1. Niels Tuning (1) Particle Physics II – CP violation Introduction N. Tuning Acknowledgements: Slides based on the course from Marcel Merk and Wouter Verkerke.

2. Niels Tuning (2) Outline 25 February: Introduction –Motivation of this course –Anti-matter –P and C symmetries 3 March: Lecture 1 –CP symmetry –K-system CP violation Oscillations –Cabibbo-GIM mechanism –Mixing 10 March: Lecture 2 –CP violation in the Lagrangian –CKM matrix, unitarity triangle –B  J/Psi Ks 17 March: Lecture 3 –3 Types of CP-violation –Measuring CP-violation –Penguins –New physics?

3. Niels Tuning (3) Literature Slides based on courses from Wouter Verkerke and Marcel Merk. W.E. Burcham and M. Jobes, Nuclear and Particle Physics, chapters 11 and 14. Z. Ligeti, hep-ph/0302031, Introduction to Heavy Meson Decays and CP Asymmetries Y. Nir, hep-ph/0109090, CP Violation – A New Era H. Quinn, hep-ph/0111177, B Physics and CP Violation

4. Introduction: it’s all about the charged current “CP violation” is about the weak interactions, In particular, the charged current interactions: Niels Tuning (4) The interesting stuff happens in the interaction with quarks Therefore, people also refer to this field as “flavour physics”

5. Motivation 1: Understanding the Standard Model Niels Tuning (5) “CP violation” is about the weak interactions, In particular, the charged current interactions: Quarks can only change flavour through charged current interactions

6. Introduction: it’s all about the charged current “CP violation” is about the weak interactions, In particular, the charged current interactions: Niels Tuning (6) In 1 st lecture next week: P-parity, C-parity, CP-parity  the neutrino shows that P-parity is maximally violated

7. Introduction: it’s all about the charged current “CP violation” is about the weak interactions, In particular, the charged current interactions: Niels Tuning (7) In 1 st lecture next week: P-parity, C-parity, CP-parity  Symmetry related to particle – anti-particle b WW u gV ub WW gV* ub

8. Niels Tuning (8) Motivation 2: Understanding the universe It’s about differences in matter and anti-matter –Why would they be different in the first place? –We see they are different: our universe is matter dominated Equal amounts of matter & anti matter (?) Matter Dominates !

9. Niels Tuning (9) Where and how do we generate the Baryon asymmetry? No definitive answer to this question yet! In 1967 A. Sacharov formulated a set of general conditions that any such mechanism has to meet 1)You need a process that violates the baryon number B: (Baryon number of matter=1, of anti-matter = -1) 2)Both C and CP symmetries should be violated 3)Conditions 1) and 2) should occur during a phase in which there is no thermal equilibrium In these lectures we will focus on 2): CP violation Apart from cosmological considerations, I will convince you that there are more interesting aspects in CP violation

10. Niels Tuning (10) Introduction: it’s all about the charged current Same initial and final state Look at interference between B 0  f CP and B 0  B 0  f CP “CP violation” is about the weak interactions, In particular, the charged current interactions:

11. Niels Tuning (11) Motivation 3: Sensitive to find new physics K*K* bb ss μ μ x s̃ b̃ g̃ B0B0 d BsBs bb s μ μ x s̃ b̃ g̃ BsBs BsBs bb s ss b x x b̃ s̃ g̃ b s s b “Box” diagram: ΔB=2 b s μ μ “Penguin” diagram: ΔB=1 “CP violation” is about the weak interactions, In particular, the charged current interactions: Are heavy particles running around in loops?

12. Recap: Interesting because: 1)Standard Model: in the heart of quark interactions 2)Cosmology: related to matter – anti-matter asymetry 3)Beyond Standard Model: measurements are sensitive to new particles Niels Tuning (12) CP-violation (or flavour physics) is about charged current interactions b s s b Matter Dominates !

