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Symmetry and Symmetry Violation in Particle Physics

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对称. 违反. Symmetry and Symmetry Violation in Particle Physics. Lecture 4 March 28, 2008. Summary Lecture 3. CP is violated in Weak-Interactions Neutral Kaon mass-matrix induced; scale  e  2x10 -3 Direct CPV in K L  pp ; scale = e ’ = 1.6 x 10 -3 e Observing CPV requires:

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  1. 对称 违反 Symmetry and Symmetry Violation in Particle Physics Lecture 4 March 28, 2008

  2. Summary Lecture 3 • CP is violated in Weak-Interactions • Neutral Kaon mass-matrix induced; scale  e 2x10-3 • Direct CPV in KLpp; scale = e’ = 1.6 x 10-3e • Observing CPV requires: • Two interfering amplitudes • One with a CP-violating weak phase • Another “common” or “strong” phase • In the W.I., the d and s quark mix  d’ & s’ • d’ =cosqcd +sinqs; s’ =-sinqcd +cosqcs • qc 120 is the “Cabibbo angle • If all quarks are in pairs, FCNC = 0 by Unitarity • (GIM Mechanism)

  3. antimatter CP: matter “charge” CP operator: CP( )= g q q’ g* q W q W† some basic process mirror For CPV:g g* (charge has to be complex)

  4. CP violating asymmetries in QM • Even if CP is violated, generating matter-antimatter differences is hard • need a CP-violating phase (f) • need 2 (or more) interfering amplitudes • + a non-zero “common” phase (d) (often called a “strong” phase)

  5. Common and weak phases “Common” (strong) phase (d): same sign for matter & antimatter  CP conserving Weak phase (f): opposite sign for matter & antimatter  CP violating B = |B|eid-if |B|eid+if f f A+B A+B B B d d A

  6. How does CPV fit into the Standard model? Clue: CPV is seen in strangeness-changing weak decays. It must have something to do with flavor-changing Weak Interactions

  7. CP Violation & Flavor mixing

  8. d’ & s’ are mixed d & s 4-quark flavor-mixing matrix Mass eigenstates Weak eigenstates

  9. how about a complex mixing matrix? b controls |DS|-1 where we see CPV incorporate CPV by making  complex? (i.e. b≠b*?) a b -b* a bGF u s W- not so simple: a 2x2 matrix has 8 parameters unitarity: 4 conditions 4 quark fields: 3 free phases Cabibbo angle # of irreducible parameters: 1

  10. 2-generation flavor-mixing cosqCsinqC -sinqC cosqC a b -b a Only 1 free parameter: the Cabibbo angle s d’ not enough degrees of freedom to incorporate a CPV complex phase s’ qC120 d

  11. Enter Kobayashi Maskawa a 3x3 matrix has 18 parameters unitarity: 9 conditions 6 quark fields: 5 free phases # of irreducible parameters: 4 3 Euler angles +1 complex phase

  12. Original KM paper (1973) From: Prog. of Theor. Phys. Vol. 49 Feb. 2, 1973 3 Euler angles CP-violating phase

  13. KM paper was in 1973, the 3-quark age 1964-1974 3x3 matrix 3 generations, i.e. 6 quarks Predicted by Glashow but not discovered until Nov.1974 6 quarks: These were not even in our 1973 dreams. 3 quarks: 4 quarks: q=+2/3 s-1/3 q=-1/3

  14. A little history • 1963 CP violation seen in K0 system • 1973 KM 6-quark model proposed • 1974 charm (4th ) quark discovered • 1978 beauty/bottom (5th) quark discovered • 1995 truth/top (6th) quark discovered

  15. CKM matrix (in 2008) * Vub u CPV phases are in the corners b f3 (g) W+ d Vtd t W+ f1 (b)

  16. The challenge * Vub u Vtd d b t W+ W+ Measure a complex phase for bu or in td or, even better, both

  17. The Key B0 = d B0 = b b d Use B0 mesons B0/B0 similar to K0/K0

  18. 小学课本 Primer on B mesons

  19. Lesson 1: Basic properties b-1/3 d+1/3 • What are B mesons? • B0 = d b B0 = b d • B+ = u b B- = b u • JPC = 0- + • t= 1.5 x 10-12 s (ct  450 mm) • How do they decay? • usually to charm: |bc|2  |bu|2 100 • How are they produced? • e+e-  (4S)  B B is the cleanest process b+1//3 d-1/3 b-1/3 u-2/3 u+2/3 b+1//3

  20. Lesson 2: “flavor-specific” B decays In >95% of B0 decays: B0 and B0 are distinguishable by their decay products semileptonic decays: X l+ n X l- n B0 B0 D hadronic decays: D X D X q C+2/3 B0 B0 D C+2/3 q

  21. Lesson 3: B  CP eigenstate decays In ~1% of B0 decays: final state is equally accessible from B0 and B0 charmonium decays: J/yKS J/yKL … B0 B0 J/y C-2/3 C+2/3 JPC=1-- charmless decays: CP=+ p+p- K+K- … B0 B0

  22. Lesson 4:The (4S) resonance 3S bb bound states BB threshold • (e+e- BB)  1nb • B0B0/B+B- 50/50 • good S/N: (~1/3) • BB and nothing else • coherent 1-- P-wave s(e+e-) hadrons 10.58GeV e+e-qq continuum (u, d, s &c)

