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CP violation Lecture 6

CP violation Lecture 6. N. Tuning. Recap. u I. u. W. W. d,s,b. d I. Diagonalize Yukawa matrix Y ij Mass terms Quarks rotate Off diagonal terms in charged current couplings. Niels Tuning ( 3 ). CKM-matrix: where are the phases?.

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CP violation Lecture 6

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  1. CP violationLecture 6 N. Tuning Niels Tuning (1)

  2. Recap uI u W W d,s,b dI • Diagonalize Yukawa matrix Yij • Mass terms • Quarks rotate • Off diagonal terms in charged current couplings Niels Tuning (3)

  3. CKM-matrix: where are the phases? • Possibility 1: simply 3 ‘rotations’, and put phase on smallest: u W d,s,b • Possibility 2: parameterize according to magnitude, in O(λ): Niels Tuning (4)

  4. This was theory, now comes experiment • We already saw how the moduli |Vij| are determined • Now we will work towards the measurement of the imaginary part • Parameter: η • Equivalent: angles α, β, γ . • To measure this, we need the formalism of neutral meson oscillations… Niels Tuning (5)

  5. Meson Decays (‘direct’) Decay Interference • Formalism of meson oscillations: • Subsequent: decay P0 f P0P0 f Interference

  6. Classification of CP Violating effects • CP violation in decay • CP violation in mixing • CP violation in interference Niels Tuning (7)

  7. Classification of CP Violating effects • CP violation in decay Example: • CP violation in mixing Example: • CP violation in interference Example: B0→J/ψKs Niels Tuning (8)

  8. Remember! Necessary ingredients for CP violation: • Two (interfering) amplitudes • Phase difference between amplitudes • one CP conserving phase (‘strong’ phase) • one CP violating phase (‘weak’ phase) 2 amplitudes 2 phases Niels Tuning (9)

  9. Remember! 2 amplitudes 2 phases Niels Tuning (10)

  10. Next • CP violation in decay • CP violation in mixing • CP violation in interference

  11. Why bother with all this? • CKM matrix has origin in LYukawa • Intricately related to quark massed… • Both quark masses and CKM elements show intriguing hierarchy • There is a whole industry of theorist trying to postdict the CKM matrix based on arguments on the mass matrix in LYukawa… Niels Tuning (12)

  12. Kaons… • Different notation: confusing! • K1, K2, KL, KS, K+, K-, K0 • Smaller CP violating effects • But historically important! • Concepts same as in B-system, so you have a chance to understand… Niels Tuning (13)

  13. Neutral kaons – 60 years of history 1947 : First K0 observation in cloud chamber (“V particle”) 1955 : Introduction of Strangeness (Gell-Mann & Nishijima) K0,K0 are two distinct particles (Gell-Mann & Pais) 1956 : Parity violation observation of long lived KL (BNL Cosmotron) 1960 : Dm = mL-mS measured from regeneration 1964 : Discovery of CP violation (Cronin & Fitch) 1970 : Suppression of FCNC, KLmm - GIM mechanism/charm hypothesis 1972 : 6-quark model; CP violation explained in SM (Kobayashi & Maskawa) 1992-2000 : K0,K0 time evolution, decays, asymmetries (CPLear) 1999-2003 : Direct CP violation measured: e’/e≠ 0 (KTeV and NA48) … the θ0 must be considered as a "particle mixture" exhibiting two distinct lifetimes, that each lifetime is associated with a different set of decay modes, and that no more than half of all θ0's undergo the familiar decay into two pions. Niels Tuning (14) From G.Capon

  14. Intermezzo: CP eigenvalue • Remember: • P2 = 1 (x  -x  x) • C2 = 1 (ψψ  ψ) •  CP2 =1 • CP | f > = | f > • Knowing this we can evaluate the effect of CP on the K0 • CP|K0> = -1| K0> • CP| K0> = -1|K0 > • CP eigenstates: • |KS> = p| K0> +q|K0> • |KL> = p| K0> - q|K0> • |Ks> (CP=+1) → pp (CP= (-1)(-1)(-1)l=0 =+1) • |KL> (CP=-1) →p pp (CP = (-1)(-1)(-1)(-1)l=0 = -1) ( S(K)=0 L(ππ)=0 ) Niels Tuning (15)

  15. 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 K1 can only be a CP=+1 state, i.e.|K1> (CP=+1) → pp (CP= (-1)(-1)(-1)l=0 =+1) decay products of K2 can only be a CP=-1 state, i.e.|K2> (CP=-1) →p p p (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 K2 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 ) Niels Tuning (16)

  16. Designing a CP violation experiment How do you obtain a pure ‘beam’ of K2 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 t1 = 0.89 x 10-10 sec t2 = 5.2 x 10-8 sec (~600 times larger!) Beam of neutral Kaons automatically becomes beam of |K2> as all |K1> decay very early on… Pure K2 beam after a while!(all decaying into πππ) ! K1 decay early (into pp) Initial K0beam Niels Tuning (17)

  17. The Cronin & Fitch experiment Essential idea: Look for (CP violating) K2 pp decays 20 meters away from K0 production point Decay of K2 into 3 pions Incoming K2 beam If you detect two of the three pionsof a K2 ppp decay they will generallynot point along the beam line Niels Tuning (18)

  18. The Cronin & Fitch experiment Essential idea: Look for K2 pp decays20 meters away from K0 production point Decay pions Incoming K2 beam If K2 decays into two pions instead ofthree both the reconstructed directionshould be exactly along the beamline(conservation of momentum in K2 pp decay) Niels Tuning (19)

