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Measurement of sin2 b with charmonium decays and gluonic penguin decays

This paper discusses the measurement of sin2b, a parameter related to CP violation, in charmonium decays and gluonic penguin decays within the framework of the Standard Model. It explores the Cabibbo-Kobayashi-Maskawa matrix, visualization of the unitarity triangle, and the effects of weak phases on decay rates. The cleanest way to measure the CP angle b is also presented, using the golden mode B0 → J/ψ KS.

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Measurement of sin2 b with charmonium decays and gluonic penguin decays

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  1. Measurement of sin2bwith charmonium decays and gluonic penguin decays Wouter Verkerke NIKHEF, Amsterdam Wouter Verkerke, NIKHEF

  2. N(B  f) ≠ N(Bf) Outline • CP violation • Introduction:Standard Model CP violation & the CKM mechanism • Testing the Standard Model:measurement of sin(2b) from charmonium KS decays • Looking for signs of new physics:measurement of sin(2b) from bs penguin decays • Comparison and summary Wouter Verkerke, NIKHEF

  3. The Cabibbo-Kobayashi-Maskawa matrix • In the Standard Model, the CKM matrix elements Vij describe the electroweak coupling strength of the W to quarks • CKM mechanism introduces quark flavor mixing • Complex phases in Vij are the origin of SM CP violation Mixes the left-handed charge –1/3 quark mass eigenstates d,s,b to give the weak eigenstates d’,s,b’. CP The phase changes signunder CP. Wouter Verkerke, NIKHEF Transition amplitude violates CP if Vub ≠ Vub*, i.e. if Vub has a non-zero phase

  4. d s b u c t Structure of the CKM matrix • The CKM matrix Vij is unitary with 4 independent fundamental parameters (including 1 irreducible complex phase) • Magnitude of elements strongly ranked (leading to ~diagonal form) • Choice of overall complex phase arbitrary – only Vtd and Vub have non-zero complex phases in Wolfenstein convention • Measuring SM CP violation  Measure complex phase of CKM elements CKM phases (in Wolfenstein convention) CKM magnitudes l l3 l l2 l3 l2 Some of the real elements in the Wolfenstein convention may have small O(l4) complex phases l=cos(qc)=0.22 Wouter Verkerke, NIKHEF

  5. Visualizing the phase – the unitarity triangle • Phases of CKM elements Vtd and Vub are related to CPV in SM • Visualization: b and g are two angles of a triangle. • Surface of triangle is proportional to amount of CPV introduced by CKM mechanism Wouter Verkerke, NIKHEF

  6. Amplitude phases and observables CP violation • How do complex phase affect decay rates • Only affects decays with >1 amplitude • Decay rate  |A|2 phase of sole amplitude does not affect rate • Consider case with 2 amplitudes with same initial and final state - Decay rate  |A1 + A2|2 2 = + |A1|2 + |A2|2 + 2|A1||A2| cos(f1-f2) A1 = |A1|*exp(if1) A2 = |A2|*exp(if2) |A1| + = f1 f2 A1+A2 |A2| Wouter Verkerke, NIKHEF

  7. A1+A2 A1+A2 Amplitude phases and observables CP violation • Observable summed amplitude clearly depends on phase difference + + = CP CP CP CP |A1| = + f1  f2 A1+A2 |A2| |A1| = + f1  f2 A1+A2 A1+A2 |A2| |A1| = + f1  f2 Wouter Verkerke, NIKHEF A1+A2 |A2|

  8. A1+A2 A1+A2 A1+A2 Amplitude phases and observables CP violation • Dependence on Df scales with amplitude ratio • Observation in practice requires amplitudes of comparable magnitude + + = CP CP CP CP |A1| = + f1  f2 A1+A2 |A2| |A1| = + f1  f2 A1+A2 |A2| |A1| = + f1  f2 Wouter Verkerke, NIKHEF A1+A2 |A2|

  9. Measuring the CKM phases from CP violation • Decay rate of interfering amplitudes sensitive to phase difference • How disentangle weak phase from overall phase difference between amplitudes? • Exploit that weak phase flips sign under CP transformation • Look at decay rates for B f and B  f CP hadronization CP CP hadronization Wouter Verkerke, NIKHEF

  10. + How the weak phase introduces observable CPV • Effect of weak phase sign flip on interfering amplitudes Bf A=a1+a2 +f d = A a2 CP CP a1 CP related to fweak A=a1+a2 Bf d + = -f A CP a1 CP a2 Wouter Verkerke, NIKHEF

