CP Violation in B Decays Lecture III Vivek Sharma University of California at San Diego http://vsharma.ucsd.edu/marialaach05.pdf

Outline of Lecture 3 Reminder: Requirement for CP Violation Three types of CP violation in B Decays General strategy for time-dependent CP asymmetry measurement Effect of Detector imperfections on CP Asymmetry Calibration measurements using data Calibrating the Detector clock Calibrating B flavor mis-identification rate Experimental measurement of sin2 in B (cc) s final states Babar & Belle Perspective from first observation of CP violation in B decays

Conditions for CP violation Two amplitudes, A1 and A2, with a relative CP-violating phase (f2) only No CP violation since magnitudes of A and A are the same! Two amplitudes, A1 and A2, with both a relative CP-violating phase 2 and CP-conserving phase (d2) Now have CP violation!

CP Violation in B Meson System Identify B final states which are arrived at by two paths B Meson is heavy  many final states, multiple “paths.” 2 classes of B decays come into play: “Tree”  spectator decay like “Penguin”  FCNC loop diagrams with u,c,t

CP Violating Effects in B decay Processes CP violation in the interference between two decay amplitudes (“Direct CP violation”) Decay amplitudes must have different CP violating and CP conserving phases. CP conserving phase from strong, final-state interaction, so difficult to interpret results in terms of CKM parameters Can measure in both B0/B0 and B+/B- decays (time-independent) CP violation in B mixing Interference is between bundle of amplitudes with on-shell (real) intermediate states and bundle of amplitudes for off-shell (virtual) intermediate states. CP violating in the interference between mixing and decay amplitudes Occurs in B0 system , one set of CP phases from mixing If only one direct B decay amplitude  has clean CKM interpretation

Reminder: CPV Phase in CKM Matrix

Experimental Results on CP Violation in B Meson system

CPV in Decay aka Direct CP Violation 2  B f

Observation of Direct CPV in B0K- + Loop diagrams from New Physics (e.g. SUSY) can modify SM asymmetry via P Clean mode with “large” rate : Measure charge asymmetry, reject large B background with Particle ID B background signal E (GeV) K separation K separation()

BaBar: First Observation of Direct CPV in B decay ! B0K+ B0K+ BABAR 4.2, syst. included BABAR background subtracted signal enhanced

Confirmation of Direct CPV by Belle at ICHEP04 ACP = -0.101  0.025  0.005 3.9s significance _ B0 K-p+ B0 K+p- 274M BB Signal=2139 53 Establishes CPV not just due to phase of B Mixing (M12) Rules out superweak model of CP violation Non-Pert QCD uncertainties large, SM CPV not precisely predictable  insufficient to prove or rule out contribution from New Physics Amp.

CPV in B0 Mixing 2  B0 f Occurs when Mass eigenstates CP eigenstates (|q/p|1 and<BH|BL> 0) The Box diagrams provide the required 2 phases Strong phases depend on quark masses and non-perturbative physics. Asymmetries are small and hard to calculate precisely (QCD) off-shell states f on-shell states f

CPV in B0 Mixing Time-dependent CP Asymmetry:

Measurement region > 200mm CPV in B0 Mixing Time dependent measurement, time measured from Z BABAR 20.7 fb-1 Sample backgrounds B(Dt): 4.3% continuum 24% direct+cascade 12% direct+fake Measurement region > 200mm

CPV in B0 Mixing BABAR So far, no experimental evidence 20.7 fb-1 So far, no experimental evidence of large CP violation in B0 mixing To a good approximation:

CPV In Interference Between Mixing and Decay + 2  B0 fcp CP asymm. can be very large and can be cleanly related to CKM angles

Tree Penguin:: u,c,t loops 

CPV In Interference Between Mixing and Decay: B0 J/K0 for J/y K0S(L) Same is true for a variety of B (cc) s final states

CPV In Interference Between Mixing and Decay Requires measurement of proper time difference t=t between the decay of Btag and BCP. S C Asymmetry

Time-Dependent CP Asymmetry with a Perfect Detector Perfect measurement of time interval t=t Perfect tagging of B0 and B0 meson flavors For a B decay mode such as B0Ks with |f|=1 sin 2b B0 Asymmetry ACP CPV

Consequences of Detector Imperfections Acp(Dt) F(Dt) Dt(ps) sin2b D sin2b True Dt, Perfect tagging: True Dt, Imperfect tagging: Measured Dt, Imperfect tagging: Must measure flavor tag Dilution. D = (1-2w) where w is mistag fraction. Must measure Dt resolution properties.

