1. Niels Tuning (1) Particle Physics II – CP violation Lecture 3 N. Tuning Acknowledgements: Slides based on the course from Wouter Verkerke and Marcel Merk.

2. Niels Tuning (2) Huishoudelijke mededeling 26 March: no lecture 2 April: 4 th (last) CP lecture 9 April: Easter 16 April: QCD (prof. peitzmann) H220 23 April: QCD (prof. peitzmann) H220 30 April: Queen’s day 7 May: QCD … 7 June (?): Mini-conference

3. Niels Tuning (3) Outline 5 March –Introduction: matter and anti-matter –P, C and CP symmetries –K-system CP violation Oscillations –Cabibbo-GIM mechanism 12 March –CP violation in the Lagrangian –CKM matrix –B-system 19 March –B  J/Psi Ks –Delta ms (26 March: No lecture) 2 April: –B-experiments: BaBar and LHCb –Measurements at LHCb

4. Niels Tuning (4) 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

5. Niels Tuning (5) : The Kinetic Part For example, the term with Q Li I becomes: Writing out only the weak part for the quarks: dLIdLI g W+W+ uLIuLI W + = (1/√2) (W 1 + i W 2 ) W - = (1/√ 2) (W 1 – i W 2 ) L=JWL=JW Recap from last week

6. Niels Tuning (6) : The Higgs Potential V(  )  Symmetry Spontaneous Symmetry Breaking: The Higgs field adopts a non-zero vacuum expectation value Procedure: Substitute: And rewrite the Lagrangian (tedious): (The other 3 Higgs fields are “eaten” by the W, Z bosons) V   Broken Symmetry ~ 246 GeV 1.. 2.The W +,W -,Z 0 bosons acquire mass 3.The Higgs boson H appears Recap from last week

7. Niels Tuning (7) : The Yukawa Part Since we have a Higgs field we can add (ad-hoc) interactions between  and the fermions in a gauge invariant way. The result is: are arbitrary complex matrices which operate in family space (3x3)  Flavour physics! doublets singlet With: (The CP conjugate of  To be manifestly invariant under SU(2) ) i, j : indices for the 3 generations! Recap from last week

8. Niels Tuning (8) : The Fermion Masses Writing in an explicit form: The matrices M can always be diagonalised by unitary matrices V L f and V R f such that: Then the real fermion mass eigenstates are given by: d L I, u L I, l L I are the weak interaction eigenstates d L, u L, l L are the mass eigenstates (“physical particles”) S.S.B Recap from last week

9. Niels Tuning (9) : The Charged Current The charged current interaction for quarks in the interaction basis is: The charged current interaction for quarks in the mass basis is: The unitary matrix: is the Cabibbo Kobayashi Maskawa mixing matrix: With: Lepton sector: similarly However, for massless neutrino’s: V L = arbitrary. Choose it such that V MNS = 1 => There is no mixing in the lepton sector Recap from last week

10. Niels Tuning (10) The Standard Model Lagrangian (recap) L Kinetic : Introduce the massless fermion fields Require local gauge invariance => gives rise to existence of gauge bosons L Higgs : Introduce Higgs potential with ≠ 0 Spontaneous symmetry breaking L Yukawa : Ad hoc interactions between Higgs field & fermions L Yukawa → L mass : fermion weak eigenstates: -- mass matrix is (3x3) non-diagonal fermion mass eigenstates: -- mass matrix is (3x3) diagonal L Kinetic in mass eigenstates: CKM – matrix The W +, W -,Z 0 bosons acquire a mass => CP Conserving => CP violating with a single phase => CP-violating => CP-conserving! => CP violating with a single phase Recap from last week

11. Niels Tuning (11) Exploit apparent ranking for a convenient parameterization Given current experimental precision on CKM element values, we usually drop 4 and 5 terms as well –Effect of order 0.2%... Deviation of ranking of 1 st and 2 nd generation ( vs 2 ) parameterized in A parameter Deviation of ranking between 1 st and 3 rd generation, parameterized through |-i| Complex phase parameterized in arg(-i) Recap from last week

12. Niels Tuning (12) Deriving the triangle interpretation Starting point: the 9 unitarity constraints on the CKM matrix Pick (arbitrarily) orthogonality condition with (i,j)=(3,1) Recap from last week

13. Niels Tuning (13) Visualizing arg(V ub ) and arg(V td ) in the () plane We can now put this triangle in the () plane Recap from last week

14. Niels Tuning (14) 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:

15. Niels Tuning (15) 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:

16. Niels Tuning (16) Solving the Schrödinger Equation From the eigenvalue calculation: Eigenvectors:  m and  follow from the Hamiltonian: Solution: (  and  are initial conditions):

17. Niels Tuning (17) 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

18. Niels Tuning (18) Measuring B Oscillations Decay probability B0B0B0B0 B0B0B0B0 Proper Time  For B 0, expect:  ~ 0, |q/p|=1 Examples:

19. Niels Tuning (19) 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 ) :

20. Niels Tuning (20) 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 =0.4 9 ~1 D0D0 0.41 10 -12 s 0.001 fs -1 ~00.01 B0B0 1.53 10 -12 s 0.507 ps - 1 0.78~0 Bs0Bs0 1.47 10 -12 s 17.8 ps -1 12.1~0.05 By the way, ħ=6.58 10 -22 MeVs x=Δm/ Γ : avg nr of oscillations before decay

21. Niels Tuning (21) 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

22. Niels Tuning (22) D-mixing just measured!

23. Niels Tuning (23) Measuring D-mixing just measured! Why important? Very interesting, because sensitive to new physics…

24. Niels Tuning (24) 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

25. Niels Tuning (25) 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!

26. Niels Tuning (26) 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

27. Niels Tuning (27) 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!

28. Niels Tuning (28) Last years course (2006)… B s mixing just measured! Δm s has been measured at Fermilab 4 weeks ago!