  11. a2 A + +fweak a1 a1 -fweak A a2 But not always… • Effect of weak phase sign flip on interfering amplitudes Bf A=a1+a2 = CP =0, need d≠0 too! Bf A=a1+a2 + = CP CP Wouter Verkerke, NIKHEF

  12. A clean way to measure the CP angle b • Find 2 interfering amplitudes with relative weak phase b • Requires CKM element Vtd • Vtd appears twice B0-B0 mixing process • Mixing process introduces a weak phase of 2band a CP-invariant phase of p/2 • Find process with two interfering amplitudes: one with mixing and one without • B  f • B  B  f • Final state f must be CP eigenstate as both B and B must decay into it phase = fdecay Df = fmixing phase = fdecay+ fmixing Wouter Verkerke, NIKHEF

  13. The golden mode B0  J/y KS • An experimentally and theoretically clean CP eigenstate fCP with no weak phase of its own is B0 J/y KS • But mixing amplitude is decay time dependent B0 f B0  B0  f B0 – B0 mixing oscillation vs decay time B0 B0  f amplitudeis decay time dependent Interference and observableCPV is decay time dependent Maximal CPV when amplitudesequal, around t = 2pDmd ~= 2tB All initial flavor 50%/50% N(B0)-N(B0) N(B0)+N(B0) All opposite flavor Wouter Verkerke, NIKHEF 2pDmd 2tB

  14. The golden mode B0  J/y KS • When mixed and unmixed amplitude are of equal magnitude • Working out the more general case gives N(B0  f) |A|2  (1-cosf)2+sin2f = 1 -2cosf+cos2f+sin2f = 2-2cos(p/2+2b)  1-sin(2b) + = sin(f) p/2+2b 1-cos(f) CP + = sin(f) p/2-2b N(B0  f) (1+cosf)2+sin2f = 2+2cos(p/2-2b)  1+sin(2b) 1+cos(f) Generalized for any decay time (0 if |l|=1) (sin(2b) if |l|=1) Even more general form that also allows for CP violation in decay amplitude Wouter Verkerke, NIKHEF

  15. The golden mode B0  J/y KS • What will it look like? • Why is it ‘golden’? • Virtually free of Standard Model pollution. Next largest decay amplitude for B0 J/y KShas same weak phase as leading diagram. • Theoretical uncertainty on procedure of order 1% Maximal CPV if A(Bf)=A(BBf) PRL 88,221803 Wouter Verkerke, NIKHEF

  16. The PEP-II B factory – specifications • Produces B0B0 and B+B- pairs via Y(4s) resonance (10.58 GeV) • Asymmetric beam energies • Low energy beam 3.1 GeV • High energy beam 9.0 GeV • Boost separates B and B and allows measurement of B0 life times • Clean environment • ~28% of all hadronic interactions is BB (4S) BB threshold Wouter Verkerke, NIKHEF

  17. PEP-II top lumi: 9.2x1033 cm-2s-1 ~10 BB pairs per second Continuous ‘trickle’ injection Reduces data taking interruption for ‘top offs’ Integrated luminosity PEP-II delivered: 254 fb-1 BaBar recorded: 244 fb-1 Most analyses use 205fb-1 of on-peak data (227M BB pairs) The PEP-II B factory – performance Lumi recorded each day beam currents Integrated luminosity beam currents Wouter Verkerke, NIKHEF

  18. The BaBar experiment • Outstanding K ID • Precision tracking (Dt measurement) • High resolution calorimeter • Data collection efficiency >95% Electromagnetic Calorimeter (EMC) 1.5 T Solenoid Detector for Internally reflected Cherenkov radiation (DIRC) SVT: 5 layers double-sided Si. DCH: 40 layers in 10 super- layers, axial and stereo. DIRC: Array of precisely machined quartz bars. . EMC: Crystal calorimeter (CsI(Tl)) Very good energy resolution. Electron ID, p0 and g reco. IFR: Layers of RPCs within iron. Muon and neutral hadron (KL) Drift chamber (DCH) Instrumented Flux Return (IFR) Silicon Vertex Detector (SVT) Wouter Verkerke, NIKHEF

  19. Silicon Vertex Detector Readout chips Beam bending magnets Beam pipe Layer 1,2 Layer 3 Layer 4 Layer 5 Wouter Verkerke, NIKHEF