Time Dependent CPV Measurement Technique Since the techniques of time-dependent analysis is common to many modes, I will now describe this in detail using the “platinum” mode B0 (cc) K0 from which CP violation in B0 decays was first established. The analysis (from 2002) based on 88 fb-1 is “old” but forms basis for all other time-dependent CPV results that I will present later

CP Violation in Picture z Separate B0 and B0 m- K- bgU(4S) = 0.55 Coherent BB pair B0 B0  J/y Ks Vivek Sharma , UCSD

Time-Dependent CPV Analysis Strategy Factorize the Time Dependent analysis into building blocks Obtain ALL analysis ingredients from DATA (avoid MC) Measurements B±/B0 Lifetimes B0 B0-Mixing CP-Asymmetries Analysis Ingredient Reconstruction of B mesons in flavor specific states B vertex reconstruction Flavor Tagging + a + b Reconstruction of neutral B mesons in CP eigenstates + a + b + c Increasing complexity Higher precision Vivek Sharma , UCSD

Calibrating The BaBar Clock: B Meson Lifetime Measurement

Measurement of the B0 and B+ Lifetime U(4s) bg = 0.55 Tag B sz ~ 110 mm Reco B sz ~ 65 mm p+ Dz Dt @ Dz/gbc K0 g D- p- K+ 3. Reconstruct Inclusively the vertex of the “other” B meson (BTAG) Fully reconstruct one B meson in flavor eigenstate (BREC) Reconstruct the decay vertex 4. compute the proper time difference Dt 5. Fit the Dt spectra Vivek Sharma , UCSD

Fully-Reconstructed B sample Flavor eigenstates Bflav : for lifetime and mixing measurements Cabibbo-favored hadronic decays “Open Charm” decays Neutral B Mesons ~21000 signal Purity: 85% Charged B Mesons Hadronic decays into final states with Charmonium ~20000 signal Purity: 85% [GeV] Vivek Sharma , UCSD

Vertex and Dt Reconstruction Beam spot Interaction Point BREC Vertex BREC daughters BREC direction BTAG direction TAG Vertex TAG tracks, V0s z Reconstruct Brec vertex from charged Brec daughters Determine BTag vertex from charged tracks not belonging to Brec Brec vertex and momentum beam spot and U(4S) momentum High efficiency (97%) Average Dz resolution is 180 mm (<|Dz|> ~ bgct = 260 mm) Dt resolution function measured from data Vivek Sharma , UCSD

tB Measurement: Unusual Situation at (4S) e-t/t true Dt B production point known eg. from beam spot LEP/SLD Dt resolution measured Dt Resolution function lifetime  = e-|Dt|/t Either Brec or Btag can decay first (this analysis) BaBar Resolution Function + Lifetime  = Need to disentangle resolution function from physics ! Vivek Sharma , UCSD

Dt Resolution Function sDz event-by-event s(Dt) from vertex errors Lifetime-like bias to Small correlation between lifetime and Resolution Function parameters ~0.6 ps Signal MC (B0) tracks from long-lived D’s in tag vertex asymmetric Resolution Function Dt (meas-true)/sDt Vivek Sharma , UCSD

Lifetime Likelihood Fit Simultaneous unbinned maximum likelihood fit to B0/B+ samples Use data to extract the properties of background events Mass distribution provides the signal probability Use the events in the sideband (mES < 5.27) to determine the Dt structure of the background events under the signal peak 19 free parameters t(B+) and t(B0) 2 Dt signal resolution 5 empirical background 12 description B0 mES B0 Bkg Dt Vivek Sharma , UCSD

