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F. Mart í nez-Vidal IFIC – Universitat de Val è ncia-CSIC

Measurement of the CKM-matrix angle g ( f 3 ) (at B Factories). International WE Heraeus Summer School on Flavor Physics and CP Violation Technische Universität Dresden (Germany) September 2 nd , 2005. Outline Introduction: CKM, UT and CPV observables Access to g

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F. Mart í nez-Vidal IFIC – Universitat de Val è ncia-CSIC

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  1. Measurement of the CKM-matrix angle g (f3)(at B Factories) International WE Heraeus Summer School on Flavor Physics and CP Violation Technische Universität Dresden (Germany) September 2nd, 2005 Outline Introduction: CKM, UT and CPV observables Access to g Experiments & analysis techniques Dalitz analysis Conclusions and perspectives F. Martínez-Vidal IFIC – Universitat de València-CSIC

  2. Introduction F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  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 • Complex phases in Vij are the origin of SM CP violation • Observing SM CP violation  access to CKM angles (in Wolfenstein convention) 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 Transition amplitude violates CP if Vub ≠ Vub*, i.e. if Vub has a non-zero phase F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  4. Visualizing the phase – the “db” unitarity triangle CKM phases (in Wolfenstein convention) Surface proportional to amount of SM CPV • and gare the two angles of the triangle (a=p-b-g) Phase of Vub (bu transition) Phase of Vtd (B0-B0 mixing) Vtd Vtd F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  5. Observables in CPV: interfering amplitudes 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| • How do complex phase affect decay rates (the basic input for any CPV observable)? • Decay rate  |A|2 phase of sole amplitude does not affect rate • Case: 2 amplitudes with same initial and final state • Decay rate  |A1 + A2|2 F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  6. Observables in CPV: interfering amplitudes A1+A2 A1+A2 • Total interfering amplitude 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 A1+A2 |A2| F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  7. Observables in CPV: interfering amplitudes A1+A2 A1+A2 A1+A2 • Dependence on phase difference 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 A1+A2 |A2| F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  8. Observables in CPV: weak phase • How disentangle weak phase from overall phase difference between amplitudes? • Weak phase flips sign under CP transformation (CP-odd) • Look at decay rates for B f and B  f CP hadronization CP CP hadronization F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  9. Observables in CPV: asymmetries …obviously, CP asymmetries depend on the weak-phase + Bf A=a1+a2 +f d = A a2 CP CP a1 CP depends on fweak A=a1+a2 Bf d + = -f A CP a1 CP a2 F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  10. Observables in CPV: asymmetries a2 A + +fweak a1 a1 -fweak A a2 • …but also the CP-even (strong) phase Bf A=a1+a2 = CP =0  need d≠0 ! Bf A=a1+a2 + = CP CP F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  11. Access to g F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  12. Access to g: B-D0K- Vub   Vcb Cabibbo & color favored (Cabibbo & color)-suppressed u K- D0 b B- b c B- D0 K- A(D0K-)l3 A(D0K-)l3ei(dB-g) relativestrong&weakphases Atot=A+A • Size of CP asymmetry depdens on • CF[CS] ~(0.2-0.6) ×) • Larger rB larger interference larger sensitivity to g ~0.4 rB |A/A|~0.1-0.3 PLB557,198(2003) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  13. Access to g: B-D0K- • Different incarnations of same principle (all theoretically clean) • CP violation effects depend on • g: weak phase difference between B decay amplitudes • dB: strong phase difference between B decay amplitudes • rB: relative magnitude of B decay amplitudes • dD : strong phase difference of