Lecture 3: Time-Dependent Asymmetries as a Test of the Standard Model CP asymmetries in CP eigenstates involving b ® ccs transitions Measuring sin2b in other channels Asymmetries in 2-body neutral B decays Brief word on future prospects and plans

Experimental Technique for B Factories Exclusive B Meson Reconstruction (4S) produces coherent B pair: t ® Dt Time-integrated asymmetries are zero B-Flavor Tagging (flavor eigenstates) lifetime, mixing analyses (CP eigenstates) CP analysis Aug 5-7, 2002 D.MacFarlane at SSI 2002

(after tagging & vertexing) CP Sample for BABAR 1506 signal candidates, purity 94% 988 signal candidates, purity 55% BABAR 81.3 fb-1 (after tagging & vertexing) Aug 5-7, 2002 D.MacFarlane at SSI 2002

Improved Tagging at BABAR 4 Physics Categories 9 Tagging Categories Sub-taggers Electron-K Muon-K Electrons Muons Kaon-psoft Kaon 1 psoft Kaon 2 Other Lepton Kaon I Kaon II Inclusive Combined Tagging NN 7% improvement in Q = eD2 (DQ = 1.9%) Aug 5-7, 2002 D.MacFarlane at SSI 2002

Flavor Tagging Performance in Data The large sample of fully reconstructed events provides the precise determination of the tagging parameters required in the CP fit Tagging category Fraction of tagged events e (%) Wrong tag fraction w (%) Mistag fraction difference Dw (%) Q = e (1-2w)2 (%) Lepton 9.1  0.2 3.3  0.6 -0.9  0.5 7.9  0.3 Kaon I 16.7  0.2 9.9  0.7 -0.2  0.5 10.7  0.4 Kaon II 19.8  0.3 20.9  0.8 -2.7  0.6 6.7  0.4 Inclusive 20.0  0.3 31.6  0.9 -3.2  0.6 0.9  0.2 ALL 65.6  0.5 28.1  0.7 Error on sin2b and Dmd depend on the “quality factor” Q approx. as: Highest “efficiency” Smallest mistag fraction BABAR 81.3 fb-1 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Comparison Tests with New Tagger Test of crucial underlying assumption: tagging the same for CP & Bflav samples BABAR 81.3 fb-1 CP vs Bflav sample Bflav sample vs MC Aug 5-7, 2002 D.MacFarlane at SSI 2002

Golden Sample: (cc)KS CP Eigenstates BELLE 78 fb-1 1996 signal candidates, purity 94% Aug 5-7, 2002 D.MacFarlane at SSI 2002

CP Eigenstate Sample: J/yKL BELLE 78 fb-1 1330 signal candidates, purity 63% Aug 5-7, 2002 D.MacFarlane at SSI 2002

Track level and event level look-up tables Tagging at Belle Track level and event level look-up tables Quality factor r varies from 0 = low likelihood 1 = high likelihood Data vs MC comparison BELLE 41.8 fb-1 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Mistag rate extracted in six bins in r from mixing fit Measuring Mistag Rate Mistag rate extracted in six bins in r from mixing fit Comparison between measured (1-2w) and quality factor r obtained in 6 bins in r r1 r2 r3 r4 r5 r6 BELLE 78 fb-1 Aug 5-7, 2002 D.MacFarlane at SSI 2002

CP Analysis: Time Distributions hCP = -1 perfect flavor tagging & time resolution realistic mistag probability & finite time resolution Aug 5-7, 2002 D.MacFarlane at SSI 2002

Time-Dependent CP Asymmetries Time-dependence of Time-dependence of CP-violating asymmetry in (Assuming no confusion of Brec state) Use the large statistics Bflav data sample to determine the mistag probabilities and the parameters of the time-resolution function Aug 5-7, 2002 D.MacFarlane at SSI 2002

Global correlation coefficient for sin2b: 13% sin2b Likelihood Fit 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 Aug 5-7, 2002 D.MacFarlane at SSI 2002