B Lifetime Fit Results B0/ B0 B World’s best measurement 2 % statistical error 1.5% systematic error Main source of systematic error Parameterization of the Dt resolution function Description of events with large measured Dt (outliers) 20 fb-1 B0/ B0 Detector Clock precisely calibrated B signal + bkg PRL 87, 201803 (2001) t0 = 1.546  0.032  0.022 ps PDG: 1.548  0.032 ps t = 1.673  0.032  0.022 ps PDG: 1.653  0.028 ps t/t0 = 1.082  0.026  0.011 PDG: 1.062  0.029 background Dt (ps) Vivek Sharma , UCSD

B Flavor (Mis)Identification (Mistag Knowledge From Data)

Using B Mixing to Measure Flavor Mistag Rate B0 B0 B Lifetime Start with a B0 beam, slowly (compared to B lifetime) a B0 component builds up But no “Mixed” events at t=0. If the detector measures some “mixed” events, it must be because it has measured the flavor of the B incorrectly ( mistag)

Analysis Strategy (II) Measurements B±/B0 Lifetimes B0 B0-Mixing CP-Asymmetries Analysis Ingredient Reconstruction of B mesons in flavor eigenstates B vertex reconstruction Flavor Tagging + a + b Reconstruction of neutral B mesons in CP eigenstates + a + b + c ü Vivek Sharma , UCSD

Measurement of B0B0 Mixing rate Vs t U(4s) bg = 0.55 Tag B sz ~ 110 mm Reco B sz ~ 65 mm p+ Dz Dt @ Dz/gbc K0 g D- p- K+ 3. Reconstruct Inclusively the vertex of the “other” B meson (BTAG) ü 4. Determine flavor of BTAG to separate Mixed and Unmixed events 1. Fully reconstruct one B meson in flavor eigenstate (BREC) ü 2. Reconstruct the decay vertex ü 5. compute the proper time difference Dt ü 6. Fit the Dt spectra of mixed and unmixed events Vivek Sharma , UCSD

Dt Spectrum of Mixed and Unmixed Events perfect flavor tagging & time resolution Decay time diff (t) in ps _ + w: the fraction of wrongly tagged events Dmd: oscillation frequency realistic mis-tagging & finite time resolution Decay time diff (t) in ps Vivek Sharma , UCSD

B Flavor Tagging Methods Hierarchical Tagging Categories For electrons, muons and Kaons use the charge correlation b c d l- n B0 D, D* W- Lepton Tag b d B0 W- W+ c s K*0 Kaon Tag NN output Not Used Multivariate analysis exploiting the other kinematic information of the event, e.g., Momentum spectrum of the charged particles Information from non-identified leptons and kaons Soft p from D* decay Neural Network Each category is characterized by the probability of giving the wrong answer (mistag fraction w) Vivek Sharma , UCSD

Flavor Tagging Performance in Data The large sample of fully reconstructed events provides the precise determination of the tagging parameters required in the CP analysis Tagging category Fraction of tagged events e (%) Wrong tag fraction w (%) Mistag fraction difference Dw (%) Q = e (1-2w)2 (%) Lepton 10.9  0.3 9.0  1.4 0.9  2.2 7.4  0.5 Kaon 35.8  1.0 17.6  1.0 -1.9  1.5 15.0  0.9 NT1 7.7  0.2 22.0  2.1 5.6  3.2 2.5  0.4 NT2 13.8  0.3 35.1  1.9 -5.9  2.7 1.2  0.3 ALL 68.4  0.7 26.1  1.2 Error on sin2b and Dmd depend on the “quality factor” Q approx. as: Highest “efficiency” Smallest mistag fraction BABAR 29.7 fb-1 Vivek Sharma , UCSD

Flavor Tagged B Meson Sample For Mixing Studies psig,i ~ 0 psig,i ~ 0.96 Background properties from sideband events Lepton Lepton Kaon NT1 NT2 Vivek Sharma , UCSD

Dt (or DZ) Resolution Function Use the event-by-event uncertainty on Dt B0 flavour sample CP sample sDt (ps) Dt Residual (ps) R(dDt) Core Tail Outlier Vivek Sharma , UCSD