  20. Čerenkov Particle Identification system • Čerenkov light in quartz • Transmitted by internal reflection • Rings projected in standoff box • Thin (in X0) in detection volume, yet precise… Wouter Verkerke, NIKHEF

  21. Selecting B decays for CP analysis • Principal event selection variables • Exploit kinematic constraints from beam energies • Beam energy substituted mass has better resolution than invariant mass Energy-substituted mass Energy difference Event shape s(DE)  15 MeV s(mES)  3 MeV BB events qq events (q=u,d,s,c) Wouter Verkerke, NIKHEF

  22. Collecting CP event samples • Collect as many (cc)s decay modes as possible in increase statistics Wouter Verkerke, NIKHEF

  23. Measuring (time dependent) CP asymmetries • Need to measure N(B0 f) and N(B0  f) • So need to know initial flavor of decay. Exploit fact that B0B0 system evolves coherently  Flavor of ‘other B’ tags flavor of B0  f at t=0 • Measure N( Y(4s)  B0( fflav)B0( fCP) ) , N( Y(4s)  B0( fflav)B0( fCP) ) and decay time difference Vertexing Tag-side vertexing ~95% efficient B-Flavor Tagging sz170 mm sz70 mm Dt=1.6 ps  Dz 250 mm Exclusive B Meson Reconstruction Wouter Verkerke, NIKHEF Dz/gbc

  24. Flavor tagging Determine flavor of Btag BCP(Dt=0)from partial decay products Leptons : Cleanest tag. Correct >95% Full tagging algorithm combines all in neural network Four categories based on particle content and NN output. Tagging performance e- e+ W- W+ n n b b c c Kaons : Second best. Correct 80-90% efficiency mistake rate W- W+ c c K- s s b K+ b W- u u Q = 30.5% W+ d d Wouter Verkerke, NIKHEF

  25. Putting it all together: sin(2b) from B0 J/y KS B0(Dt) B0(Dt) ACP(Dt) = Ssin(DmdDt)+Ccos(DmdDt) • Effect of detector imperfections • Dilution of ACP amplitude due imperfect tagging • Blurring of ACP sine wave due to finite Dt resolution sin2b Imperfect flavor tagging Dsin2b Finite Dt resolution Wouter Verkerke, NIKHEF Dt Dt

  26. Measurement method: tagging efficiency & time resolution • Flavor tagging performance and decay time resolution are measured from sample of Y(4s)  B0(fflav) B0(fflav) events • Determine flavor of 1st B with usual flavor tagging algorithm • Determine flavor of 2nd B from explicit reconstruction in flavor eigenstate 1 Imperfect flavor tagging D Finite Dt resolution Wouter Verkerke, NIKHEF

  27. (cc) KS (CP odd) modes hep-ex/0408127 Combined golden modes result for sin2b J/ψKL (CP even) mode sin2β = 0.722  0.040 (stat)  0.023 (sys) No evidence for additional CPV in decay |λ|=0.950±0.031(stat.)±0.013 (2002 measurement: sin(2β) = 0.741±0.067±0.034) Wouter Verkerke, NIKHEF

  28. Consistency checks J/ψKS(π+π-) Lepton tags ηF=-1 modes Χ2=1.9/5 d.o.f. Prob (χ2)=86% Χ2=11.7/6 d.o.f. Prob (χ2)=7% Wouter Verkerke, NIKHEF

  29. Standard Model interpretation 4-fold ambiguity because we measure sin(2b), not b Measurement of sin(2b) now real precision testof Standard Model 2 1 without sin(2b) Results are still statistics dominated and will be for the foreseeable future h 3 4 r Wouter Verkerke, NIKHEF Method as in Höcker et al, Eur.Phys.J.C21:225-259,2001

  30. Standard Model interpretation 4-fold ambiguity because we measure sin(2b), not b Measurement of sin(2b) now real precision testof Standard Model 2 1 Results are still statistics dominated and will be for the foreseeable future with sin(2b) h • Four-fold ambiguity becausewe measure sin(2b), not b • b  -b, b  b+p • We can eliminate 1st ambiguity if we also know cos(2b) • More precisely, we only need to know the sign of cos(2b) 3 4 r Wouter Verkerke, NIKHEF Method as in Höcker et al, Eur.Phys.J.C21:225-259,2001