BABAR Result for sin2b hCP = -1 hCP = +1 sin2b = 0.755  0.074 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Checks with control samples where no asymmetry expected Belle Result for sin2b BELLE 78 fb-1 Checks with control samples where no asymmetry expected Sample “sin2b” B0 ®D*+p- 0.035±0.032 B0 ®J/yK* -0.021±0.093 B0 ®D*ln 0.004±0.017 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Belle Result for sin2b hCP = -1 hCP = +1 BELLE 78 fb-1 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Pure Gold: Lepton Tags Alone BABAR 81.3 fb-1 220 lepton-tagged hf = -1 events 98% purity 3.3% mistag rate 20% better Dt resolution Aug 5-7, 2002 D.MacFarlane at SSI 2002

Check “null” Control Sample at BABAR Input Bflav sample to CP fit No asymmetry expected Sample “sin2b” Bflav 0.021±0.022 B+ 0.017±0.025 Aug 5-7, 2002 D.MacFarlane at SSI 2002

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 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Monte Carlo Correction Potential bias on sin2b evaluated by fitting full MC in 2 ways: Fitting data-sized signal MC samples with mistag fractions and Dt resolution fixed to the MC truth values (see plot) Average bias = +0.012  0.005 Same as above except mistag fractions and Dt resolution from Breco MC Average bias = +0.014  0.005 One possible source of bias comes from neglecting the known correlation between the mistag fractions and s(Dt) Estimates from toy and full MC indicate a bias at the level of +0.004 We correct the fitted sin2b by subtracting 0.014 and assign a systematic error of 0.010 to this correction Aug 5-7, 2002 D.MacFarlane at SSI 2002

Comparison of Resolution Functions Aug 5-7, 2002 D.MacFarlane at SSI 2002

Subsample Checks Aug 5-7, 2002 D.MacFarlane at SSI 2002

World Average sin2b BABAR BELLE CDF ALEPH OPAL World average Aug 5-7, 2002 D.MacFarlane at SSI 2002

Standard Model Constraints Aug 5-7, 2002 D.MacFarlane at SSI 2002

Summary of sin2b from ccs modes Precision measurements of sin2b from charmonium modes now available World average Results have been improving by more than just luminosity gain Million BB pairs July 00 Feb 01 July 01 Mar 02 July 02 sin2b = 0.741 ± 0.067 (stat) ± 0.033 (syst) BABAR-PUB-02/008, hep-ex/0207042, submitted to PRL sin2b = 0.719 ± 0.074 (stat) ± 0.035 (syst) BELLE-CONF-0201, hep-ex/0207098, submitted to ICHEP2002 sin2b = 0.734 ± 0.055 (stat+sys) The Standard Model remains unscathed, but the high statistics future of B Factories will provide further opportunities to challenge the theory Aug 5-7, 2002 D.MacFarlane at SSI 2002

CP Violation in the B System CPV through interference of decay amplitudes Aug 5-7, 2002 D.MacFarlane at SSI 2002

CP Violation in the B System off-shell states f on-shell states f CPV through interference of decay amplitudes CPV through interference of mixing diagram Expected to be very small Aug 5-7, 2002 D.MacFarlane at SSI 2002

Formalism for CP Violation in Mixing Time-dependent CP Asymmetry: constant with time See for instance Bañuls & Bernabéu hep-ph/0005323 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Characterizing the Dilepton Sample Search for asymmetry in same-sign dilepton sample containing 20381 events BABAR 20.7 fb-1 Sample backgrounds B(Dt): 4.3% continuum 24% direct+cascade 12% direct+fake Measurement region > 200mm Aug 5-7, 2002 D.MacFarlane at SSI 2002

Determination of AT BABAR So far, no experimental evidence 20.7 fb-1 BABAR PRL 88, 231801 (2002) So far, no experimental evidence of large CP violation in B0 mixing To a good approximation: Aug 5-7, 2002 D.MacFarlane at SSI 2002

*Would be zero if one assumed CP invariance in cascade decays Systematic Errors Source s(AT) [%] Sample Detection asymmetry for electrons 0.5 Direct electrons in semileptonic B decays 0.6 Direct muons in semileptonic B decays Non-BB background asymmetry 0.7 Off-resonance data BB background asymmetry 0.9 * On-resonance data with Dz < 100mm Total 1.4 Statistical Error 1.2 *Would be zero if one assumed CP invariance in cascade decays Aug 5-7, 2002 D.MacFarlane at SSI 2002