13. Personal impression: People think it is a complicated part of the Standard Model (me too:-). Why? Non-intuitive concepts? –Imaginary phase in transition amplitude, T ~ e iφ –Different bases to express quarks states, d’=0.97 d + 0.22 s + 0.003 b –Oscillations (mixing) of mesons: |K 0 > ↔ |  K 0 > Complicated calculations? Many decay modes? “Beetopaipaigamma…” –PDG reports 347 decay modes of the B 0 -meson: Γ 1 l + ν l anything ( 10.33 ± 0.28 ) × 10 −2 Γ 347 ν ν γ<4.7 × 10 −5 CL=90% Niels Tuning (13)

14. Let’s start slowly… Niels Tuning (14)

15. Niels Tuning (15) What is evidence for the existence of anti-matter? Energetic photons produced in matter/anti-matter annihilation –Look at spectrum of photons in universe and look for spikes –Main problem: photons can not travel unlimited distances in the universe because of interactions with remaining cosmic background radiation and gases etc… –Conclusion: No anti-matter in 20Mpc radius. –How to look further into space? Better: Look for anti-Helium nuclei flying through space –Positrons, anti-protons can occasionally be produced in various processes, but producing anti-Helium is way too complicated by ‘regular means’: Only viable source of anti-Helium are fusion processes in ‘anti-stars’ –Presence/absence of anti-Helium says something about existence of anti-matter in distant regions of space –Large rest mass of Helium nuclei allows them to travel much further through space than photons  Conclusions of anti-Helium searches cover much larger region of space

16. Niels Tuning (16) The AMS experiment – Searching for He In essence as small particle physics experiment in space –AMS-01 brought to space through flight of Discovery shuttle –Can detect and identify many types of cosmic rays

17. Niels Tuning (17) Results of the AMS experiment Zero anti-helium found, plenty of Helium found –Rigidity of tracks is measure of particles momentum –Very high energy Helium nuclei have traveled from far  Says something about spatial reach of experiment ‘Universe with pockets of anti-matter’ hypothesis increasingly unlikely –Future AMS-02 experiment will (launch 2007) will have much increased range

18. Niels Tuning (18) Introduction – positron discovery by Anderson Result: discovery of a positively charged electron-like particle dubbed the ‘positron’ –Experimental confirmation of existence of anti-matter! Lead plate to slow down particle in chamber Incoming particle (high momentum / low curvature) Outgoing particle (low momentum / hi curvature) e + (63 MeV) 6mm Pb e + (23 MeV)

19. Niels Tuning (19) Introduction – positron discovery by Anderson 4 years later Anderson confirmed this with   e + e - in lead plate using  from Thorium carbide source

20. Niels Tuning (20) Introduction – anti-neutrino: Savannah river Decisive experiment close to Savannah River nuclear reactor in South Carolina in 1956 (Nobel prize 1995) Idea: nuclear reactor provides enormous anti-neutrino flux from fission O(10 13 ) /cm 2 /sec –Try to detect inverse beta decay: + p +  n + e + (Beta decay: n  p + + e - + ) n e +  p + p +  n e + Cross over e - Invert reaction

21. Niels Tuning (21) Introduction – anti-neutrino: Savannah river How do you detect + p +  n + e + –Look for the positron through the reaction e + e -   and detect 2 photons produced simultaneously. Savannah river Detector: –Tank with 200 liters of water with 40 kg of CdCl 2 dissolved in it. –Surrounded by 110 photomultipliers for photon detection Clean signal found  direct proof of existence of neutrino –Nobel prize 1995  ν + n  p + + e - not observed –   ν ≠ ν, Lepton number must be conserved From inverse beta decay From detector material

22. Niels Tuning (22) Introduction - What about the other anti-particles? Dirac equation: for every (spin ½) particle there is an anti-particle –It took a bit longer, but more were discovered Anti-proton (1955) and anti-neutron (1955) using cyclotrons Reactions with particles and anti-particles –Q: How do you produce anti-particles anyway? –A: In pairs with particles, e.g.   e + e - But this is not the whole story as we will see later General rule: crossing symmetry –In any existing reaction you can move a particle through the arrow while turning it into an anti-particle –Example: e -   e -  (Compton scattering)   e + e - (Pair creation) Move e - to right Move  to left ( = )

23. Niels Tuning (23) Definition and discovery of C,P,CP violation

24. Niels Tuning (24) Continuous vs discrete symmetries Space, time translation & orientation symmetries are all continuous symmetries –Each symmetry operation associated with one ore more continuous parameter There are also discrete symmetries –Charge sign flip (Q  -Q) : C parity –Spatial sign flip ( x,y,z  -x,-y,-z) : P parity –Time sign flip (t  -t) : T parity Are these discrete symmetries exact symmetries that are observed by all physics in nature? –Key issue of this course

25. Niels Tuning (25) Example: People believe in symmetry… Instruction for Abel Tasman, explorer of Australia (1642): “Since many rich mines and other treasures have been found in countries north of the equator between 15 o and 40 o latitude, there is no doubt that countries alike exist south of the equator. The provinces in Peru and Chili rich of gold and silver, all positioned south of the equator, are revealing proofs hereof.”