  23. _ Lesson 5:B0B0 mixing A B0 can become a B0 (and vice versa) V* b u,c,t td d tb d b u,c,t V* td tb These have a weak phase: f1 (only short-distance terms are important)

  24. bd: * * * Vub Vud Vcb Vcd Vtb Vtd + + b u d b c d b t d * * * Ά=VubVud f(mu) + VcbVcd f(mc) + VtbVtd f(mt) * * * GIM: VubVud+VcbVcd+VtbVtd = 0  Ά = 0if: mu = mc = mt

  25. Large mt overides GIM but, mt >> mc & mu: GIM cancellation is ineffective t-quark dominates V* td V* td B0 B0 mixing transition is strong (and this allows us to accesses Vtd)

  26. Y.H. Zheng, PhD Thesis Also Y.H. Zheng et al., Phys Rev. D 67 092004 (2003) N(B) – N(B) N(B) + N(B)

  27. What makes B’s interesting? The large t-quark mass: mt=174 GeV

  28. Neutral meson mixing phenomenology Neutral B mesons are produced as flavor eigenstates: B0 or B0 B0(t) B0(t) B0(t) B0(t) |B1> = p |B0> + q |B0> |B2> = p |B0> - q |B0> B1 & B2 If CPV is small: q ≈ p ≈1/2

  29. Time dependence of B0 (B0) mesons( pq1/√2 ) |B0(t)> = ( |B0> (1+eiDmt)+ |B0>(1-eiDmt))e-Gt common phase |B0(t)> = (|B0>(1+eiDmt)+ |B0>(1-eiDmt))e-Gt Dm = m2-m1G = (G1 + G2)/2

  30. Can we measure f1? • two processes: B0fcp& B0  B0 fcp • weak phase: 2f1 • common phase: Dmt Yes!!

  31. Interfere BfCPwith BBfCP Sanda, Bigi & Carter: J/y Vcb B0 KS  + V*2 td J/y sin2f1 V* Vtb Vcb td B0 B0 eiDmt B0 KS V* Vtb td td

  32. What do we measure? Flavor-tag decay (B0 or B0 ?) Asymmetric energies J/ e fCP e t=0 KS z B - B B + B sin21 more B tags t z/cβγ (tags) more B tags This is for CP=-1; for CP=+1, the asymmetry is opposite

  33. Requirements for CPV • Many B mesons • “B-factory” & the ϒ(4S) resonance • Reconstruct+isolate CP eigenstate decays • Kinematic variables for signal +(cont. bkg suppr+PID). • “Tag” flavor of the other B • Measure decay-time difference • Asymmetric beam energies, high precision vertexing(Δz) • Likelihood fit to the t distributions

  34. PEPII B factory in California Stanford Linear Accelerator Ctr BaBar Detector

  35. The PEPII Collider (magnetic separation) Int(L dt)=131 fb-1 On resonance:113 fb-1 9 x 3.0 GeV; L=(6.5 x 1033)/cm2/sec

  36. Superconducting Coil (1.5T) Silicon Vertex Tracker (SVT)[5 layers] e+ (3 GeV) e- (9 GeV) Drift Chamber [40 stereo lyrs](DCH) CsI(Tl) Calorimeter (EMC) [6580 crystals]. Cherenkov Detector (DIRC) [144 quartz bars, 11000 PMTs] Instrumented Flux Return (IFR) [Iron interleaved with RPCs]. The BaBar Detector

  37. KEK laboratory in Japan Tsukuba Mountain KEKB Collider KEK laboratory

  38. KEKB • Two rings • e+ : 3.5 GeV 1.5A • e- : 8.0 GeV 1.1A • ECM : 10.58 GeV • Luminosity: • target: 1034cm-2 s-1 • ach’ved: 1034cm-2 s-1 • (~20 B’s/s)

  39. elle A magnetic spectrometer based on a huge superconducting solenoid

  40. Step 2: Select events p+p- B0 J/ Ksevent m+m- Tracking chamber only

  41. Drift chamber for tracking & momentum measurement

  42. Drift chamber cell Charged particle track E-field - - - - - - - - + 16mm - - Drift speed  50mm/nsec Position resolution  150 mm - - - - 17mm

  43. Same event in the entire Detector J/ KS B0 J/ Ksevent

  44. Kinematic variables for the ϒ(4S) in CM: E=Ecm/2 J/y KS B0 e+ e- e- e+ B0 E=Ecm/2 invariant mass: Beam-constrained mass:

  45. Kinematic variables for the Υ(4S) s10MeV Energy difference: s  2.5 MeV Beam-constrained mass:

  46. B0ψ KL signal event Event display J/ KL 1399±67 signal KL “crash” pB* (cms) [2332 events with a purity of 0.60]

  47. Step 3: Check the other tracks to see if the other meson is a B0 or a B0 ? ? ? ? ? ?

  48. Flavor-tagging the other B Figure of merit(Q) =ε(1-2 w)2a.k.a effective tagging efficiency • Inclusive Leptons: • high-p lb c ln • intermed-p l+s l n • Inclusive Hadrons: • high-p p- B0D(*)+p-, D(*)+r-, etc. • intermed-p K- K- X, p-p0 • low-p p+ D0p+ Belle: effective efficiency = 30 %

  49. Distinguishing different particle types dE/dx Ionization density in the drift chamber (dE/dx)