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Accelerator and Detector

This article discusses the KEKB accelerator and Belle detector, highlighting their design, achieved luminosity, and future upgrades. It explores the use of crab cavities for beam stability and the capabilities of the Belle detector for particle identification and CP violation measurements. Additionally, it explains the extraction of the angle gamma (γ) using the Wolfenstein parameterization and GLW method.

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Accelerator and Detector

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  1. Accelerator and Detector

  2. KEK-B accelerator Two separate rings: 8GeV(e-)/3.5GeV(e+) Finite crossing angle Design luminosity = 1034 cm-2sec-1 Achieved lum =1.06 1034 cm-2sec-1 Belle logged: 158 fb-1 KEKB Collider

  3. Future upgrade planned for 2005 [luminosity:factor of 2 ] For a finite crossing angle  Geometrical luminosity loss  Beam instability Without crab cavities: 22mrad With crab cavities: Complete overlap of beams Crab cavities Head-on collision

  4. Belle Detector Aerogel Cherenkov cnt. n=1.015~1.030 SC solenoid 1.5T 3.5GeV e+ CsI(Tl) TOF counter 8GeV e- Tracking + dE/dx Si vtx. det. 3 lyr. DSSD m / KL detection 14/15 lyr. RPC+Fe

  5. Particle identification • Particle identification: ACC, TOF , dE/dx from CDC PID(K) = = pKdE/dx pKTOF pKACC • Very good in a wide momentum range

  6. Upgrade (fall-2003): New beam-pipe SR mask SR mask No SR mask New beam-pipe is longer , 16cm 24cm

  7. Upgrade (fall-2003): New beam-pipe HER Downstream Double walled Be beampipe HER QCSLE LER mask LER QC2 QCSRP QC1 BC3 HER Upstream Removed for new beam-pipe

  8. Upgrade (fall-2003): New beam-pipe SR mask SR mask No SR mask New beam-pipe is longer , 16cm 24cm

  9. Upgrade (fall-2003): cont… • More synchrotron radiation protection LER HER QC1 QC2 LER mask BC3 Saw tooth shape No SR hits Beam-pipe

  10. Upgrade (fall-2003): New beam-pipe SR mask No SR mask New beam-pipe is longer , 16cm 24cm

  11. Upgrade (fall-2003): SVD2 • Increase the number of layers , 3 layers  4 layers • smaller radius for inner-most layer • Better vertex resolution (  1/distance 1st detection layer)

  12. Upgrade (fall-2003): New Vertex Detector(SVD2)

  13. An event with new Vertex Detector

  14. CP violation and Unitarity of CKM matrix What is ? g

  15. Standard Model lagrangian for q-W interaction Lint(t) =  d3x (LqW(x) + L†qW(x)) LqW(x)= VijUi  ( 1- 5) Dj W Dj (x ) = Ui (x ) = V= (CKM matrix) Experimentally, V has a hierarchical structure. ( = 0.22)

  16. Transformation of Lint under CP exchanges particle (n)  antiparticle ( n ) CP: flips momentum sign ( p  -p ) keeps the spin z-component () the same   under CP, LqW transforms as CP LqW(x) P†C† =  ud Vij (Ui (x’) ( 1- 5) Dj(x’) W(x’))†  * x ’ =( t , -x) If ud can be chosen such that ud Vij = Vij * (1) * * Then, Lint(t) becomes invariant under CP: • CP LqW(x) P†C† =L†qW(x) • CP Lint(t) P†C† = d3x CP (LqW(x) + LqW(x)) P†C† = d3x (LqW(x) + LqW(x) ) = Lint(t)

  17. Condition for CP invariance ud Vij = Vij * * Condition (1) is equivalent to rotating the quark phases to make Vij all real In general, there are 5 phase differences for 6 quarks  5 elements of VCKM can be set to real always + 3 phases can be related to Euler angles There is one phase which cannot be removed CP violation

  18. Wolfenstein parameterization Wolfenstein parameterization

  19. What is the angle  ? Orthogonality of d-colmn and b-column: * * * VudVub + VcdVcb + VtdVtb = 0 ⃔ * * VtdVtb VudVub  ⃔ ⃔   * VcdVcb a * ⃔ = arg  b * -b  = arg CKM fitter: 39°   80° @ 95% C.L

  20. Methods to extract the angle  s u b - K - Vub o - - D u c Vcb b - c B - s o B D - K - - - - u u u u • One needs interference between D0K- and D0K- D0 and D0 decay to common final state Example: K+K-, KS0 etc ( CP eigenstates) KS+- Dalitz analysis K*K (singly Cabibbo suppressed mode) K+- ( doubly Cabibbo suppressed mode) I will discuss

  21. (*)- B -> D K - - CP (Gronau , London and Wyler) PLB 253(1991)483 PLB 265(1991)172