26. Niels Tuning (26) Three Discrete Symmetries 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 Charge Conjugation, C –Charge conjugation turns a particle into its anti-particle e +  e -, K -  K + Time Reversal, T –Changes, for example, the direction of motion of particles t  -t  

27. Niels Tuning (27) P-parity experiments Before 1956 physicists were convinced that the laws of nature were left-right symmetric. Strange? –A “gedanken” experiment: Consider two perfectly mirror symmetric cars: What would happen if the ignition mechanism uses, say, 60 Co  decay? “L” and “R” are fully symmetric, Each nut, bolt, molecule etc. However the engine is a black box Person “L” gets in, starts, ….. 60 km/h Person “R” gets in, starts, ….. What happens? “L” “R” Gas pedal driver Gas pedal driver

28. Niels Tuning (28) The situation in 1956 Nothing hints at the existence of any kind of Parity violating physics… –Reminder: Parity: (x,y,z)  (-x,-y,-z) –If universe is parity-symmetric, inverting all spatial coordinates would not changes laws of physics 1956: Lee and Yang publish a paper Question of Parity Conservation in Weak Interactions/ –Suggestion: Weak interaction might violate Parity symmetry. Originated from discussions at April HEP conference in Rochester, NY. Following Yang's presentation Richard Feynman brought up the question of non-conservation of parity. –Feynman himself later said, "I thought the idea (of parity violation) unlikely, but possible, and a very exciting possibility." Indeed Feynman later made a fifty dollar bet with a friend that parity would not be violated.

29. Niels Tuning (29) Parity symmetry – The situation in 1956 When the paper appeared, physicists were not immediately prompted into action. The proposition of parity non-conservation was not unequivocally denied; rather, the possibility appeared so unlikely that experimental proof did not warrant immediate attention. The physicist Freeman Dyson wrote of his reaction to the paper: "A copy of it was sent to me and I read it. I read it twice. I said, `This is very interesting,' or words to that effect. But I had not the imagination to say, `By golly, if this is true it opens up a whole new branch of physics.' And I think other physicists, with very few exceptions, at that time were as unimaginative as I."

30. Niels Tuning (30) Parity symmetry – the experiment Madame Wu –Another immigrant was now to play the next major role, Madame Chien-Shiung Wu. Arriving at Berkely in 1936 from Shanghai, Wu was one of the most ardently pursued coeds on campus. But she was also a hard worker who abhorred the marked absence of women from the American scientific establishment. She says, "... it is shameful that there are so few women in science... In China there are many, many women in physics. There is a misconception in America that women scientists are all dowdy spinsters. This is the fault of men. In Chinese society, a woman is valued for what she is, and men encourage her to accomplishments --- yet she retains eternally feminine." Idea from experiment in collaboration with Lee and Yang: Look at spin of decay products of polarized radioactive nucleus –Production mechanism involves exclusively weak interaction

31. Niels Tuning (31) Intermezzo: Spin and Parity How does the decay of a particle with spin tell you something about parity? Gedanken-experiment: decay of X  a + b –Spin: |1,1>  |½, ½ > + |½, ½> –It is important that X is maximally polarized: only then there is a single solution for the spin of the decay products. If not, e.g. |1,0>  |½, +½> + |½, -½> |1,0>  |½, -½> + |½, +½> 

32. Niels Tuning (32) Intermezzo: Spin and Parity and Helicity We introduce a new quantity: Helicity = the projection of the spin on the direction of flight of a particle H=+1 (“right-handed”) H=-1 (“left-handed”)

33. Niels Tuning (33) Intermezzo: Spin and Parity and Helicity Spin is quantized  Helicity is quantized –Possible H values for S=1/2: H=-1 and H=+1 –Most particles are linear combination of H=+1 and H=-1 states –Angular distribution for particles observed in specific helicity eigenstate: Superposition of H=+1 and H=-1 states I() RH = 1 - (v/c) cos  I() LH = 1 + (v/c) cos  H=+1 (“right-handed”) H=-1 (“left-handed”) + Constant If both helicities are produced equally in decay. If not angular distribution will not be flat