  31. Measuring cos(2β) with B0→J/ψK*0(KSπ0) • Decay B0 J/ψ K*0(KSp0) is one of charmonium samples used to measure sin(2b) • But it is a scalar  vector vector decay, so there are 3 decay amplitudes with different polarizations • Composition in terms of amplitudes (in transversity basis) • A0 – Longitudinal polarization (57%) • A// – Transverse polarization (20%) J/y and K* polarization parallel • AT – Transverse polarization, (23%) J/y and K* polarization perpendicular • In sin2b measurement we account for this by using a weighted average of CP eigenvalues of +0.51 CP-even (h=+1) CP-odd (h=-1) Wouter Verkerke, NIKHEF

  32. Measuring cos(2β) with B0→J/ψK*0(KSπ0) • But if you also include angular information from the decay products you can disentangle the 3 amplitudes • Many extra terms in time-dependent decay rate, includingtwo that are proportional to cos(2β) : angular amplitudes decay angles: Wouter Verkerke, NIKHEF

  33. Measuring cos(2β) with B0→J/ψK*0(KSπ0) • We know many of the amplitudes, phase differences • From measurement of B±→J/yK*±and B0→J/yK*0 (K+p-) using time-integrated angular analysis Amplitude phase differences(with 2-fold ambiguity) Amplitude magnitudes “solution 1” “solution 2” Plug into time dependent cross section Wouter Verkerke, NIKHEF

  34. Measuring cos(2β) with B0→J/ψK*0(KSπ0) • We know many of the amplitudes, phase differences • From measurement of B±→J/yK*±and B0→J/yK*0 (K+p-) using time-integrated angular analysis PROBLEM! We don’t know the sign of the phase difference, so we can only measure cos(2b) except for its sign But to break the ambiguity in b we precisely need the sign! Amplitude phase differences(with 2-fold ambiguity) Amplitude magnitudes “solution 1” “solution 2” Plug into time dependent cross section Wouter Verkerke, NIKHEF

  35. K*0(890) (P-wave) Non-resonant (S-wave) Measuring cos(2β) with B0→J/ψK*0(KSπ0) • Solution: find a new way to measure the sign of the phase differences d//-d0 and dT-d0 • Central idea: include (Kp) S-wave in angular analysis ‘non-resonant events’: • Extra terms due to interference of S-wave and P-wave contributions to Kp final state and help solve the ambiguity Wouter Verkerke, NIKHEF

  36. ○ solution 1: unphysical solution BABAR OR ● solution 2: physical solution ○ LASS data Breaking the ambiguity • Why it works: Phase difference ds-d0 has special property as consequence of Wigner causality: Physical solution must have negative slope around m(K*) “solution 1” (ds-d0)/p “solution 2” mKp (GeV/c2) Wouter Verkerke, NIKHEF

  37. hep-ex/0411016 cos(2β) with B0→J/ψK*0(KSπ0) – result • cos(2β) from 104 tagged B0→J/y(KSp0)*0 decays • Now quantify probability that sign of cos(2b) >0 • Use MC approach to include non-Gaussian effects with floating sin(2β) with sin(2β) fixed to 0.731 Negative value ofcos(2b) excludedat 86.6% CL distribution of cos(2β) results from a set of 2000 data-sized Monte Carlo samples, generated with cos(2β)=0.68 Wouter Verkerke, NIKHEF

  38. Standard Model interpretation Measurement of sin(2b) now real precision testof Standard Model 2 1 Results are still statistics dominated and will be for the foreseeable future h Solutions 2 & 4 excluded at 86.6% CL 3 4 r Wouter Verkerke, NIKHEF Method as in Höcker et al, Eur.Phys.J.C21:225-259,2001

  39. 3 Switching from charmonium to penguin modes • Golden mode B0  J/y KS now precision measurement of CKM CPV • But CPV also a good place to look for signs of new physics • ‘New Physics’ couplings are expected to have non-zero phases, and may cause deviations in measured CPV • Good place to look for new physics are loop diagrams • Loop diagrams are dominated by heavy particles in the loop  contribution of new physics may be non-negligible • Look at decay modes where loop diagram is leading order: bs penguins charmonium decay (fweak=0) bs penguin decay (fweak=0) new physics? f K0 Wouter Verkerke, NIKHEF

  40. 3 3 Switching from charmonium to penguin modes • Measurement works otherwise as usual • Interfere decay amplitude with mixing + decay amplitude • Also works with several other decay amplitudes (h’K0, f0K0,…) • Leading order SM for CPV is same as golden modes • But not all modes are as clean as B0 J/y KS golden mode, so • Watch for other SM decay amplitudes that contribute, e.g. f=2b f=0 f=0 f , But highly suppressed as |Vub| tiny f = g! Wouter Verkerke, NIKHEF

  41. Penguin olympia – ranking channels by SM pollution Naive (dimensional) uncertainties on sin2 Decay amplitude of interest SM Pollution f f Gold Silver Bronze Wouter Verkerke, NIKHEF Note that within QCD Factorization these uncertainties turn out to be much smaller !

