Quarks and leptons come in three “generations”. Gauge bosons mediate their interactions. •  B physics = studies of production and decay of the bottom (b) quark. Can learn about the weak interaction between the quarks, esp. the Cabibbo- (CKM) matrix. •  Interesting phenomena expected, e.g. ÇP.
Coupling of quarks and W±  and Z° bosons Examples: μ • muon decay • neutron    decay Heavy quarks (s, c, b, t) are unstable. Transitions across the generations are possible: Quark flavors are not conserved in the C.C. weak int’s. Mass and flavor eigenstates connected by the CKM matrix. V CKM
L WµU¡Y "V¡JD¡ Vtd Vts Vtb Need to determine the elements V ij experimentally.
|Vub|/|Vcb| ~ 0.1 Vtb, Vts, Vtd: t quark couplings. In principle from t decays, but hard in practice. Can use B decay processes where the t quark is involved in the loop, e.g. particle-antiparticle oscillations of the neutral B mesons.
Why B Physics at a Hadron Machine ? Because the production rates are high. • Not only B 0 , B + , but also B 9 , baryons, B c • Lorentz boost,     ~ 2 - 4. Vertex resolution not an issue. Need to trigger on B decays, though. So far relied on leptons: • Single leptons (e, μ) - B • Di-leptons    (μμ, eμ) рт > 2 GeV/c - B     J/ψ X,  J/ψ     μ†µ¯  <p†(B)> ~ 10 GeV/c - b     e v X,  b     u v X’ purity ~ 20% (J/  ) рт > 8 GeV/c <p T (B)> ~ 20 GeV/c purity ~ 40%
• Silicon micro- strip detector Impact parameter = (13+40/p ) μm • Central tracking chamber (pτ) /pτ ~ 0.001 pτ • Lepton detection Collected  ~ 110 pb-1 in 1992 - 96.
● ～ 240 k J/ψ µ†µ¯. •  Mass resolution ~ 16 MeV/c². •  ~ 20% from B decays, others direct / χc J/ψ
•  Mass measurements of B +, B 0 s and Λ b. •  Lifetime measurements of B+, B0, B0s, Λь. •  Bo-Bo oscillations and flavor tagging. •  sin(2  ) from Bo/Bo    J/ψ Kos. •  B c meson. •  Rare decay searches (FCNC decays) • Inclusive b and B production. •  bb production correlations. •  b-quark fragmentation fractions, f w, f d, f s ... •  Onium production (J/  ,   ) –  Prompt and non-prompt (from B,   c) production –  Production polarization
CDF 1.00+0.17 +0.10 1.06+0.13 ±0.10 1.065±0.022±0.033 new 1.09±0.07±0.03 1.079±0.064±0.041 0.99±0.14+0.05 .0.04 1.03 + 0.14 ±0.09 1.037+0.025 ±0.024 1.066±0.02 τ (B¯)/τ (Bg)
•  2nd order weak interaction. • Decay probability: PBo   Bo (t) = L e-t/t (l + cos  mt)       Unmixed RBo  Bo (t) = ½ e-t ½ (1 – cos  mt) Mixed •  Oscillation frequency = ∆m= mH- mL : mq • Eventually   ms /  md     |Vts| / |Vtd| with less theory uncertainty Ingredients for Bo-Bo Oscillation Measurements • Proper decay time • Decay flavor (Bo      l+ v X vs Bo      l+ v X) • Production flavor, b or b ?  Flavor tagging Flavor tagging is the hardest part (for CDF). Conventional approach:  b and ̄are produced in pairs. identify the flavor of the other B semileptonic decay leptons, kaons,  jet charge infer the flavor of the signal B
Exploit charge-flavor correlation with a nearby pion (Gronau, Nippe, Rosner). Example: D*+     D 0   +. Since B* \ B , use pions from B** B    (resonant) or Fragmentation b      B (non-resonant). The correlations are the same if it is resonant or not. Tagging Dilution No tag is perfect. e.g. for lepton tag: • Leptons from b    c • Bo, Bos mixes. • Fakes. Probability of misidentification W Dilution  D = 1 - 2W. Oscillation amplitude reduced by a factor D. (unmixed - mixed) / total = cos(  m t) D cos(  m t) Tag effectiveness =   D², is the efficiency of the tag. Mixing from l- D(*) and same-side pion tag Asymmetry = (RS-WS) / Total Charm signal near l- (a) Do K- +. (b) D+ K- (c) D*+ Do + Do + K- +, K- 0 (d) D*+ Do +, Do K- + m = 0.471+0.078  ± 0.034 ps¯ D(B +) = 0.27± 0.03± 0.02 D(Bº) = 0.18± 0.03± 0.02
Do +, followed by
m = 0.516 ± 0.099 +0.029 W = 0.325± 0.033± 0.012 D = 0.350± 0.070.