34. Niels Tuning (34) Note on Helicity Note that Helicity is not generally a Lorentz- invariant observable –Sign of particle momentum p is relative to observer. –A second observer ‘overtaking’ the particle from the lab observer perspective will see the particle moving in the opposite direction (p’ = -p)  It see the opposite Helicity Exception for massless particles: –You cannot overtake massless particles moving at speed of light –Helicity for massless particles is Lorentz-invariant intrinsic property

35. Niels Tuning (35) A realistic experiment: the Wu experiment (1956) Observe radioactive decay of Cobalt-60 nuclei –The process involved: 60 27 Co  60 28 Ni + e - + e – 60 27 Co is spin-5 and 60 28 Ni is spin4, both e- and e are spin-½ –If you start with fully polarized Co (S Z =5) the experiment is essentially the same (i.e. there is only one spin solution for the decay) |5,+5>  |4,+4> + |½,+½> + |½,+½> S=1/2 S=4

36. Niels Tuning (36) The Wu experiment – 1956 Experimental challenge: how do you obtain a sample of Co(60) where the spins are aligned in one direction –Wu’s solution: adiabatic demagnitization of Co(60) in magnetic fields at very low temperatures (~1/100 K!). Extremely challenging in 1956!

37. Niels Tuning (37) The Wu experiment – 1956 The surprising result: the counting rate is different –Electrons are preferentially emitted in direction opposite of 60 Co spin! –Careful analysis of results shows that experimental data is consistent with emission of left-handed (H=-1) electrons only at any angle!! ‘Backward’ Counting rate w.r.t unpolarized rate ‘Forward’ Counting rate w.r.t unpolarized rate 60 Co polarization decreases as function of time

38. Niels Tuning (38) The Wu experiment – 1956 Physics conclusion: –Angular distribution of electrons shows that only pairs of left- handed electrons / right-handed anti-neutrinos are emitted regardless of the emission angle –Since right-handed electrons are known to exist (for electrons H is not Lorentz-invariant anyway), this means no left-handed anti-neutrinos are produced in weak decay Parity is violated in weak processes –Not just a little bit but 100% How can you see that 60 Co violates parity symmetry? –If there is parity symmetry there should exist no measurement that can distinguish our universe from a parity-flipped universe, but we can!

39. Niels Tuning (39) Our universe vs a parity-flipped universe What happens to helicity in parity-flipped universe? –Momentum flips sign –Spin stays the same –Helicity is product and flips sign Conclusion: –Any process that produces right-handed anti-neutrinos in our universe will produce left-handed anti-neutrinos in the mirrored universe. –If left and right-handed neutrinos are not produced at the same rate the physics in the mirrored universe is different Direction of motion Orientation of spin Direction of motion Orientation of spin righthanded H=+1 lefthanded H=-1 P

40. Niels Tuning (40) Parity violation in weak decays Apply parity operation to 60 Co decay e- LH e Our universe e- RH e e- LH e e- RH e P-Flipped universe

41. Niels Tuning (41) Parity violation in weak decays Apply parity operation to 60 Co decay e- LH e Our universe (RH anti-neutrinos only) Allowed e- RH e Forbidden e- LH e Allowed e- RH e Forbidden P-Flipped universe (LH anti-neutrinos only) Preferential direction of electrons is forward Preferential direction of electrons is backward

42. Niels Tuning (42) So P is violated, what’s next? Wu’s experiment was shortly followed by another clever experiment by L. Lederman: Look at decay  +   +  –Pion has spin 0, ,  both have spin ½  spin of decay products must be oppositely aligned  Helicity of muon is same as that of neutrino. Nice feature: can also measure polarization of both neutrino ( + decay) and anti-neutrino ( - decay) Ledermans result: All neutrinos are left-handed and all anti-neutrinos are right-handed ++  

43. Niels Tuning (43) Charge conjugation symmetry Introducing C-symmetry –The C(harge) conjugation is the operation which exchanges particles and anti-particles (not just electric charge) –It is a discrete symmetry, just like P, i.e. C 2 = 1 C symmetry is broken by the weak interaction, –just like P ++   (LH) --  C OK

44. Niels Tuning (44) The Weak force and C,P parity violation What about C+P  CP symmetry? –CP symmetry is parity conjugation (x,y,z  -x,-y,z) followed by charge conjugation (X  X) ++ ++  ++  ++ Intrinsic spin PC    CP CP appears to be preserved in weak interaction!