CP Violation in the B System CPV through interference of decay amplitudes CPV through interference of mixing diagram CPV through interference between mixing and decay amplitudes Directly related to CKM angles for single decay amplitude Aug 5-7, 2002 D.MacFarlane at SSI 2002

CP Formalism Revisited For B0 decays, allowing for more than one amplitude contributing to the decay to fCP Amplitude ratio CP eigenvalue Full time-dependent distributions and CP asymmetry: Aug 5-7, 2002 D.MacFarlane at SSI 2002

Search for Direct CP in Golden Sample Redo fits tagged time distributions of CP sample with sine and cosine terms (assuming DG = 0) If more than one amplitude contributes |l| might be different from 1 Probing new physics: only use hCP = -1 sample (contains no mixing background) No evidence of direct CP violation due to decay amplitude interference Coefficient of the “sine” term unchanged Aug 5-7, 2002 D.MacFarlane at SSI 2002

Other Modes for sin2b Provide an independent measurement of CP violation Some possible b ® sss modes fKS is CP = -1 with Iml = -sin2b Sensitive to new physics in b ® s loop diagram Pure b ® s penguin process? Other examples h’KS is CP=+1 K+K-KS appears to be mostly CP=+1 according to Belle Possible double-charm modes B ® D*+D*- or B ® D*D channels No KS mixing, but penguins? Other charmonium modes Aug 5-7, 2002 D.MacFarlane at SSI 2002

BABAR Results for fKS BABAR 81.3 fb-1 Ncand = 66 Purity = 50% BABAR-CONF-02/016, hep-ex/0207070 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Belle Results for b ® sss BELLE-CONF-0225 mbc Aug 5-7, 2002 D.MacFarlane at SSI 2002

More CP channels: B ® D*+D*- BABAR 81.3 fb-1 Tree Penguin Cabibbo suppressed Ncand = 102 Purity = 82% No KS mixing contribution Potential for significant Penguin contamination BABAR-CONF-02/014, hep-ex/0207072 Aug 5-7, 2002 D.MacFarlane at SSI 2002

CP Composition of B0  D*+D*- Measure small CP odd fraction (corrected for acceptance): R = 0.07  0.06 (stat)  0.03 (syst) Preliminary BABAR 81.3 fb-1 Aug 5-7, 2002 D.MacFarlane at SSI 2002

The PDF The decay rate f+(f-) for a B tagged as a B0 (B0) Aug 5-7, 2002 D.MacFarlane at SSI 2002

CP Asymmetry Fit Results Preliminary If Penguins are negligible i.e., about 2.7s difference Aug 5-7, 2002 D.MacFarlane at SSI 2002

Testing the Origins of CPV a g b Aug 5-7, 2002 D.MacFarlane at SSI 2002

CP Violation in B0 ® π+π- Decays Decay distributions f+(f-) when tag = B0(B0) For single weak phase from tree diagram Cpp = 0, Spp = sin2a |  |  1  must fit for direct CP Im ()  sin2  need to relate asymmetry to  With additional weak phase from penguin diagram Cpp  0, Spp = sin2aeff Aug 5-7, 2002 D.MacFarlane at SSI 2002

Competing Amplitudes for B  h+h- Tree diagrams Penguin diagrams s K+ p- B0 s K+ p- B0 Penguin dominated: Potential direct CPV and constraints on g d p+ p- B0 d p+ p- B0 |Penguin| ~ 0.3|Tree| Complicates extraction of a from mixing induced CPV Aug 5-7, 2002 D.MacFarlane at SSI 2002