D decay amplitudes • rD: relative magnitude of D decay amplitudes • For multi-body D decays, last two described by Dalitz decay model Gronau, London, Wyler Use B-D0[CP±]K-decays PLB253, 483 (1991) PLB265, 172 (1991) GLW Atwood, Dunietz, Soni Use B-D0[K+p-]K- and B-D0[K-p+]K- decays ADS PRL78, 3257 (1997) PRD63, 036005 (2001) PRD68, 054018 (2003) PRD70, 072003 (2004) Dalitz (GGSZ) Bondar (Belle), Giri, Grossman, Soffer, Zupan Use multibody D decays, eg. B-D0[K0Sp+p-]K- decays F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  14. GLW method 3 independent measurements (ACP+ RCP+ = - ACP- RCP-) vs 3 unknowns (rB, dB, g) 8-fold g ambiguity (rB,dB) different for BD0K, BD*0K, BD0K* • Reconstruct BD(*)0K(*) with CP-even and CP-odd D0/D0 final states • CP modes: quite small D0 branching ratio: e.g. Br(D0K+K-)~4x10-3 • Many modes: • CP-even : K+K-, p+p- CP-odd : KSp0, KSw, KSf, KSh • Observables Normalize to D0 decay into flavour state (eg. K-p+) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  15. ADS method • Same idea as for GLW method, but different D0 final state: doubly-Cabibbo-suppressed decay, [K+p-]D , instead of CPES • Small BFs (~10-6), but amplitudes of comparable size expect maximum CPV • Observables: PLB592, 1 (PDG2004) rD2 = (0.3650.021)% dD: D decay strong phase unknown (scan all values) No DCS signal so far… 2 independent measurements vs 3 unknowns (rB, dB, g) The system can be solved with BD*0K decays PRD70, 091503 (2004) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  16. Dalitz method • Reconstruct BD(*)0K(*) with Cabibbo-allowed D0/D0KSp+p- • If D0/D0 Dalitz f(m+2,m-2) is known (included charm phase shiftdD): B-: B+: No D mixing No CP violation in D decays 2 Schematic view of the interference |M-|2 = • Relatively large BFs: BF[(B  D0K)(D0K0 )]=(2.20.4)10-5 • Only charged tracks in final state  high efficiency/low bkg • g ambiguity only 2-fold (g ↔ g+p) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  17. Dalitz method: sensitivity to g weight = • Sensitivity varies strongly over Dalitz plane • Second derivative of the log(L) event-by-event  weight the event points : weight = 1 The highest the weight the more important the event forgmeasurement DCS D0 K*(892)+p- D0 KSr rB=0.12 g=70° d=180° DCS D0 K0*(1430)+p- F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  18. Access to 2b+g: B0D(*)+p-/r- Similarly: golden  mode at LHCb Use interference between PLB427, 179 (1998) Doubly-Cabibbo suppressed b  u transition Favored b  c transition Vcd V*ub V*ud u,c,t Vcb u,c,t ~l4 ~l2 ~0.02 from moduli (small CP asymmetry, ~2%) • Favored decay has “large” branching ratio (~0.3-0.8%) • …but need huge statistics partial and full reconstruction • rB(*) must be obtained from external measurements + SU(3) (theory error 30%, under discussion among theorists) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  19. Experiments & analysis techniques F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  20. Experiments: BaBar at PEP-II (SLAC) “Storied Royal Elephant” 1.5T solenoid DIRC (PID) 144 quartz bars 11000 PMs EMC 6580 CsI(Tl) crystals e+ (3.1GeV) Drift Chamber 40 stereo layers e- (8.9 GeV) Silicon Vertex Tracker 5 layers, double-sided sensors Instrumented Flux Return iron / RPCs/LSTs (muon / neutral hadrons) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  21. Experiments: Belle at KEK-B (KEK) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  22. Analysis techniques • Reconstruct D0/D*0 mesons in the various decay modes • Combine with fast tracks K/p/K* to make B candidates Particle ID Primary K/p separation uses DIRC (qC) Combine dE/dx from SVT and DCH Aerogel+ToF+dE/dx Information combined into likelihoods Wide momentum coverages Check high momentum performance with D*D0p samples F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  23. Analysis techniques • Veto significant/potentially dangerous B decay backgrounds • E.g. B-[p+p-]DK- has background from B- [p+K-]Dp- • Suppress continuum e+e-qq (q=u,d,s,c) background using • Angular distribution: B flight direction • Event shape variables: • Signal: almost at rest • Background: “jetty” • Use multivariate variables • Fisher discriminant • Neural Net • Resonance masses, decay angles, helicity in PPV, VPP decays (eg. DKSw, K*-KSp-) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  24. Analysis techniques • Cut based signal selection • Signal region maximum Likelihood fit: • CP parameters • Global Maximum Likelihood fit: • Yields (signal + bkg) • CP parameters • Characterize B candidates using • Beam constrained mass: • B mesons produced almost at rest • Resolution ~3 MeV dominated by beam energy spread • Energy difference: • Energy of B candidate almost equal to half beam energy • Resolution ~10-50 MeV depends on neutrals in final state • Select best B candidates based on invariant masses of daughter particles • Signal extracted using maximum likelihood fits to mES, DE, Fisher, PID, etc. • Use sidebands and control samples to check backgrounds F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  25. Example: exclusive reconstruction of B-D0K*- Y(4S) =1 for signal events K*- B- D0 KSp+ p- KSp+ p+p- p+p- F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  26. Dalitz analysis F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  27. D0 KSp+p-Dalitz model • Dalitz method requires knowledge of • |f(m+2,m-2)| can be extracted from tagged D0 rates from e+e- continuum • Tag using charge of soft pion from D*+  D0p+ decays • …but phase difference variation dD(m+2,m-2) requires assumption of Dalitz model • In the isobar model formalism a three-body D0 decay proceeds mostly via 2-body decays (1 resonance + 1 particle) • With CP-tagged DKSp+p- decays the amplitude is • Can use tagged D mesons from CLEO-c to measure directly cosdD, removing (or largely reducing) the model dependence D0ABC decaying through a resonance r=[AB] PRD63, 092001 (2001) PRL89, 251802 (2002) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  28. D0 KSp+p-Dalitz model: nominal H. Pilkuhn, The interactions of hadrons, North-Holland (1967), Amsterdam Angular dependence Vertex form factors of the D0 meson and the resonance r (model underlying quark structure of the D0 and the resonance r) Usually, parameterized using Blatt-Weisskopf penetration factors J. Blatt and V. Weisskopf, Theoretical Nuclear Physics. John Wiley & Sons (1952), New York • The D0 amplitude fADcan be parameterized as a coherent sum of Breit-Wigner amplitudes (quasi 2-body terms) plus a constant term (non-resonant) Relative amplitudes and phases Lorentz invariant amplitude for resonance r containing angular dependence Relativistic Breit-Wigner with mass dependent width sij=[s12,s13,s23] depending on the resonance KSp-(m-2), KSp+(m+2), p+p- F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  29. D0 KSp+p-Dalitz model: nominal 82k tagged D0 events, 97% purity • 17 amplitudes: 13 distinct resonances + 3 DCS K* resonances + 1 non-resonant term • Not so good for p+p- S-waveneed controversial s(500) and s’(1000) scalars to describe reasonably well the data • Masses and widths fixed to PDG2004 values except for s and s’ (fitted) CA K*(892) r(770) DCS K*(892) hep-ex/0504039 c2/dof3824/3022=1.27 F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  30. D0 KSp+p-Dalitz model: nominal • D0 decay model identical to BaBar • 19 amplitudes: 13 distinct resonances + 5 DCS K* resonances[same as BaBar + DCS K*(1680) + DCS K*(1410)] + 1 non-resonant term DCS K*(892) • DCS K*(1680) and DCS K*(1410) excluded in BaBar model because: • number of expected events is very small • the K*(1680) and the DCS K*(1680) overlap in the same Dalitz region  the fit returns ~ the same CA and DCS amplitudes r(770) CA K*(892) c2/dof2.30 (dof=1106) PRD70, 072003 (2004) hep-ex/0411049 F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  31. D0 KSp+p-Dalitz model: nominal • The relative amplitudes arand phases dras obtained from the ML fit Sum of fit fractions : 124% Sum of fit fractions : 123% F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  