1. Niels Tuning (1) Particle Physics II – CP violation Lecture 1 N. Tuning Acknowledgements: Slides based on the course from 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 –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 the course from Wouter Verkerke. 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. Niels Tuning (4) 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! Recap from last week 100% P violation: All ν’s are lefthanded Allν’s are righthanded

5. Niels Tuning (5) Intermezzo: What operator is C ? Full solutions of Dirac equations: 4 independent solutions for the Dirac spinors: Try “ansatz”:

6. Niels Tuning (6) Intermezzo: What operator is C ? Particle  Anti-particle: C=iγ 2 γ 0 Dirac equation: In EM field: Positron: Flip charge: e → -e Possible choice for Cγ 0 : (in Dirac representation) Cγ 0 = iγ 2 Try out on a example spinor (e.g. electron with pos. helicity):

7. Niels Tuning (7) Introduction to K 0 physics Now focusing on another little mystery in the domain of ‘strange’ mesons: what precisely is a K 0 meson? –Quark contents: K 0 =  sd, K 0 =  ds First: what is the effect of C and P conjugation on the K 0 /K 0 -bar particles? –P|K 0 > = -1|K 0 >(because  qq pair) –C|K 0 > = |K 0 >(because K 0 is anti-particle of K 0 & l+s=0) Knowing this we can evaluate the effect of CP on the K 0 –CP|K 0 > = -1|K 0 >

8. Niels Tuning (8) What are the K 0 CP Eigenstates Thus K 0 and K 0 are not CP eigenstates, –Somewhat strange since they decay through weak interaction which appears to conserve CP! Nevertheless it is possible to construct CP eigenstates as linear combinations –Remember QM: You can always construct wave functions as linear combinations of the solutions of any operator (like the Hamiltonian) –|K 1 > = 1/2(|K 0 > - |K 0 >) –|K 2 > = 1/2(|K 0 > + |K 0 >) –Proof is exercise for today Does it make sense to look at linear combinations of |K 0 > and |K 0 >? –I.e does |K 1 > represent a real particle?

9. Niels Tuning (9) K 0 /K 0 oscillations Well it might, because it turns out that the weak interaction can turn a K 0 particle into a K 0 particle! –Weird? Yes! Impossible? No! –In can be done using two consecutive weak interactions: Important implication for nature of K 0 particle –Q: If a K 0 can turn into a K 0 at any moment, how do you know what particle you’re dealing with? –A: You don’t. Any particle in the lab is always a linear combination of the two  It makes as much sense to talk about K 1 and K 2 eigenstates as it does to talk about K 0 and K 0 eigenstates K0K0 S=1 Weak force (X) Weak force S=0 S=-1 K0K0 S=-1

10. Niels Tuning (10) So what is the K 0 really? The K 0 meson is something you can only describe with quantum mechanics It is a linear combination of two particles! –You can either see it as a combination of |K 0 > and |K 0 >, eigenvalues of Strangeness (+1 vs +1) and undefined CP –Or you can see it as a combination of |K 1 > and |K 2 >, eigenvalues of CP (+1, -1), with undefined strangeness –Both representations are equivalent. Kaons are typically produced in strong interactions in a strangeness eigenstate (K 0 or K 0 ) Kaons decay through the weak interaction as eigenstates of CP (K 1 or K 2 ) –Since K 1 and K 2 don’t have definite S, S is not conserved in weak decays as we already know –If you believe a particle must have a single well defined lifetime, then K 1 and K 2 are the ‘real’ particles

11. Niels Tuning (11) So what is the K 0 really? Graphical analogy – Any object with two components can be decomposed in more than one way K0K0 Anti-K 0 K2K2 K1K1 |K>

12. Niels Tuning (12) Decays of neutral kaons Neutral kaons is the lightest strange particle  it must decay through the weak interaction If weak force conserves CP then –decay products of K 1 can only be a CP=+1 state, i.e. |K 1 > (CP=+1) →   (CP= (-1)(-1)(-1) l=0 =+1) –decay products of K 2 can only be a CP=-1 state, i.e. |K 2 > (CP=-1) →  (CP = (-1)(-1)(-1)(-1) l=0 = -1) You can use neutral kaons to precisely test that the weak force preserves CP (or not) –If you (somehow) have a pure CP=-1 K 2 state and you observe it decaying into 2 pions (with CP=+1) then you know that the weak decay violates CP… ( S( K )=0  L( ππ )=0 )