Analysis Overview Analysis issues: charmless two-body B decays Rare decays! BR ~ 10-5-10-6 → need lots of data (B Factories) Large background from e+e- → qq → need background suppression Ambiguity between p and K → need excellent PID (DIRC or ACC) CP analysis issues: Need to determine vertex position of both B mesons → standard vertex separation algorithms Need to know the flavor of “other” B → standard tagging algorithms Analysis proceeds at BABAR in two steps: Use kinematic, topological, and PID information in a global ML fit to extract yields for pp, Kp, and KK decays, as well as the asymmetry AKp Exclude vertexing & tagging information to avoid systematic error Add vertexing and tagging information to extract Spp and Cpp Yields and AKp fixed to result of the first fit Aug 5-7, 2002 D.MacFarlane at SSI 2002

Pion mass assumed for all tracks, so shift in DE for Kp and KK decays Kinematics Pion mass assumed for all tracks, so shift in DE for Kp and KK decays s(mES)  2.6 MeV/c2 (DE)  26 MeV Kp KK pp Signal Monte Carlo Sideband Sideband Aug 5-7, 2002 D.MacFarlane at SSI 2002

Background Suppression Background is due to light-quark production e+e- →qq (q=u,d,s,c) Jetty topology, distinct from spherical B decays Cut on angle qS between sphericity axes of B candidate and the remaining particles in the event: |cos(qS)| < 0.8, removes 83% bkg, 20% signal Define Fisher discriminant F derived from momentum flow in the event Used directly in the ML fit Sideband Data Signal MC Aug 5-7, 2002 D.MacFarlane at SSI 2002

Branching Fraction Fits Projections in mES and DE Proj eff: 52% pp pp 26070 two-prong candidates (97% background, mostly continuum) BF Likelihood includes PDFs for: mES, DE, Fisher, qc for + & - tracks Proj eff: 79% Kp Kp BABAR 81.3 fb-1 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Branching Fraction Results Preliminary Mode Yield BR [10-6] ACP(Kp) B0 → p+p- 157±19 4.7±0.6±0.2 B0 → K+p- 589±30 17.9±0.9±0.7 -0.102±0.050±0.016 B0 → K+K- 1±8 <0.6 [90%CL] BABAR 81.3 fb-1 BABAR-PUB-02/009, hep-ex/0207055 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Two-Body Tagged Sample Tagging efficiency is very different for signal and bkg Strong bkg suppression in lowest mistag categories (Lepton/Kaon) Different bkg tagging efficiencies for pp, Kp, KK Sum of p+p-/K+p-: No particle ID used until the fit is performed BABAR 81.3 fb-1 Untagged category also used Aug 5-7, 2002 D.MacFarlane at SSI 2002

CP Asymmetry Results from BABAR Fit projection in sample of pp-selected events qq + Kp For CP asymmetry add tagging and Dt measurement to likelihood but fix yields and AKp BABAR 81.3 fb-1 m Preliminary Aug 5-7, 2002 D.MacFarlane at SSI 2002

App vs. mES in sample of pp-selected events Crosschecks App vs. mES in sample of pp-selected events Inspect pp-selected sample 2-param fit consistent with full fit Asymmetry vs. mES Yields consistent with measured value of Cpp, which do not suggest large direct CP violation Toy MC generated over all allowed values of Spp and Cpp Expected errors consistent with data No significant bias observed Validated in large samples of signal and background MC events Systematic errors dominated by uncertainty in PDF shapes signal bins Aug 5-7, 2002 D.MacFarlane at SSI 2002

Belle Signal for B → p+p– Reject most of Kp feedthrough with PID systems 5.271 GeV/c2 5.287 GeV/c2 p+p– Kp qq p+p–+Kp |DE|<0.067 GeV other rare decays BELLE 41.8 fb-1 BELLE, hep-ex/0204002 Aug 5-7, 2002 D.MacFarlane at SSI 2002

B → p+p– Time Distributions 162 events after vertexing and flavor tagging |DE| < 0.067 GeV B0 tagged – 5 5 Dt (ps) Flavor Blind total qq + Kp p+p– Dt (ps) p+p– B0 tagged – 5 5 Dt (ps) p+p– Aug 5-7, 2002 D.MacFarlane at SSI 2002

B → p+p– Fit Result BELLE p+p– sample 41.8 fb-1 (BG subtracted) – 5 5 Dt (ps) B0 tagged BELLE, hep-ex/0204002 control sample Aug 5-7, 2002 D.MacFarlane at SSI 2002