32. D0 KSp+p-Dalitz model: no s scalars • s(500) scalar seems to be confirmed by BES Collaboration • And Dalitz fit to tagged D0 KSp+p- sample is clearly much worse La Thuile G. Li, BES Collaboration BJ/ data c2/dof4757/3022=1.57 vs 1.27 F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  33. D0 KSp+p-Dalitz model: no s scalars • …but adding BW’s in the isobar model: • breaks the unitarity of the S (scattering) matrix • BW is only valid for single, isolated resonance • For broad, overlapping and many channel resonances we need a more general approach  K-matrix formalism (Argand diagram) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  34. D0 KSp+p-Dalitz model: K-matrix for pp S-wave • K-Matrix formalism overcomes the main limitation of the BW model to parameterize large and overlapping S-wave pp resonances • non trivial dynamics due to presence of broad, overlapping, and many channel resonances • avoid introduction ad hoc of not established s scalars • By construction unitarity is satisfied: • S: scattering operator • T : transition operator • r : phase space matrix • K-matrix D0 3-body amplitude pp S-wave amplitude K-matrix (decay) initial production vector (production) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  35. D0 KSp+p-Dalitz model: K-matrix for pp S-wave • Use V.V. Anisovich & A.V. Sarantev parameterization Eur.Phys.Jour.A16, 229 (2003) Adler zero term to accommodate singularities coupling constant of the K-matrix pole mato the ith channel: 1=pp, 2=KK, 3=multi-meson (4p), 4=hh, 5=hh´ slow varying parameter of the K-matrix element (non-resonant), with F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  36. D0 KSp+p-Dalitz model: K-matrix for pp S-wave • 9 distinct resonances + 3 DCS K* resonances + K-matrix pp S-wave r(770) ppS-wave term (c2/dof~unchanged) Sum of fit fractions : 116% Unitarity guaranteed for pp S-wave component (by construction) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  37. B-D(*)0K(*)- selection D0K D*0(D0p0)K D*0(D0g)K D0K*[KSp] hep-ex/0504039 Hep/ex-0507101 227×106BB D0K**[KSp] D0K D*0K hep-ex/0411049 hep-ex/0504013 275×106BB F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  38. B-D(*)0K(*)- Dalitz plot distributions B+D0K+ B-D0K- B+D0K+ B-D0K- Differences between B+ and B- signifies direct CP violation F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  39. Some peculiarities: B-D*0K- strong phase PRD70, 091503 (2004) • For B-D*0K- decays • D*± decaying into CP eigenstates D0p0,D0g • hD* = hp,ghD(-1)l=1 , l=1 for parity/angular momentum conservation • hg= -1⋅hp • D*±→D0±p0 • D*±→D0∓g Opposite CP eigenstate Effective strong phase shift of p between D0p0 and D0g helps in the determination of g F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  40. Some peculiarities: B-D0K*- amplitude • The K*-(892) has an non-zero intrinsic width (~50 MeV)  B Dalitz plot • Selection of B±→DK*[KSp] decays results in the interference of B±→DK*± • and B±→D[KSp±]non-K* • A general parameterization of the B±→D[KSp±] decay amplitude can be found wich accounts by construction for the K* and non-K* contributions p= B decay phase space point A = real amplitude XS=[KSp] state F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  41. Some peculiarities: B-D0K*- amplitude • Let us introduce now the following notation: • And the effective CP parameters • The general decay rate is then: • The effective CP parameters xS±, yS±, rS2depend on the phase space selected region without introducing any bias on the g measurement hep-ex/0211282 If K*- intrinsic width ~ 0 (K- case) k=1, dS=dB, rS=rB F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  42. Fit results Determine x=rBcos(dBg), y=rBcos(dBg), for each decay mode from ML fit to B+ and B- Dalitz distributions y y D*0K yS D0K B+ D0K* B- B+ d d d B+ B- B- x xS x 1- and 2-s contours for n=2 dof (DlnL= 0.5, 1.921) y y yS D0K* D0K D*0K B+ B+ B- d d d B- B+ B- x x xS F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  43. From (x,y) to g, dB and rB Measured CP parameters: (x,y)  B decay mode  12-dimensional space Excellent Gaussian behavior Frequentist distillery (Neyman’s construction for confidence intervals) Perform ~1010 pseudo-experiments (Toy Monte Carlo) (g,dB,rB) parameters: (rB,dB)  B decay mode and g  7-dimensional space Non-Gaussian for low stat. samples & near physical boundary (rB>0) D0K D*0K D0K* (stat.