Need better theory to improve precision in |Vtd|۰Or, measure   m². mtop・ Another CDF contribution to B physics theory
J/ψ Kos
• Now the amplitude is the quantity of interest. • Final state = J/ψ K 0 S     μ+μ-  + -     “Trivial” • I nitial state, B 0 or B 0 ?   Flavor Tagging • Decay time: Not necessary at CDF, but helps.
(M uuxx M R 0)/O M Koς) - M(Bo) ] [ Mass(J\ M Apply 3 flavor tags, count B 0 vs B 0 . Extract raw asymmetry = D sin(2  ) Divide it by tag dilution     sin(2  ) Apply 3 Flavor Tagging Methods • Same-side “pions” • Leptons •  Jet charge Measure tag dilution from ~ 1000 B+     J/ψ K+ decays. (For SST,   extrapolation of lepton-D meas.)
Precise lifetime sample: Asymmetry vs. time. Less precise lifetime sample: Time-integrated Asym x (1+x d ² ) / X d = sin (2) sin(2 ) = +0.79 + 0.41 - 0.44 (stat + syst). PRD 61, 072005 (2000) Constraints on the unitarity triangle sin(2 ) : four solutions,  1,  2,  1+ ,  2+   (  2=  /2-  1). bound Not much constraint now, but should be interesting in Run-II.
• b    s  FCNC transition PRL 83, 3378 (1999) •  Z° penguin and box diagram in addition to EM penguin. • | V ts | •  SM predicts B.R. ~ 10-7 to 10-6. • New physics could enhance it. •  Has yet to be observed. l+l can be resonant, e.g. J/ψ, ψ(2S). Indistinguishable from b   ccs Look at non-resonant mass region. Bo • 4 candidates •  BR < 5.2 X 10-6 @90% CL  • BR < 4.0 X 10-6 @90% CL •  SM: (5.9 ± 2.1) X 10-7        • SM: (2.0 ± 0.7) X 10-6 Expected signal ~ 0.5 event each. Should see a handful of signal events in Run II.
l+l- • Vtd for Bo,   Vts for Bos • Helicity suppressed. • B.R. very small. SM predictions: - Bo µ†µ¯ (1.5± 1.4) x 10-10 - Bos µ† µ¯   (3.5± 1.0) x 10-9 - Bo e+ e-    (3.4± 3.1) x 10-15 - Bos e+ e-    (8.0± 3.5) x 10-14
PRD 57, 3811 (1998) Still long way to go… One candidate in the overlap region of Bo and Bos mass windows. B.R. < 8.6 x 10-7 for Bo B.R. < 2.6 x 10-6 for Bos @ 95% C.L. Also looked for decays to e+ µ- , e- µ+ B.R. < 4.5 x 10-6 for Bo B.R. < 8.2 x 10-6 for Bos PRL 81, 5742 (1998)

Accelerator
•      s = 2000 GeV • 6 bunches     36, 108. • New 120 GeV Main Injector • Luminosity = 1032 cm-²s-1 •   L dt = 2 fb-1  (2 years) Detector • Tracking system • FE electronics • Trigger/DAQ • Plug calorimeter • Extended muon coverage Retained good momentum resolution & lepton ID.