Crosscheck with B → K+p- Sample asymmetry Dt (ps) Events / 20 MeV K+p– other rare decay pp feed across qq DE [GeV] Null Asymmetry Aug 5-7, 2002 D.MacFarlane at SSI 2002

Comparison of Results BABAR Belle App +0.30±0.25±0.04 Spp +0.02 ±0.34±0.05 A2pp+S2pp ≤ 1 Aug 5-7, 2002 D.MacFarlane at SSI 2002

Consistent with SM expectations Interpretation? Gronau and Rosner, Phys. Rev. D65, 093012 (2002) BABAR Result Spp and Cpp are determined by a, b, |P/T|, and d. Consistent with SM expectations Aug 5-7, 2002 D.MacFarlane at SSI 2002

PEP-II Luminosity Projections Equivalent expectation for Belle Aug 5-7, 2002 D.MacFarlane at SSI 2002

Possible PEP-II upgrade Aug 5-7, 2002 D.MacFarlane at SSI 2002

Projections for CP Asymmetry Measurements Some rough estimates Expression of Interest at KEK for 1035 machine in spring 2002 Ongoing workshops to examine this or higher luminosity options Snowmass 2001 study of 1036 concept and physics capability Aim to be competitive and complementary to LHCb, BTeV on time scale of end of the decade Physics case still being explored; still very early days in the exploration of these possibilities Requires completely new vacuum and rf system, mostly new detector (current technologies cannot handle backgrounds) Aug 5-7, 2002 D.MacFarlane at SSI 2002

Future Tests of the Standard Model Assumes |Vcb| ~ 3% and |Vub| ~ 10% Much experimental and theoretical work underway to achieve this New results on inclusive/exclusive semileptonic decays Will be entering an era of very large tagged samples Assumes Dms known to <1% from Tevatron in 2004? ca. 2007: s(sin2b) ~ 1% a ~ 5o, g ~ 10o Illustration of SM breakdown Aug 5-7, 2002 D.MacFarlane at SSI 2002

World average dominated by BELLE and BABAR Summary Now in the era of B Factories, with a renaissance of experimental and theoretical activity in B physics Data samples are 5 times larger than CLEO; will be 10 times larger within a few years July 2001 saw the beginnings of this program But…still working towards a definitive systematic test of Standard Model expectations and constraints Motivation for these and upcoming facilities is to provide a definitive test of CP violation in the Standard Model Unambiguous observation of CP violation in the B system World average dominated by BELLE and BABAR July 2002: Textbook plots! Aug 5-7, 2002 D.MacFarlane at SSI 2002

Bibliography: Lecture 3 [sin2b] Belle Collab, PRL 86, 2509 (2001) [sin2b] Belle Collab, PRL 87, 091802 (2001) [sin2b] Belle Collab., hep-ex/0202027, to appear in PRD [sin2b] Belle Collab., hep-ex/0207098, submitted to ICHEP2002 [sin2b] BABAR Collab., PRL 86, 2515 (2001) [sin2b] BABAR Collab., PRL 87, 091801 (2001) [sin2b] BABAR Collab., hep-ex/0201020, to appear in PRD [sin2b] BABAR Collab., hep-ex/0203007, submitted to Moriond2002 [sin2b] BABAR Collab., hep-ex/0207042, submitted to PRL and ICHEP2002 [phi-KS] Belle Collab., BELLE-CONF-0225, submitted to ICHEP2002 [phi-KS] BABAR Collab., hep-ex/0207070, submitted to ICHEP2002 [D*D*] BABAR Collab., hep-ex/0207072, submitted to ICHEP2002 [h+h-] BABAR Collab, PRD 65, 051502 (2002) [h+h-] Belle Collab., PRL 89, 071801 (2002) [h+h-] BABAR Collab., hep-ex/0207055, submitted to PRL Snowmass 2001, SuperBABAR Report, SLAC-PUB-8970 Belle Collab., SuperKEKB EOI, http://belle.kek.jp/~yamauchi/EoI.ps.gz Aug 5-7, 2002 D.MacFarlane at SSI 2002