The CKM Angles a and b a/f2 g/f3 b/f1 Introduction Measuring b/f1 Theory overview Experiments at B-factories Measuring b/f1 Measuring a/f2 Summary a/f2 g/f3 b/f1

The Cabibbo-Kobayashi-Maskawa Matrix The weak interaction can change the favor of quarks and lepton Quarks couple across generation boundaries Mass eigenstates are not the weak eigenstates The CKM Matrix rotates the quarks from one basis to the other Vcb Vub u d t c b s l l3 l2 l=sin(qc)=0.22 d’ Vud Vus Vub d s’ = Vcd Vcs Vcb s b’ Vtd Vtb b

Visualizing CKM information from Bd decays The Unitarity Triangle The CKM matrix Vij is unitary with 4 independent fundamental parameters Unitarity constraint from 1st and 3rd columns: i V*i3Vi1=0 Testing the Standard Model Measure angles, sides in as many ways possible Area of triangle proportional to amount of CP violation u Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb c t CKM phases (in Wolfenstein convention) unitarity 4 parameters (3 real, 1 complex phase) many representations. Wolfenstein – matches hierarchy shown on previous slide In this representation the Vtd and Vub – the small elements in the corner carry a complex phase. UT will be our guide for the remainder of the talk.

Three Types of CP Violation I) Indirect CP violation/CP violation in mixing K®pp, K®pln, expected to be small (SM: 10-3) for B0’s II) Direct CP violation: Prob(B®f) ¹ Prob(B®f) e¢/e in K®pp Br(B0®K-p+) ¹ Br(B0®K+p-) III) Interference of mixing & decay: Prob(B(t)®fCP) ¹ Prob(B(t)®fCP) B0®yKs (CKM angle b) B0®p+p- (CKM angle a) Due to quantum numbers of Y(4S) and B meson we must measure time dependant quantities to see this CP violation Only CP violation possible for charged B’s In this talk we will be discussing type III) CP violation

CP Violation at the Y(4S) CP violation from the interference between two paths, decay with and without mixing mixing q/p |BL>=p|B0>+q|B0> |BH>=p|B0>- q|B0> Measure time dependent decay rates & Dm from B0B0 mixing Direct CP Violation: C¹ 0 |Af/Af|≠1→ direct CP violation |q/p|≠1→ CP violation in mixing Sf and Cf depend on CKM angles

Getting the Data Sample Use e+e- annihilations at Y(4S) to get a clean sample of B mesons At Y(4S) produce B-/B+ (bu/bu) and B0B0 (bd/bd) mesons mB0 ~ mB- ~ 5.28 GeV BB Threshold motivation for asymmetric B factory The Y(4S) - a copious, clean source of B meson pairs 1 of every 4 hadronic events is a BB pair No other particles produced in Y(4S) decay Equal amounts of matter and anti-matter

Note: 1fb-1 ~ 1.1 million BB pairs B Factories To get the large data set necessary to measure CP-violation with B’s use B-factories SLAC and KEK Both factories have attained unprecedented high luminosities: >1034/cm/s2 BaBar has 352 fb-1 and Belle has 610fb-1 of data Note: 1fb-1 ~ 1.1 million BB pairs

Asymmetric e+e- Colliders KEKII PEPII KEK/SLAC are asymmetric e+e− colliders KEK: 8 GeV (e-)/3.5 GeV (e+) SLAC: 9 GeV (e-)/3.1 GeV (e+) B travels a measurable distance before decay: SLAC: bg=0.56 → bgct~260mm KEK: bg=0.42 → bgct~193mm

Detectors at Asymmetric e+e- Colliders Both detectors feature: Charged particle tracking (silicon+drift chambers + 1.5T B-field) Electromagnetic calorimetry (CsI) ® g and electron ID p/K/p separation up to the kinematic limit BABAR: dE/dx+DIRC Belle: dE/dx+aerogel+ToF Muon/KL identification

Key Analysis Techniques Threshold kinematics: we know the initial energy of the Y(4S) system Therefore we know the energy and magnitude of momentum of each B Event topology Signal Signal (spherical) explain that the initial state is known Delta E the beam energy is better known (2-3 MeV) than the reconstructed energy (20 MeV) -> mes Background Background (jet-structure) Most analyses use an unbinned maximum likelihood fit to extract parameters of interest