13. Niels Tuning (13) Designing a CP violation experiment How do you obtain a pure ‘beam’ of K 2 particles? –It turns out that you can do that through clever use of kinematics Exploit that decay of K into two pions is much faster than decay of K into three pions –Related to fact that energy of pions are large in 2-body decay –  1 = 0.89 x 10 -10 sec –  2 = 5.2 x 10 -8 sec (~600 times larger!) Beam of neutral Kaons automatically becomes beam of |K 2 > as all |K 1 > decay very early on… Initial K 0 beam K 1 decay early (into ) Pure K 2 beam after a while! (all decaying into πππ ) !

14. Niels Tuning (14) The Cronin & Fitch experiment Incoming K 2 beam Decay of K 2 into 3 pions If you detect two of the three pions of a K 2   decay they will generally not point along the beam line Essential idea: Look for (CP violating) K 2   decays 20 meters away from K 0 production point

15. Niels Tuning (15) The Cronin & Fitch experiment Incoming K2 beam Decay pions If K 2 decays into two pions instead of three both the reconstructed direction should be exactly along the beamline (conservation of momentum in K 2   decay) Essential idea: Look for K 2   decays 20 meters away from K 0 production point

16. Niels Tuning (16) The Cronin & Fitch experiment Incoming K 2 beam Decay pions Result: an excess of events at =0 degrees! K 2   decays (CP Violation!) Essential idea: Look for K 2   decays 20 meters away from K 0 production point K 2   decays Note scale: 99.99% of K   decays are left of plot boundary CP violation, because K 2 (CP=-1) changed into K 1 (CP=+1 )

17. Niels Tuning (17) Cronin & Fitch – Discovery of CP violation Conclusion: weak decay violates CP (as well as C and P) –But effect is tiny! (~0.05%) –Maximal (100%) violation of P symmetry easily follows from absence of right-handed neutrino, but how would you construct a physics law that violates a symmetry just a tiny little bit? Results also provides us with convention-free definition of matter vs anti-matter. –If there is no CP violation, the K 2 decays in equal amounts to  + e - e (a)  - e + e (b) –Just like CPV introduces K 2  ππ decays, it also introduces a slight asymmetry in the above decays (b) happens more often than (a) –“Positive charge is the charged carried by the lepton preferentially produced in the decay of the long-lived neutral K meson”

18. Niels Tuning (18) Kaons: K 0,K 0, K 1, K 2, K S, K L, … The kaons are produced in mass eigenstates: –| K 0 >:  sd –|  K 0 >:  ds The CP eigenstates are: –CP=+1: |K 1 > = 1/  2 (|K 0 > - |  K 0 >) –CP= -1: |K 2 > = 1/  2 (|K 0 > + |  K 0 >) The kaons decay as short-lived or long-lived kaons: –|K S >: predominantly CP=+1 –|K L >: predominantly CP= -1 η +- = (2.236 ± 0.007) x 10 -3 |ε| = (2.232 ± 0.007) x 10 -3

19. Niels Tuning (19) What do we know now? C and P are both violated by the weak interaction because neutrinos can only be produced in a single helicity state (LH neutrinos and RH anti-neutrinos) –Results from Wu and Lederman experiments You can associate a P quantum number to all hadrons and a C quantum number to all hadrons that are their own anti-particle –These C and P quantum numbers are conserved in any reaction not involving the weak interaction The K 0 meson is a special particle that really exists as a combination of two particle: the K 0 / K 0 combination or the K 1 / K 2 combination at your choice The Cronin and Fitch experiment shows that in addition to C and P violation the product CP is also violated, but only a tiny little bit –Origin of CP violation sofar unknown  Topic of future section

20. Niels Tuning (20) Schematic picture of selected weak decays K 0  K 0 transition –Note 1: Two W bosons required (S=2 transition) –Note 2: many vertices, but still lowest order process… d ss K0K0 K0K0 s uu W W dd

21. Niels Tuning (21) Strangeness violation in W mediated decays In 1963 N. Cabibbo made the first step to formally incorporate strangeness violation in W mediated decays 1)For the leptons, transitions only occur within a generation 2)For quarks the amount of strangeness violation can be neatly described in terms of a rotation, where  c =13.1 o Weak force transitions u d’ = dcos c + ssin c W+W+ Idea: weak interaction couples to different eigenstates than strong interaction weak eigenstates can be written as rotation of strong eigenstates