Mixing Likelihood Fit on Reconstructed B0 Sample Unbinned maximum likelihood fit to flavor-tagged neutral B sample Fit Parameters Dmd 1 Mistag fractions for B0 and B0 tags 8 Signal resolution function 2 x 8 Empirical description of background Dt 16+3 B lifetime fixed to the PDG value tB = 1.548 ps 44 total free parameters All Dt parameters extracted from data Vivek Sharma , UCSD

Mixing Measurement with Fully Reconstructed B Sample T=2/m 1-2w Precision measurement consistent with world average  Well calibrated detector for Flavor tagging Vivek Sharma , UCSD

CP Analysis Analysis Strategy (Step III) Measurements B±/B0 Lifetimes B0 B0-Mixing CP-Asymmetries Analysis Ingredient Reconstruction of B mesons in flavor eigenstates B vertex reconstruction Flavor Tagging + a + b Reconstruction of neutral B mesons in CP eigenstates + a + b + c ü ü Vivek Sharma , UCSD

Measurement of CP Asymmetry U(4s) bg = 0.55 Tag B sz ~ 110 mm CP B sz ~ 65 mm m+ Dz Dt @ Dz/gbc K0 g p+ p- Ks0 m- 3. Reconstruct Inclusively the vertex of the “other” B meson (BTAG) ü 4. Determine the flavor of BTAG to separate Mixed and Unmixed events ü 1. Fully reconstruct one B meson in CP eigenstate (BCP) 2. Reconstruct the decay vertex ü 5. compute the proper time difference Dt ü 6. Fit the Dt spectra of B0 and B0 tagged events Vivek Sharma , UCSD

Charmonium+K0 CP Sample for BABAR (’02) 1506 signal candidates, purity 94% 988 signal candidates, purity 55% BABAR 81.3 fb-1 (after tagging & vertexing) Vivek Sharma , UCSD

Dt Spectrum of CP Events perfect flavor tagging & time resolution realistic mis-tagging & finite time resolution CP PDF Mistag fractions w And resolution function R Mixing PDF determined by flavor sample Vivek Sharma , UCSD

sin2b Likelihood Fit Description Combined unbinned maximum likelihood fit to Dt spectra of Bflav and CP samples Fit Parameters # Main Sample Sin2b 1 Tagged CP sample Mistag fractions for B0 and B0 tags 8 Tagged flavor sample Signal resolution function Empirical description of background Dt 17 Sidebands B lifetime from PDG 2002 tB = 1.542 ps Mixing frequency from PDG 2002 Dmd = 0.489 ps-1 Total parameters 34 Global correlation coefficient for sin2b: 13% All Dt parameters extracted from data Correct estimate of the error and correlations

Control Sample: non-CP sample with CPV=0 Final check of residual detector biases on CP=0 control sample of fully reconstructed, flavor specific sample (BD etc) Input Bflav sample to CP fit No CP asymmetry expected Measure Sample “sin2b” Bflav 0.021±0.022 B+ 0.017±0.025

BABAR Result for sin2b (July 2002) hCP = -1 hCP = +1 sin2b = 0.755  0.074

Pure Gold : (Clean) Lepton Flavor Tags BABAR 81.3 fb-1 220 lepton-tagged hf = -1 events 98% purity 3.3% mistag rate 20% better Dt resolution CP asymmetry is obvious !

Systematic Errors on sin2b from BABAR s[sin2b] Description of background events 0.017 CP content of background components Background shape uncertainties, peaking component Composition and CP content of J/yKL background 0.015 Dt resolution and detector effects Silicon detector residual misalignment Dt resolution model (Gexp vs 3G, Bflav vs BCP) Mistag differences between BCP and Bflav samples (MC) 0.012 Fit bias correction and MC statistics 0.010 Fixed lifetime and oscillation frequency 0.005 Total 0.033

Updated (ICHEP04) sin2b results from Charmonium Modes BABAR Limit on direct CPV

Belle Results on sin2b from Charmonium Modes BKS Sample Belle 2005 New Belle value lower than in ’03 but still consistent with BaBar’04

