Particle Physics: Status and Perspectives Part 6: Symmetries

1. Particle Physics: Status and PerspectivesPart 6: Symmetries SS 2018 Manfred Jeitler

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”).

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8. Looking at particles more closely Do particles behave just like balls in a game of billiards? Is there room for any asymmetries? K p e

9. 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 • two-neutron state: • 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 !

10. triplet and singlet spin states

13. 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

14. parity violation Chien-ShiungWu 吴健雄 Chen Ning Yang (楊振寧) and Tsung-Dao Lee (李政道) (Nobel prize 1957)

15. 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 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: unit vector in direction of electron spin • σ.p is pseudoscalar • mirror flips one but not the other

16. parity violation

17. 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 usually flies very fast (v/c ~ 1) • it is a lepton -- the “neutral sibling” of the electron • what should we expect?

18. the helicity of the neutrino

19. 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- )

20. neutrinos P

21. neutrinos and antineutrinos P C CP

22. 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

23. pion decay • dominant pion decay mode: • could also decay as π+e+ + νe • in both cases, lepton and neutrino have opposite helicity • they fly apart (opposite momentum) • pion has zero spin  conflict with angular momentum conservation • due to its higher mass, the muon is not so fast (not so “relativistic”) and “does not care” so much • suppression by factor 1 – v/c • therefore, π+e+ + νe is strongly suppressed compared to π+ μ+ + νμ • suppressed by factor 104

24. the neutral kaon system • kaons are mesons that contain one light quark (u, d,anti-u, anti-d) and one strange-type quark (i.e., strange or anti-strange) • quark model allows us to build two neutral kaons: • K0 = d anti-santi-K0 = s anti-d • however, the physical particles we find are linear combinations of these two: • KL ~ K0 - anti-K0 KS ~ K0 + anti-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 anti-K0 is formed by Strong interactions, these particles “oscillate” (transform into one another)

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

26. box and penguin graphs

27. 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

28. 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

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

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

31. 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)

32. 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-

33. 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“ /

34. 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

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

36. 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

37. 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

38. 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!

39.  Makoto Kobayashi Toshihide Maskawa  Nobel prize 2008 (together with Yoichiro Nambu)

40. Nicola Cabibbo

41. 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“

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

43. 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

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

45. 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?

46. Comparing particles to coupled pendulums KL KS K0 K0

47. 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 ? =

48. 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

49. 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

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