22. Niels Tuning (22) Cabibbos theory successfully correlated many decay rates Cabibbos theory successfully correlated many decay rates by counting the number of cos c and sin c terms in their decay diagram

23. Niels Tuning (23) Cabibbos theory successfully correlated many decay rates There was however one major exception which Cabibbo could not describe: K 0   +  - –Observed rate much lower than expected from Cabibbos rate correlations (expected rate  g 8 sin 2  c cos 2  c ) d ++ --  u cos c sin c W W ss

24. Niels Tuning (24) The Cabibbo-GIM mechanism Solution to K 0 decay problem in 1970 by Glashow, Iliopoulos and Maiani  postulate existence of 4 th quark –Two ‘up-type’ quarks decay into rotated ‘down-type’ states –Appealing symmetry between generations u d’=cos( c )d+sin( c )s W+W+ c s’=-sin( c )d+cos(c)s W+W+

25. Niels Tuning (25) The Cabibbo-GIM mechanism Cabibbo-GIM mechanism introduces clean formalism for quark ‘flavour’ violations in the weak interaction: The weak interaction (W boson) couples to a rotated set of down-type states Tiny problem at time of introduction: there was no evidence for a 4 th quark –Fourth ‘charm’ quark discovered in 1974  Vindication of Cabbibo/GIM mechanism Lepton sector unmixed Quark section mixed through rotation of weak w.r.t. strong eigenstates by  c

26. Niels Tuning (26) The Cabibbo-GIM mechanism How does it solve the K 0   +  - problem? –Second decay amplitude added that is almost identical to original one, but has relative minus sign  Almost fully destructive interference –Cancellation not perfect because u, c mass different d ++ --  u cos c +sin c d ++ --  c -sin c cos c ss ss

27. Niels Tuning (27) From 2 to 3 generations 2 generations: d’=0.97 d + 0.22 s (θ c =13 o ) 3 generations: d’=0.97 d + 0.22 s + 0.003 b NB: probabilities have to add up to 1: 0.97 2 +0.22 2 +0.003 2 =1 –  “Unitarity” !

28. Niels Tuning (28) What do we know about the CKM matrix? Magnitudes of elements have been measured over time –Result of a large number of measurements and calculations Magnitude of elements shown only, no information of phase

29. Mixing Niels Tuning (29)

30. Niels Tuning (30) Dynamics of Neutral B (or K) mesons… No mixing, no decay… No mixing, but with decays… (i.e.: H is not Hermitian!)  With decays included, probability of observing either B 0 or B 0 must go down as time goes by: Time evolution of B 0 and  B 0 can be described by an effective Hamiltonian:

31. Niels Tuning (31) Describing Mixing… Where to put the mixing term? Now with mixing – but what is the difference between M 12 and  12 ? M 12 describes B 0  B 0 via off-shell states, e.g. the weak box diagram  12 describes B 0  f  B 0 via on- shell states, eg. f=     Time evolution of B 0 and  B 0 can be described by an effective Hamiltonian:

32. Niels Tuning (32) Solving the Schrödinger Equation From the eigenvalue calculation: Eigenvectors:  m and  follow from the Hamiltonian: Solution: (  and  are initial conditions):

33. Niels Tuning (33) B Oscillation Amplitudes For B 0, expect:  ~ 0, |q/p|=1 For an initially produced B 0 or a  B 0 it then follows: (using: with

34. Niels Tuning (34) Measuring B Oscillations Decay probability B0B0B0B0 B0B0B0B0 Proper Time  For B 0, expect:  ~ 0, |q/p|=1 Examples:

35. Niels Tuning (35) Let’s summarize … p, q: Δm, Δ Γ: x,y: mixing often quoted in scaled parameters: Historically, in the K- system ε is used: q,p,M ij, Γ ij related through: with Time dependence (if ΔΓ~0, like for B 0 ) :

