is described by the Cabibbo-Kobayashi-Maskawa matrix: • so, the three generations of quarks are not completely separated, but “mix”, so that quarks of the heavier generations can decay into those of the lighter generations • in the Standard Model, CP-violation can be explained by a non-trivial complex phase in this matrix • this would not be possible with only two generations • so, third generation was actually predicted by CP-violation theory!

35. the Cabibbo-Kobayashi-Maskawa matrixand the”unitarity triangle“ • this matrix desribes a mixture of states whose total number does not change; so the matrix has to be unitary: V  V+= V+ V= 1or • this yields the relation which can be graphically represented in the form of one of six so-called „unitarity triangles“

36. normalized to 1 the unitarity triangle Im i    0 1 Re

37. CPT There are powerful theoretical arguments and experimental evidence for CPT conservation, i.e. CPT (X) = X in this case we must conclude: CP (X)  XT (X)  X

38. Conservation of symmetry C P CP T CPT gravitation      electromagnetism      strong interaction      weak interaction X X x x

39. direct measurement of T-violation As shown before, the physical states KL and KS are linear combinations: KL  K2 + e K1 KS  K1 + e K2 However, K1 andK2 are also linear combinations : K1 = K0 + `0 K2 = K0 - `0 What does a “linear combination of states” mean?

40. Comparing particles to coupled pendulums KL KS K0 K0

41. Measure T-violation by comparing K0  K0 and K0 K0 Compare rates for neutral kaons which are created as K0 and decay as K0 with the inverse process:  K0 K0  K0 K0 ? =

42. Identifying K0and K0 at creation time It is hard to separately create K0 and K0, usually both kinds of particles are produced. Tagging due to “strangeness conservation in strong interactions”: pp  K0p+ K- pp  K0 p- K+ S K0, K++1 K0, K--1

43. Identifying K0and K0 at decay time Selecting “semileptonic decays” of neutral kaons, K pen, we observe only K0 p- e+ n K0 p+ e- n due to the so-called “DS = DQ rule”: d d K0 p- s u W+ e+ n

44. The CPLEAR experiment at CERN Antiprotons p hit a hydrogen target

45. Direct measurement of T-violation by CPLEAR at CERN

46. T-violation has been seen via CP-violation in neutral kaons (CPT-conservation!). • T-violation has been observed directly by measuring the probabilities for K0  K0andK0 K0.

47. particle physics and cosmology: the big bang

48. Matter in the universe At the time of the Big Bang, particles and antiparticles were created in equal amounts. Today, the universe consists mostly of matter, not antimatter. Where has all the antimatter gone? How come we are still around? CP-violation is an important condition for this “baryon asymmetry” (Sakharov, 1965).

49. Sakharov conditions • baryogenesis: to get from an originally symmetric state (matter = antimatter) to the present state (matter >> antimatter), the following three conditions must be met: • 1) baryon number violation • obvious • 2) no thermal equilibrium • else, for each process creating matter at the cost of antimatter, the inverse process would take place with equal probability • 3) CP-violation • else, for each process creating matter at the cost of antimatter, the CP-mirrored, inverse process would take place with equal probability • --> CP-violation of vital importance for us • or would you like to be one of zillions of photons, just playing with other photons? • but the known sources of CP-violation are not enough • your task: go and find the source of CP-violation that allows for baryogenesis! • proposed mechanism: leptogenesis • we do not know how many leptons (neutrinos) there are • mechanism that transforms leptons into baryons could create the observed baryon asymmetry

50. proton decay? • if baryon number conservation is violated (Sakharov condition #1), the proton could decay • for example, p --> e+ π0 • no other conservation law forbids this • another argument for possible proton decay: there is no field that corresponds to baryon number conservation • in gauge theories, long-range fields give rise to absolutely conserved quantities • proton decay is definitely very slow • good for us: else, we would have problems with radiation damage! • experimental limits very low • half-life > 1036 years (“Superkamiokande” detector, Japan) • spin-off: neutrino detectors