  19. The Cronin & Fitch experiment Essential idea: Look for K2 pp decays20 meters away from K0 production point Decay pions K2 ppdecays(CP Violation!) Incoming K2 beam K2 ppp decays Result: an excess of events at Q=0 degrees! • CP violation, because K2 (CP=-1) changed into K1 (CP=+1) Note scale: 99.99% of K ppp decaysare left of plot boundary Niels Tuning (20)

  20. Nobel Prize 1980 "for the discovery of violations of fundamental symmetry principles in the decay of neutral K mesons" The discovery emphasizes, once again, that even almost self evident principles in science cannot be regarded fully valid until they have been critically examined in precise experiments. James Watson Cronin 1/2 of the prize University of Chicago Chicago, IL, USA b. 1931 Val Logsdon Fitch 1/2 of the prize Princeton University Princeton, NJ, USA b. 1923 Niels Tuning (21)

  21. 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 withconvention-free definition ofmatter vs anti-matter. If there is no CP violation, the K2 decaysin equal amounts top+ e-ne (a)p- e+ne (b) Just like CPV introduces K2 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” Niels Tuning (22)

  22. strong interactions: must conserve strangeness leave little free energy – unlikely! Intermezzo: Regeneration • Different cross section for σ(p K0) thanσ(pK0) • Elastic scattering: same • Charge exchange : same • Hyperon production: more for K0 ! • What happens when KL-beam hits a wall ?? • Thenadmixture changes…: |KL> = p| K0> - q|K0> • Regeneration of KS ! • Could fake CP violation due to KS→π+π-… Niels Tuning (23)

  23. KS and KL Usual (historical) notation in kaon physics: Modern notation used in B physics: Regardless of notation: KL and KSare not orthogonal: Niels Tuning (24)

  24. Three ways to break CP; e.g. in K0→ π+π- Niels Tuning (25)

  25. Classification of CP Violating effects • CP violation in decay • CP violation in mixing • CP violation in interference Niels Tuning (26)

  26. Time evolution Niels Tuning (27)

  27. B-system 2. CP violation in mixing K-system CPLEAR, Phys.Rep. 374(2003) 165-270 BaBar, (2002) CPLear (2003)

  28. B-system 2. CP violation in mixing K-system BaBar, (2002) NA48, (2001) L(e) = (3.317  0.070  0.072)  10-3 Niels Tuning (29)

  29. B-system 3.Time-dependent CP asymmetry B0→J/ψKs BaBar (2002) Niels Tuning (30)

  30. B-system 3.Time-dependent CP asymmetry K-system K0→π-π+ B0→J/ψKs ~50/50 decay as Ks and KL + interference! K0 _ K0 p+p- rate asymmetry CPLear (PLB 1999) BaBar (2002)

  31. The Quest for Direct CP Violation Indirect CP violation in the mixing:  Direct CP violation in the decay: ’ A fascinating 30-year long enterprise: “Is CP violation a peculiarity of kaons? Is it induced by a new superweak interaction?” Niels Tuning (32)

  32. B system 1. Direct CP violation K system K0→π-π+ K0→π-π+ B0→K+π- B0→K-π+ K0→π0π0 K0→π0π0 Different CP violation for the two decays  Some CP violation in the decay! ε’≠ 0 Niels Tuning (33)

  33. Niels Tuning (34)

  34. d Ks ~~ d g,b,…? s B s b t φ s Hints for new physics? 1) sin2β≠sin2β ? 2) ACP (B0K+π-)≠ACP (B+K+π0) ? 4th generation, t’ ? 3) βs≠0.04 ? 4) P(B0s→B0s) ≠ P(B0s←B0s) Niels Tuning (35)

  35. Present knowledge of unitarity triangle Niels Tuning (36)

  36. “The” Unitarity triangle • We can visualize the CKM-constraints in (r,h) plane

  37. Present knowledge of unitarity triangle

  38. I) sin 2β

  39. I) sin 2β

  40. II) εand the unitarity triangle: box diagram CP violation in mixing

  41. II) εand the unitarity triangle: box diagram

  42. II) εand the unitarity triangle: box diagram Im(z2)=Im( (Rez+iImz)2)=2RezImz

  43. II) εand the unitarity triangle ρ Niels Tuning (44)

  44. III.) |Vub| / |Vcb| • Measurement of Vub • Compare decay rates of B0 D*-l+n and B0 p-l+n • Ratio proportional to (Vub/Vcb)2 • |Vub/Vcb| = 0.090 ± 0.025 • Vub is of order sin(qc)3 [= 0.01]

  45. IV.) Δmd and Δms • Δm depends on Vtd • Vts constraints hadronic uncertainties

  46. Present knowledge of unitarity triangle Niels Tuning (47)

  47. d Ks ~~ d g,b,…? s B s b t φ s Hints for new physics? 1) sin2β≠sin2β ? 2) ACP (B0K+π-)≠ACP (B+K+π0) ? 4th generation, t’ ? 3) βs≠0.04 ? 4) P(B0s→B0s) ≠ P(B0s←B0s) Niels Tuning (48)

  48. More hints for new physics? • 5) εK ? • Treatment of errors… • Input from Lattice QCD BK • Strong dependence on Vcb Niels Tuning (49)

  49. More hints for new physics? 6) Vub: 2.9σ?? BR(B+→τυ)=1.68 ± 0.31 10-4 Predicted: 0.764± 0.087 10-4 (If fBd off, then BBd needs to be off too, to make Δmd agree) ? |Vub| avg from semi-lep |Vub| from fit |Vub| from B→τν From: H.Lacker, and A.Buras, Beauty2011, Amsterdam Niels Tuning (50)

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