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CP violation Lecture 6

CP violation Lecture 6. N. Tuning. Lecture 6. Recap Lecture 1. Diagonalize Yukawa matrix Y ij Mass terms Quarks rotate Off diagonal terms in charged current couplings. Niels Tuning ( 3 ). What do we know about the CKM matrix?. Magnitudes of elements have been measured over time

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CP violation Lecture 6

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  1. CP violationLecture 6 N. Tuning

  2. Lecture 6

  3. Recap Lecture 1 • Diagonalize Yukawa matrix Yij • Mass terms • Quarks rotate • Off diagonal terms in charged current couplings Niels Tuning (3)

  4. 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 Recap Lecture 2 Magnitude of elements shown only, no information of phase Niels Tuning (4)

  5. Recap Lecture 2 Exploit apparent ranking for a convenient parameterization • Given current experimental precision on CKM element values, we usually drop l4 and l5 terms as well • Effect of order 0.2%... • Deviation of ranking of 1st and 2nd generation (l vs l2) parameterized in A parameter • Deviation of ranking between 1st and 3rd generation, parameterized through |r-ih| • Complex phase parameterized in arg(r-ih)

  6. Recap Lecture 2 “The” Unitarity triangle • We can visualize the CKM-constraints in (r,h) plane

  7. Recap Lecture 3 (2-component state in P0 and P0 subspace) Neutral Meson Oscillations (1) • Start with Schrodinger equation: • Find eigenvalue: • Solve eigenstates: • Eigenstates have diagonal Hamiltonian: mass eigenstates!

  8. Recap Lecture 3 Neutral Meson Oscillations (2) • Two mass eigenstates • Time evolution: • Probability for |P0>  |P0> ! • Express in M=mH+mL and Δm=mH-mL Δm dependence

  9. Recap Lecture 3 Neutral Meson Oscillations (3)Box diagram and Δ m

  10. Recap Lecture 3 Some algebra for the decay P0 f Interference P0 f P0P0 f

  11. Recap Lecture 3 Meson Decays (‘direct’) Decay Interference • Formalism of meson oscillations: • Subsequent: decay

  12. Recap Lecture 3 Classification of CP Violating effects • CP violation in decay • CP violation in mixing • CP violation in interference

  13. 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 ?

  14. Lecture 6

  15. 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 (almost): • |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)

  16. 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)

  17. 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)

  18. 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)

  19. 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)

  20. 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)

  21. 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

  22. 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”

  23. 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. From G.Capon

  24. strong interactions: must conserve strangeness leave little free energy – unlikely! 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-…

  25. Kaons: K0,K0, K1, K2, KS, KL, … The kaons are produced in flavour eigenstates: | K0>: sd |K0>: ds The CP eigenstates are: CP=+1: |K1> = 1/2 (|K0> - |K0>) CP= -1: |K2> = 1/2 (|K0> + |K0>) The mass eigenstate are (decaying as short-lived or long-lived kaons): |KS>: predominantly CP=+1 |KL>: predominantly CP= -1 • η+-= (2.236 ± 0.007) x 10-3 • |ε| = (2.232 ± 0.007) x 10-3 Niels Tuning (25)

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

  27. Three ways to break CP in K0→ π+π-

  28. Time evolution

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

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

  31. B-system - 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)

  32. 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?”

  33. B system 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

  34. Last hour

  35. Present knowledge of unitarity triangle

  36. Present knowledge of unitarity triangle

  37. I) sin 2β

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

  39. II) εand the unitarity triangle ρ

  40. 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]

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

  42. Present knowledge of unitarity triangle

  43. m < 0.000003 m < 0.19 m < 18.2 e   me  0.51099890 m  105.658357 m  1777.0 mu  3 mc  1200 mt  174000 md  7 ms  120 mb  4300 quark mixing (4) u’ d’ s’ u d s Vijq = Standard Model: 25 free parameters Elementary particle masses (MeV): Electro-weak interaction: neutrino mixing (4) e(0)  1/137.036 mW  80.42 GeV mZ  91.188 GeV mH >114.3 GeV e   1 2 3 Vijl = mH >114.3 GeV ATLAS LHCb Strong interaction: s(mZ) 0.117

  44. W- b gVub u The CKM matrix • Couplings of the charged current: • Wolfensteinparametrization: • Magnitude: • Complex phases:

  45. The CKM matrix • Couplings of the charged current: • Wolfensteinparametrization 1) 2) 3) • Magnitude: • Complex phases:

  46. The CKM matrix • Couplings of the charged current: • Wolfensteinparametrization: • Complex phases: • Magnitude:

  47. PEP-II accelerator schematic and tunnel view SLAC: LINAC + PEPII Linac HER LER

  48. PEP-2 (SLAC) Coherent Time Evolution at the (4S) B-Flavor Tagging Exclusive B Meson Reconstruction Vertexing &Time DifferenceDetermination

  49. pT of B-hadron η of B-hadron LHCb: the Detector • High cross section • LHC energy • Bs produced in large quantities • Large acceptance • b’s produced forward • Small multiple scattering • Large boost of b’s • Trigger • ↓ Low pT • Leptons + hadrons (MUON, CALO) • Particle identification (RICH)

  50. m < 0.000003 m < 0.19 m < 18.2 e   me  0.51099890 m  105.658357 m  1777.0 mu  3 mc  1200 mt  174000 md  7 ms  120 mb  4300 quark mixing (4) u’ d’ s’ u d s Vijq = Standard Model: 25 free parameters Elementary particle masses (MeV): Electro-weak interaction: neutrino mixing (4) e(0)  1/137.036 mW  80.42 GeV mZ  91.188 GeV mH >114.3 GeV e   1 2 3 Vijl = mH >114.3 GeV ATLAS LHCb Strong interaction: s(mZ) 0.117

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