+syst. uncertainties) 1- and 2-s contours for n=7 dof 2 fold (±p) ambiguities for both g and dB rB rB krS F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  44. g, dB and rB results non-K* systematic error since non-K* contribution neglected in nominal fit The importance of rB … (amin where CP is conserved, ie. rB=0 or g=0) Significance of direct CPV 2.3s 2.4s …getting close to evidence F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  45. Comments on systematic uncertainties • Experimental systematic uncertainty accounts for: • PDF shapes of selection variables (mES, DE, Fisher, etc.) • Background fractions and Dalitz shapes • Efficiency variations across Dalitz plane (including tracking efficiency) • Invariant mass resolution • Biases from control samples • Dalitz model systematic uncertainty includes: • No s scalars • By far, the dominant contribution: ~11o • Using K-matrix pp S-wave model, the effect goes down to ~3o • Not yet used in current measurement (conservative for now) • Other variations have much smaller effects (ie. fine tuning of model ~ little effect on g): • fit uncertainty of the phases and amplitudes from D0 tagged sample fit • Vertex form factors FD=Fr=1 • Constant BW width • Alternative lineshape for r (Gounaris-Sakurai) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  46. g from DK (all methods) • Constraints on g from WA D(*)K(*) decays • Constraints in the (r,h) plane on g from WA D(*)K(*) decays (GLW+ADS) and Dalitz methods compared to the predictions from the global CKM fit (excluding these measurements) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  47. Conclusions & perspectives F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  48. Conclusions and perspectives • Measurement of g at B Factories seemed an impossible mission few years ago ! • ...certainly is not an easy task (need lot of data, many methods and channels, a lot of brainstorming,...) • 3 clean methods towards extraction of g in place: • ...all hindered by smallness of rB • ...but ready for more precise measurements in the coming few years • Other methods studied or under study (not shown here), but not yet useful • First meaningful measurements already available • Dalitz method is the currently “golden” channel for g, but need all channels and strategies to improve errors and resolve ambiguities • Old Dalitz plot technique is becoming the new paradigm for other measurements too • Getting close to evidence of direct CP violation in DK (3s) • What’s next? F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  49. Conclusions and perspectives • Improving statistical error: • Larger data sample • Goal for B Factories is increase statistics 2x by ’06 and 4x by ~’08. On track... • Add other D0 decay channels: KsK+K-, p+p-p0, KSp+p-p0 Dalitz analysis from a tagged D0 sample 13323 signal events 227×106BB Exclude KSp0 events hep-ex/0207089 hep-ex/0505084 Expected ~90 BD(*)K events in 210 fb-1.Toy MC studies indicate small but not negligible gain on g High background, difficult analysis (but possible). Not clear the gain in g sensitivity F. Martínez-Vidal , Measurements of the CKM-matrix angle g

  50. Conclusions and perspectives • Reduce Dalitz model dependence: • K-matrix for pp S-wave (KSp+p- channel) • Use CP-tagged D mesons decaying to KSp+p- to measure directly the (cosine of) phase difference variation (dD) • Overall, seems feasible an ultimate precision ~ 5o for 2 ab-1 (~2008) • Could be better or worse depending on ultimate value of rB (> or <0.1) F. Martínez-Vidal , Measurements of the CKM-matrix angle g

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