  22. Gronau-London-Wyler method to extract  - B- DCPK- where Dcp  (D0 ± D0 ) - • Amp(B- DCPK-) = Amp(B-  D0K-) + Amp(B-  D0K-) - KS0, KS, KS, KS, KS’ K+K-, +- D0 and D0 CP + modes  2 diagrams CP - modes s u b -  K - Vub o - - D u c Vcb - b B c s * o - =arg(Vub) D - B K - - - - u u u u Color-favored Color-suppressed ~  Vcb ~Vub

  23. GLW method cont… Strong final-state-interaction phase: B-  D0K- relative to B-  D0K- isei _ _ • Amp(B- DCPK-) = |Amp(B-  D0K-)| + |Amp(B-  D0K-)| ei(+) _ • Amp(B+ DCPK+)= |Amp(B+ D0K+)| + |Amp(B- D0K+)| ei(-) — A(B- D0K-) A(B- DCPK-)  — A(B- D0K-) = A(B+ D0K+) - A(B+ DCPK+) A(B+ D0K+)

  24. GLW method cont… _ • Amp(B- DCPK-) = |Amp(B-  D0K-)| + |Amp(B-  D0K-)| ei(+) _ • Amp(B+ DCPK+)= |Amp(B+ D0K+)| + |Amp(B- D0K+)| ei(-) — A(B- D0K-) A(B- DCPK-)   — A(B- D0K-) = A(B+ D0K+) - A(B+ DCPK+)  A(B+ D0K+) Reconstruct the two triangles   Non-vanishing strong phase (  0)  Direct CP violation

  25. GLW method cont… One can measure  even if =0( No strong phase) no direct CPV One needs to measure the sides and reconstruct triangle  — A(B- D0K-) A(B- DCPK-)  — A(B- D0K-) = A(B+ D0K+) - A(B+ DCPK+) A(B+ D0K+)

  26. Problem: Color-suppressed mode B- D0K- B- D0K-  and  K+- K+- — A(B- D0K-)  How to measure ? - Ratio of amplitudes ~ 1  Good or Bad ? Method of Atwood, Dunietz and Soni

  27. Theoretical solution One can instead measure: R1,2 = DCP Dnon-CP R /R = 1 + r2  2r cos()cos() B(B-  D1,2K-) + C.C DCP where R = B (B-  D1,2-) + C.C R1 + R2 = 2( 1 + r2) r = |BKD|/|BKD| 2 In principle one can obtain r Useful inequality: Sin2 < R 1,2 R1 or R2 < 1.0 (assuming small r )

  28. Solution - B (B-  D1,2K-) B(B+  D1,2K+)  2r sin()sin() A1,2 = = R1,2 + B (B-  D1,2K-) B (B+  D1,2K+) 4 measurements : A1,2 and R1,2 But A1R1= - A2R 2 r = |BKD|/|BKD| 3 independent measurements  3 unknowns ( r , , ) Solve !

  29. Variables to identify signal B  f1….. fn Energy and absolute value of momentum is known: EB = Ebeam = 5.29 GeV E  PB = = 0.34 GeV/c • Requires that the candidates satisfy   EB = |PB| =| | Mbc Peaks at: 0.0 GeV 5.279 GeV  Instead of EB and PB , we historically use Energy difference  M ~ 2.5 MeV ~  10 better inv mass Beam constrained mass bc

  30. Hadronic cross sections @(4S) peak energy channel (nb) 1.05 1.39 0.35 0.35 1.30 (4S) uu dd ss cc Hadronic total 4.44 ~ 76% is qq 2 jet-type (“ continuum events”) The continuum is monitored by taking data just below the (4S) resonance (60 MeV) off (4S)  x on (4S)(Belle) KEK-B operates here • Rare decay background is usually dominated by continuum

  31. Suppressing continuum events • Variables to distinguish signal from continuum events • CosB signal ~ sin2 continuum ~ flat B B e+ e- Continuum BB Signal

  32. Suppressing continuum signal  • Fisher discriminant of variables x = (x1…….xn) • F =  .x : constants to be chosen to maximize separation(S)between signal and background , S = func (FS , FB ) • = 0    continuum Xi = Fox-Wolfram moments continuum signal Get values of ’s

  33. Suppressing continuum Most effective way to suppress the continuum events  Combine Fisher discriminant(F) and cosB Likelihood ratio (LR) _ _ L(BB) LR(BB) = _ L(BB) + L(qq) continuum _ _ _ signal L(BB) = L(BB)(F) x L(BB)(cosB) _ { 0 for continuum events _ LR(BB) peak at: 1 for signal(BB) events Performance( B- D0[K-+]- ) : LR > 0.4 keeps 87.5% signal removes 73% continuum LR

  34. Results for calibration mode B- D0K-(-) @78fb-1 /K separation by Aerogel Cherenkov Counter ( with dE/dx, and TOF) Prompt Kaon is reconstructed with pion mass assumption shifts E by -49 MeV Allows simple cuts/fits : B-  D0 K- B-  D0 - 347.5±21 6058±88 B-  D0 - 134.4±14.7 B-D0*-, D0- continuum B-D0*K-, D0K*- D00, D0 D00, D0 R = = 0.077 ± 0.005(stat) ± 0.006(sys)