  42. Selecting penguin decays – Experimental issues • From an experimental point of view, penguin decays are more difficult to select • Signal branching fraction O(20) times smaller • Particle identification more challenging (high-p K± PID vs l± PID) • Basic fit strategy same as for J/y KS except • Strong DIRC Particle ID to separate pions from kaons • Event shape monomials (L0,L2), and B kinematics optimally combined in Multivariate Analyzer [MVA] • Neural Network (NN) or Fisher Discriminant • 6-dimensional ML fit using (1) beam-energy substituted B mass (mES), (2)B-energy difference (E), (3) the resonance mass,(4) the resonance decay angle, (5)the Multivariate Analyzer, and (6) t Cherenkov PID performance Wouter Verkerke, NIKHEF

  43. hep-ex/0502019 Selection of ‘golden penguin mode’ B0  K0 • Modes with KS and KLare both reconstructed (Opposite CP) full background continuum bkg 114 ± 12 signal events 98 ± 18 signal events Plots shown are ‘signal enhanced’ through a cut on the likelihood on thedimensions that are not shown, and have a lower signal event count Wouter Verkerke, NIKHEF

  44. CP analysis of ‘golden penguin mode’ B0  K0 (Opposite CP) S(fKS) = +0.29 ± 0.31(stat) S(fKL) = -1.05 ± 0.51(stat) Combined fit result(assuming fKL and fKS have opposite CP) Standard Model Prediction S(fK0) = sin2b = 0.72 ± 0.05 C(fK0) = 1-|l| = 0 0.9s hfK0 Wouter Verkerke, NIKHEF

  45. Reaching for more statistics – B0  K0 revisited • Analysis does not require that ss decays through f resonance, it works with non-resonant K+K- as well • 85% of KK is non-resonant – can select clean and high statistics sample • But not ‘golden’ due to possible additional SM contribution with ss popping • But need to understand CP eigenvalue of K+K-KS: • f has well defined CP eigenvalue of +1, • CP of non-resonant KK depends angular momentum L of KK pair • Perform partial wave analysis • Estimate fraction of S wave (CP even) and P wave (CP odd) and calculate average CP eigenvalue from fitted composition K+K- Nsig = 452 ± 28(excl.  res.) OK Not OK Wouter Verkerke, NIKHEF

  46. CP analysis of B  K+K- KS • Result of angular analysis • Result consistent with cross checkusing iso-spin analysis (Belle) • Result of time dependent CP fit hfSK+K-KS/(2fCP-even-1)] = +0.55 ±0.22 ± 0.04 ±0.11 Wouter Verkerke, NIKHEF (stat) (syst) (fCP-even)

  47. Large statistics mode Reconstruct many modes ’   + –, 0      ,  + –0 KS + – ,00 Modest statistics mode CP analysis more difficult Requires thorough estimate of CP dilution due to interference in B0   +–KS Dalitz plot hep-ex/0502017 hep-ex/0406040 The Silver penguin modes: B0 h’KS & B0  f0KS B0 f0(980)KS B0 h’KS Fit finds 152 ± 19 events Fit finds 819 ± 38 events Wouter Verkerke, NIKHEF

  48. The Silver penguin modes: B0 h’KS & B0  f0KS B0 f0(980)KS B0 h’KS hfK0 hfK0 sin2 [cc] @ 0.6 sin2 [cc] @ 3.0 Wouter Verkerke, NIKHEF

  49. hep-ex/0503018 The bronze penguin modes: B0 w KS (New!) • Modest statistics mode (BF  5 x 10-6) Nsig = 96 ± 14 sin2 [cc] @ 0.7 Wouter Verkerke, NIKHEF

  50. hep-ex/0408062 The bronze penguin modes: B0 p0 KS • Experimentally challenging! – Construct decay vertex, decay time without tracks from primary vertex • Use beam line as constraint • Use only KS decays with at least 4 hits in the silicon tracker to obtain required precision, ~60% meets requirements KS beam line p0 hfK0 sin2 [cc] @ 1.3 Wouter Verkerke, NIKHEF

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