CP Violation in B Decays Firmly Established

Lessons From sin2 Measurement With B0K0 In 2001, large CP Violation in B system was observed in this mode by BaBar and Belle. It was the first instance of CPV outside the Kaon system. It was also the first instance of a CPV effect which was O(1) in contrast with the Kaon system and confirms the 1972 conjecture of Kobayashi & Maskawa. It excludes models with approximate CP symmetry (small CPV). In 2005 sin2 is a precision measurement (5%) and agrees well with the constraints in the - plane from measurements of the CKM magnitudes. Now it appears unlikely that one will find another O(1) source of CPV and the enterprise now moves towards looking for corrections rather than alternatives to the SM/CKM picture Focus now shifts to measurements of time-dependent asymmetries in rare B decays which are dominated by Penguin diagrams in the SM and where New Physics could contribute to the asymmetries

End of Lecture 3 Tomorrow: Measurements of angles  and  ++ =? “Sin2” in bs Penguin decay Status of Unitarity Triangle Future Directions : Tevatron, LHC-b….

Direct CPV in B- K- 0 Belle Belle BaBar Not in BK- + Belle ACP(Kp0 ) = 0.04  0.05  0.02 Belle ACP(Kp0 ) = 0.06  0.06  0.01 BaBar

CP Violation In B Decays: SM Expectations Group various amplitudes in B decays by the associated CKM couplings Helpful in categorizing B Decays: where CPV is cleanly interpretable (quantitative) in SM Where Hadronic uncertainties pollute interpretation of measured CPV

Decay Amplitude Weak Phase Structure in CPV Most B decay final states have contributions from both “Tree” and 3 “Penguin” (Pt,Pc,Pu) diagrams. All Tree diagrams (Spectator, W-exchange, W-Annihilation, rescattering) have same weak phase The three Pi can have different Weak and Strong phases EW penguins “suppressed” due to EW coupling

B Decay Amplitude Weak Phase Structure

Decay Amplitude Weak Phase Structure in CPV

Decay Amplitude Weak Phase Structure in CPV

Three Major “Classes” of B Decays For CPV

CPV in B0 Mixing 2  B0 f off-shell states f on-shell states f

Mixing Measurement at Belle (Hadronic Modes) Mistag rate BELLE 29.1 fb-1 Vivek Sharma , UCSD

The “Platinum” Final State dominant decay amplitude

Sin2b Likelihood Fit Fit Parameters Combined unbinned maximum likelihood fit to Dt spectra of flavor and CP sample Fit Parameters sin2b 1 Mistag fractions for B0 and B0 tags 8 Signal resolution function 8 Empirical description of background Dt 17 B lifetime fixed (PDG value) tB = 1.548 ps Mixing Frequency fixed (PDG value) Dmd = 0.472 ps-1 tagged CP samples tagged flavor sample 35 total free parameters All Dt parameters extracted from data Correct estimate of the error and correlations

Mixing Measurement with Fully Reconstructed B Sample 29.7 fb-1 Dt [ps] Precision measurement consistent with world average  Well calibrated detector for Flavor tagging Vivek Sharma , UCSD

Dt Resolution Function Core Tail Outlier Use the event-by-event uncertainty on Dt Dt Residual (ps) R(dDt) B0 flavour sample CP sample sDt (ps) Different bias scale factor For each tagging category Vivek Sharma , UCSD

B0 B0 Mixing Asymmetry with Hadronic Sample Unfolded raw asymmetry Folded raw asymmetry |Dt| [ps] Flavor mistag rate well calibrated from mixing measurement Dt [ps] BABAR 29.7 fb-1 Vivek Sharma , UCSD

Belle Results on sin2b from Charmonium Modes 2003

Dmd Measurement in Comparison With World WA: 0.496 ± 0.007 ps-1 Precision Dmd measurement 3% statistical error 2% systematic error dominated by MC correction BaBar Measurements Well Calibrated Detector for B flavor tagging Vivek Sharma , UCSD