36. Niels Tuning (36) Compare the mesons: P0P0P0P0 P0P0P0P0 Probability Time  Probability  <><> ΔmΔmx=Δm/Γy=ΔΓ/2Γ K0K0 2.6 10 -8 s5.29 ns -1 Δm/ Γ S =0.49 ~1 D0D0 0.41 10 -12 s0.001 fs -1 ~00.01 B0B0 1.53 10 -12 s0.507 ps -1 0.78~0 Bs0Bs0 1.47 10 -12 s17.8 ps -1 12.1~0.05 By the way, ħ=6.58 10 -22 MeVs x=Δm/ Γ : avg nr of oscillations before decay

37. Niels Tuning (37) For example... Compare D-mixing to B-mixing Short range mixing (described by M 12 ) Long range mixing (described by Γ 12 ) Compare to B-system: Less Cabibbo suppressed: ~|V tb V td * | 2 ~| λ 3 | 2 : “ just” small Less GIM: suppressed: ~(m t 2 -m c 2 ) : big Expected to be small! Cabibbo suppressed: ~|V ub V cb * | 2 ~| λ 3 λ 2 | 2 : very small GIM suppressed: ~(m s 2 -m d 2 ) : small

38. Niels Tuning (38) Last years course: D-mixing just measured!

39. Niels Tuning (39) Measuring D-mixing just measured! Why important? Very interesting, because sensitive to new physics…

40. Niels Tuning (40) D-mixing just measured! How? Look for D 0  K + π - decays: sensitive to mixing, because: –Direct decay is suppressed: M~|V cd ||V us |= O (λ 2 ) “Double Cabibbo Surpressed” –Decay after mixing not suppressed: M~|V cd ||V ud |= O(1) “Cabibbo Favoured” cc u D0D0 D0D0 D0D0

41. Niels Tuning (41) D-mixing just measured! Investigate D 0  K + π - D 0  K + π - : 4,030 events, partially through D 0  D 0  K + π - ! D 0  K - π + : 1,141,500 events K+K+ π-π- How do we distinguish D 0  K + π - from D 0  D 0  K + π - ?  Look at decay time dependence!

42. Niels Tuning (42) Measuring B 0 mixing What is the probability to observe a B 0 /B 0 at time t, when it was produced as a B 0 at t=0? –Calculate observable probility *(t) A simple B 0 decay experiment. –Given a source B 0 mesons produced in a flavor eigenstate |B 0 > –You measure the decay time of each meson that decays into a flavor eigenstate (either B 0 orB 0 ) you will find that

43. Niels Tuning (43) Measuring B 0 mixing You can really see this because (amazingly) B 0 mixing has same time scale as decay – =1.54 ps – m=0.5 ps -1 –50/50 point at m   –Maximal oscillation at 2m  2 Actual measurement of B 0 /B 0 oscillation –Also precision measurement of m!

44. Niels Tuning (44) Two years ago (2006)… B s mixing just measured!

45. Niels Tuning (45) Δm s : Standard Model Prediction V ts CKM Matrix Wolfenstein parameterization Ratio of frequencies for B 0 and B s  = 1.210 +0.047 from lattice QCD -0.035 V ts ~ 2 V td ~ 3   Δm s ~ (1/ λ 2 ) Δm d ~ 25 Δm d

46. Niels Tuning (46) Δm s : Unitarity Triangle CKM Matrix Unitarity Condition

47. Niels Tuning (47) Δm s : What B s Decays? large signal yields (few 10 thousands) correct for missing neutrino loss in proper time resolution superior sensitivity in lower m s range small signal yields (few thousand) momentum completely contained in tracker superior sensitivity at higher m s

48. Niels Tuning (48) Δm s : Tagging the B Production Flavor vertexing (same) side “opposite” side e, 

49. Niels Tuning (49) ΔmsΔms Δm s =17.77 ±0.10(stat)±0.07(sys) ps -1 cos(Δm s t) Proper Time t (ps) hep-ex/0609040 BsBs bb b ss st tt W W BsBs g̃BsBs BsBs bb s ss b x x b̃ s̃ g̃

50. Niels Tuning (50) Mixing  CP violation? NB: Just mixing is not necessarily CP violation! However, by studying certain decays with and without mixing, CP violation is observed Next: Measuring CP violation

51. Niels Tuning (51) Outline 25 February: Introduction –Motivation of this course –Anti-matter –P and C symmetries 3 March: Lecture 1 –CP symmetry –K-system –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?

52. Niels Tuning (52) Compare the mesons: t (ps)