29. Niels Tuning (29) 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

30. Niels Tuning (30) Δm s : Unitarity Triangle CKM Matrix Unitarity Condition

31. Niels Tuning (31) 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

32. Niels Tuning (32) Δm s : Tagging the B Production Flavor vertexing (same) side “opposite” side e, 

33. Niels Tuning (33) 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

34. Niels Tuning (34) 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

35. Niels Tuning (35) Back to finding new measurements Next order of business: Devise an experiment that measures arg(V td )and arg(V ub ). –What will such a measurement look like in the () plane?   CKM phases Fictitious measurement of  consistent with CKM model

36. Niels Tuning (36) Reduction to single (set of 2) amplitudes is major advantage in understanding B 0 mixing physics A mixing diagram has (to very good approximation) a weak phase of 2 –An experiment that involves interference between an amplitude with mixing and an amplitude without mixing is sensitive to the angle ! Small miracle of B physics: unlike the K 0 system you can easily interpret the amount of observable CP violation to CKM phases! The B 0 mixing formalism and the angle β

37. Niels Tuning (37) Find the right set of two amplitudes General idea to measure b: Look at interference between B 0  f CP and B 0  B 0  f CP –Where f CP is a CP eigenstate (because both B 0 and B 0 must be able to decay into it) Example (not really random): B 0  J/ K S B 0  f B 0  B 0  f

38. Niels Tuning (38) Measuring  with B 0  J/ K S We’re going to measure arg(V td 2 )=2 through the interference of these two processes We now know from the B0 mixing formalism that the magnitude of both amplitudes varies with time B 0  f B 0  B 0  f

39. Niels Tuning (39) How can we construct an observable that measures β What do we know about the relative phases of the diagrams? B 0  f B 0  B 0  f (strong)= (weak)=0(weak)=2 (mixing)=/2 There is a phase difference of i between the B 0 andB 0 Decays are identical K 0 mixing exactly cancels V cs

40. Niels Tuning (40) How can we construct an observable that measures β The easiest case: calculate (B 0  J/ K S ) at t=m –Why is it easy: cos(mt)=0  both amplitudes (with and without mixing) have same magnitude: |A 1 |=|A 2 | –Draw this scenario as vector diagram –NB: Both red and blue vectors have unit length += /2+2 1-cos() sin() cos() N(B 0  f)  |A| 2  (1-cos) 2 +sin 2  = 1 -2cos+cos 2 +sin 2  = 2-2cos(/2+2)  1-sin(2)

41. Niels Tuning (41) How can we construct an observable that measures β Now also look at CP-conjugate process Directly observable result (essentially just from counting) measure CKM phase  directly! CP + = /2+2 + = /2-2 N(B 0  f)  |A| 2  (1-cos) 2 +sin 2  = 1 -2cos+cos 2 +sin 2  = 2-2cos(/2+2)  1-sin(2) N(B 0  f)  (1+cos) 2 +sin 2  = 2+2cos(/2-2)  1+sin(2) 1-cos() sin() 1+cos()

42. Niels Tuning (42) Measuring A CP (t) in B 0  J/ K S What do we need to observe to measure We need to measure 1)J/ and K S decay products 2)Lifetime of B 0 meson before decay 3)Flavor of B 0 meson at t=0 (B 0 orB 0 ) First two items relatively easy –Lifetime can be measured from flight length if B 0 has momentum in laboratory Last item is the major headache: How do you measure a property of a particle before it decays?

43. Niels Tuning (43) B 0 (t) A CP (t) = sin(2β)sin(m d t) sin2 Dsin2 Putting it all together: sin(2) from B 0  J/ K S Effect of detector imperfections –Dilution of A CP amplitude due imperfect tagging –Blurring of A CP sine wave due to finite t resolution Imperfect flavor tagging Finite t resolution tt tt

44. Niels Tuning (44) Combined result for sin2 sin2β = 0.722  0.040 (stat)  0.023 (sys) J/ψ K L (CP even) mode (cc) K S (CP odd) modes hep-ex/0408127 A CP amplitude dampened by (1-2w) w  flav. Tag. mistake rate

45. Niels Tuning (45) 4 Consistency with other measurements in (,) plane   Method as in Höcker et al, Eur.Phys.J.C21:225-259,2001 Prices measurement of sin(2β) agrees perfectly with other measurements and CKM model assumptions The CKM model of CP violation experimentally confirmed with high precision! 4-fold ambiguity because we measure sin(2), not  1 2 3 without sin(2)

46. Niels Tuning (46) Remember the following: CP violation is discovered in the K-system CP violation is naturally included if there are 3 generations or more CP violation manifests itself as a complex phase in the CKM matrix The CKM matrix gives the strengths and phases of the weak couplings CP violation is apparent in experiments/processes with 2 interfering amplitudes –Often using “mixing” to get the 2 nd decay process The angle β is measured through B 0  J/ K S

47. Niels Tuning (47) Outline 5 March –Introduction: matter and anti-matter –P, C and CP symmetries –K-system CP violation Oscillations –Cabibbo-GIM mechanism 12 March –CP violation in the Lagrangian –CKM matrix –B-system 19 March –B  J/Psi Ks –Delta ms (26 March: No lecture) 2 April: –B-experiments: BaBar and LHCb –Measurements at LHCb

48. Niels Tuning (48) Compare the mesons: t (ps)