45. Niels Tuning (45) Conserved properties associated with C and P C and P are still good symmetries in any reaction not involving the weak interaction –Can associate a conserved value with them (Noether Theorem) Each hadron has a conserved P and C quantum number –What are the values of the quantum numbers –Evaluate the eigenvalue of the P and C operators on each hadron P|> = p|> What values of C and P are possible for hadrons? –Symmetry operation squared gives unity so eigenvalue squared must be 1 –Possible C and P values are +1 and -1. Meaning of P quantum number –If P=1 then P|> = +1|> (wave function symmetric in space) if P=-1 then P|> = -1 |> (wave function anti-symmetric in space)

46. Niels Tuning (46) Figuring out P eigenvalues for hadrons QFT rules for particle vs. anti-particles –Parity of particle and anti-particle must be opposite for fermions (spin-N+1/2) –Parity of bosons (spin N) is same for particle and anti-particle Definition of convention (i.e. arbitrary choice in def. of q vs q) –Quarks have positive parity  Anti-quarks have negative parity –e - has positive parity as well. –(Can define other way around: Notation different, physics same) Parity is a multiplicative quantum number for composites –For composite AB the parity is P(A)*P(B), Thus: –Baryons have P=1*1*1=1, anti-baryons have P=-1*-1*-1=-1 –(Anti-)mesons have P=1*-1 = -1 Excited states (with orbital angular momentum) –Get an extra factor (-1) l where l is the orbital L quantum number –Note that parity formalism is parallel to total angular momentum J=L+S formalism, it has an intrinsic component and an orbital component NB: Photon is spin-1 particle has intrinsic P of -1

47. Niels Tuning (47) Parity eigenvalues for selected hadrons The  + meson –Quark and anti-quark composite: intrinsic P = (1)*(-1) = -1 –Orbital ground state  no extra term –P( + )=-1 The neutron –Three quark composite: intrinsic P = (1)*(1)*(1) = 1 –Orbital ground state  no extra term –P(n) = +1 The K 1 (1270) –Quark anti-quark composite: intrinsic P = (1)*(-1) = -1 –Orbital excitation with L=1  extra term (-1) 1 –P(K 1 ) = +1 Meaning: P| + > = -1| + >

48. Niels Tuning (48) Figuring out C eigenvalues for hadrons Only particles that are their own anti-particles are C eigenstates because C|x>  |x> = c|x> –E.g.  0,,’, 0,,, and photon C eigenvalues of quark-anti-quark pairs is determined by L and S angular momenta: C = (-1) L+S –Rule applies to all above mesons C eigenvalue of photon is -1 –Since photon is carrier of EM force, which obviously changes sign under C conjugation Example of C conservation: –Process  0   C=+1( 0 has spin 0)  (-1)*(-1) –Process  0   does not occur (and would violate C conservation)

49. Niels Tuning (49) What do we know now? C.S. Wu discovered from 60 Co decays that the weak interaction is 100% asymmetric in P-conjugation –We can distinguish our universe from a parity flipped universe by examining 60 Co decays L. Lederman et al. discovered from π + decays that the weak interaction is 100% asymmetric in C-conjugation as well, but that CP-symmetry appears to be preserved –First important ingredient towards understanding matter/anti- matter asymmetry of the universe: weak force violates matter/anti-matter(=C) symmetry! –C violation is a required ingredient, but not enough as we will learn later Next: a precision test of CP symmetry conservation in the weak interaction

50. Niels Tuning (50) Outline 25 February: Introduction –Motivation of this course –Anti-matter –P and C symmetries 3 March: Lecture 1 –CP symmetry –K-system CP violation Oscillations –Cabibbo-GIM mechanism –Mixing 10 March: Lecture 2 –CP violation in the Lagrangian –CKM matrix, unitarity triangle –B  J/Psi Ks 17 March: Lecture 3 –3 Types of CP-violation –Measuring CP-violation –Penguins –New physics?