SVX II
• Radii 2.5 cm to 11 cm • 5 layers • Double-sided, 90° and 1.2° stereo • Main vertex detector Intermediate silicon layers (ISL) • 3 more layers at R = 20 - 29 cm • Construction similar to SVX II • Precision tracking to higher eta. • Aid linking from COT to SVX. Significant Japanese contributions : SVX II Hiroshima, Okayama I SL Osaka City, Tsukuba Silicon Vertex Trigger : SVT Can trigger on all-hadronic final states such as + -.  Bos Bo D - Use silicon information at the 2nd level trigger • Find a track in the main tracker COT. • Extrapolate toward the SVX. • Find SVX hits along the road. • Calculate impact parameter wrt the primary vertex (beam spot). • Resolution ~ 40 μm at 1 GeV/c. New additions for B physics: Time-of-flight counter I nnermost Si layer CDF-II TOF counter
Detector
• Located at r = 1.4 m • I nside 1.4 Tesla solenoid • Scintillator Bicron BC408 4 x 4 x 270 cm³ • Hamamatsu R7761 PMTs 38 mm, 19-stage fine mesh • Goal:   τ ~ 100 ps
Purpose
• 2   K/   separation up to 1.6 GeV/c • B flavor tagging

Detector
• Single-sided • At radius ~ 1.6 cm, minimize effect of multiple scattering. • Can operate up to ~ 5 fb-¹ Purpose I mprove impact parameter resolution : ~  9 µm for high pτ 10 µm alignment

Signal
• Bos     D-s  +, D-s  + • ~20 k  events / 2 fb-1  6 TOF • I mproves flavor tags.
• Helps at lower xs.
Layer 00
• I mproves vertex • I mproves vertex determination. proper time  resolution. • Helps at higher x 。 Once the oscillations are established,   ms will be determined to a few %. → B。 frequency  xs=Δmsτ egrated Luminosity B Physics in CDF Run II Two Major Goals: Precision sin(2) from B 0 / B 0    J/ψ K 0 S I. II. Bos - Bos  Oscillation      Δms / Δms η | V tsl Can be the first meaningful test of the unitarity triangle. Run II (cont'd)    Probing angle    (phase of V ub) • B o       +  - once thought to be the mode for sin2(  -  -  ). (assuming b     u tree dominance over penguin) • CLEO finds much larger K-  + and tiny   +   -. • Not just small rates, but also means penguin pollution. Relation to sin(2  ) less clear. • Strategies proposed, but are challenging experimentally... New approach : R. Fleischer, Phys. Lett. B 459, 306 (1999). Throw in B os     K+K-, measure asymmetries in both B o and B os . In general, for a decay Bo     f (f = CP eigenstate) : Acp(t) = Adir cos( mt) + Amix sin( mt). Adir : “direct” CP violation,  Amix : CP violation thru mixing. Experimentally, measure 4 A’s from Bº      +  - and Bº s     K K -. Then extract   ,   and penguin and tree decay amplitudes. Angle   (phase of Vub)  continued Four CP asymmetries to measure.  (  = sin   c) • Adir(Bo       +   -)  =   -2d sin    sin    / (1 - 2d cos     cos    + d²) • Amix(Bo       +   -)  = [ sin2(  + ) - 2d cos    sin(2  + ) + d² sin2  ] / [1 - 2d cos    cos   + d² ] If no penguin, • Adir(Bos     KtK-) ~ 2( 2/d) sin   sin Adir = 0        (Bo, Bos) • Amix(Bos     K+K-) ~ 2( 2/d) cos   sin Four unknowns to extract : Amix = sin2( + ) (Bo) | Amix = sin(2 )    (Bos) •  ,   = angles of the unitarity triangle.  | • d = ratio of penguin (P) to tree (T) decay amplitudes, = phase of “P/T” d ei        |Vcb/Vub| / (1-  ²/2) [ P /  (T+P) ] Expect ~5 k Bo      +  -, ~10 k Bo s     K+K- angle to ~10°. Tree
• CDF does B physics pretty well. • Run-I results cover virtually all aspects of B physics. • Run II should produce further interesting results, in particular -  sin(2  ) precision of ±  (0.043 to 0.084). – ms up to ~ 40 ps-¹. - angle   to ± 10 degrees.