  35. Results for B- D1K-(-) mode CP-even For B- D0[K+K-]K- B- D0[+-]K-  23 background  100 B- K+K-K- B- K-+- Can be estimated from D0 sideband data  included in systematic error 47.3±8.9 683.4±32.8 15.6±6.4 R = =0.093±0.018±0.008 Double ratio R1 = 1.21 ±0.25 (stat)±0.14 (sys) 22.1±6.1 25±6.5 CP asymmetry A1 = +0.06 ± 0.19 (stat)±0.04(sys)

  36. Results for B- D2K-(-) mode CP-odd For B- D0[KS]K- where +-0 background For B- D0[K*-+]K- where K*-KS- and + +0 KS- invariant mass difference> 75 MeV 52.4±9.0 648.3±31.0 R = =0.108±0.019±0.007 6.3±5.0 Double ratio R2 = 1.41 ±0.27 (stat)±0.145(sys) 29.9±6.5 20.5±5.6 CP asymmetry A2 = - 0.19 ± 0.17 (stat)±0.05(sys) A1,2and R1,2 are useful quantities for determining 

  37. Measuring  using B- DCPK- mode Using the measured value of and R1,2 A1,2 We find: R1 R2 r = |BKD|/|BKD| r2 = = 0.31  0.21 2 Just 1.5 away from physical boundary: r2 =0 otherwise r would be imaginary A lot more statistics needed for this method to be useful This corresponds to r = 0.57 0.19 very unlikely (theory: 0.1 0.2)

  38. Measurement of “r” s u b - K - Vub o - - D u c Vcb b - c B - s o D - B K - - - - u u u u r =

  39. Measurement of “r” using B0 D0K0 mode s c b K- o - D - Vcb Vcb u u o B b o B- c o K D s - - - - u u d d BF(B0D0K0)=(5.0±1.3)  10-5 r =  (CKM factor)(color factor)  r  0.2 0.45 ??  Color factor= ~ ~ 0.4

  40. Measuring  using B- DCPK- mode Assume we measured r = 0.2 , what would be? A1,2 =0 R1,2 = 1.4 1 + r2  2r cos()cos() |A1,2|=0.25 1.2 R2(-1) A1,2 =  2r sin()sin() R1,2 1.0 R1(-1) R1,2 Taken from Gronau 0.8 A1,2 =0 0.6  (degrees) At 1, the angle  <33 or  >   > Excluded by CKM fit

  41. *- Additional modes: B- DCPK mode Same principle as B- -> DCPK- decay: K- to be replaced by K*- First step: Flavor specific modes D0 K-+ , K-+0 , K-+-+ Only KS- is used (K-0 could be included worry: handling background) 169.5±15.4 16 

  42. *- Consistency check: B- D0K mode Yields in KS- mass and helicity bins • Points with error bars  data •  • Hatched histogram  Signal Monte Carlo Fit to E for each bin

  43. *- B- DCPK mode 13.1 ± 4.3 B- D1K*- 4.3 7.2 ± 3.6 2.4 B- D2K*- A1 = -0.02 ± 0.33(stat) ± 0.07(sys) CP asymmetries : A2 = 0.19± 0.50(stat) ± 0.04(sys) Cannot now constrain  -> need more data

  44. Additional modes: Atwood, Dunietz and Soni method K- K- Doubly Cabibbo Suppressed Cabibbo Allowed K+- D0 D0 1  Maximum Interference B- B- Measure B- DK- in two decay modes of D: e.gK+- and KS0 ( their CP conjugates) [B- (K+-)K-] [B+ (K-+)K+] [B- (KS0)K-] [B+ (KS0)K+] Solve for   ,  ,  and r K+- KS0

  45. Additional modes: ADS method @78fb-1 Only ~ 10-12 events, Cabibbo-suppressed D0K down by ~1/15 E E Promising method but requires lots & lots of data

  46. Other related decay modes

  47. B-D0(KS+-)K- Dalitz analysis - Previously: B- DCPK- where DCP =(D0  D0 ) both D0 and D0 decays to CP eigenstates ( K+K-..) - D0K0p+p- DKSp+p- D0K0p+p- Amp(B+ ->DK+) = f(m+2,m-2) + r. ei( + ) f(m-2 , m+2 ) where m+/-2= M2(KS+/-) r = |BKD|/|BKD| f( m+2,m-2) =  ak. ei Ak(m+2,m-2) + b ei -> both 2-body resonances and non-res component

  48. Simple example Suppose allDKS+p- decays are via K*p D0K*+p- D0K*-p+ KS p+ KS p- M(KS p+)2 Dalitz plot interference M(KS p-)2

  49. Reality is more complex ( & better) D0KS p+p- many amplitudes & strong phases(13) lots of interference K*p KSs KSf2 KSr

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