How to Measure Time Dependent Decay Rates We need to know the flavour of the B at a reference t=0. Dz = Dt gbc At t=0 we know this meson is B0 B 0 rec B 0 (4S) bg =0.56 l - (e-, m -) B 0 tag The two mesons oscillate coherently : at any given time, if one is a B0 the other is necessarily a B0 In this example, the tag-side meson decays first. It decays semi-leptonically and the charge of the lepton gives the flavour of the tag-side meson : l - = B 0 l + = B 0. Kaon tags also used. Dt picoseconds later, the B 0 (or perhaps it is now a B 0) decays. There is an additional slight complication as our B0B0bar pair is in a coherent state Tagging explain lepton tag. We also use a kaon tag from a subsequent D decay. Combined the tagging efficiency is roughly 30%

The Many Ways to Measure sin2b Can use 3 different categories of B0 decays to measure b: With this device and the rest of the BaBar detector we then collected almost 230 million BB events and analyzed the data looking for psiKs final states plus, of course, a tag for the other B in the event. We ended up with 7730 events and shown here is the decay time difference for B0 tags and B0bar tags clear difference. no asymmetry in the background. The second plot shows the raw asymmetry and the fit result is golden mode

Precise Measurement of sin2b from B0®charmonium K0 Theoretically very clean: ACP(t)=Sfsin(DmDt)-Cfcos(DmDt) The dominant penguin amplitude (suppressed by l2Cab) has same phase as tree SM prediction: Cf=0 Þ ACP(t)=Sfsin(DmDt) confirmed by recent model-independent analyses [e.g. PRL 95 221804 (2005)] DS=0.000±0.012 Experimentally very clean: Many accessible decay modes with (relatively) large BFs B→ψK0~8.5x10-4 B→ψ(2S)K0~6.2x10-4 B→χc1K0~4x10-4 B→ηcK0~1.2x10-3 CP odd CP even

Precise Measurement of sin2b from B0®charmonium K0 hep-ex/0507037 386x106 BB sin2b=0.652±0.039±0.020 (was 0.728±0.056±0.023, Nov. 2004 PR D71, 072003, 152x106 BB) (cc) KS (CP odd) modes J/y KL (CP even) mode PRL94, 161803 (2005) 227x106 BB sin2b=0.722±0.040±0.023

Brief history of sin2b from B0charmonium K0 1s CKM fit 2s World Average sin2b[WA]=0.687±0.032 From external constraints sin2bUTFit= 0.793±0.033 (sides) sin2bUTFit=0.734±0.024 (all) Great success for Standard Model Great success for all of us theorists, experimentalists, accelerator physicists

Resolving the sin(2b) Ambiguity sin(2b) is the same for b, p/2-b, p+b, 3p/2-b Belle: Use bcud [B 0DCP(Ksp+p-) h0] decays [A.Bondar, T.Gershon, P.Krokovny, PL B624 1 (2005)] Theoretically clean (no penguins), Neglect DCS B0DCPh0 decay Interference of Dalitz amplitudes sensitive to cos2b Dalitz model fitted in D*-tagged D0 decays f1=(16±21±12)o rules out f1=68o @ 97% CL [Belle. hep-ex/0507065] BABAR: B0J/yK*0(K*0Ksp0) Extract cos2b from interference of CP-even and CP-odd states (L=0,1,2) in time-dependent transversity analysis cos2b<0 excluded at 86% C.L. [BABAR, PRD 71, 032005 (2005)] h0=p0,h,w

These decays suffer from potential penguin-pollution: b®d penguin amplitude has different weak & strong phases with respect to tree. BABAR: B0® J/yp0 updated measurements [hep-ex/0603012, submitted PRD-RC]: Br(B0® J/yp0)=(1.94±0.22±0.17)x10-5 SJ/yp0=-0.68±0.30±0.04 CJ/yp0=-0.21±0.26±0.09 Consistent with previous Belle results: PRL93, 261801 (2004) SJ/yp0=-0.72±0.42±0.09 CJ/yp0=-0.01±0.29±0.03

CP-odd fraction extracted with transversity analysis: D*+D*-: [PRL 95, 151804 (2005)] VV decay: both CP-odd and CP-even components. CP-odd fraction extracted with transversity analysis: fodd=0.125±0.044±0.070 S+=-0.75±0.25±0.03 C+=+0.06±0.17±0.03 D(*)+D- [PRL 95, 131802 (2005)]: SDD =-0.29±0.63±0.06 CDD =+0.11±0.35±0.06 SD*+D-=-0.54±0.35±0.07 CD*+D-=+0.09±0.25±0.06 SD*-D+=-0.29±0.33±0.07 CD*-D+=+0.17±0.24±0.04 D*+D- D*-D+ D+D-

All results consistent with SM expectation of tree dominance DSDD≡SDD-sin2b~0.02-0.05 [Z-Z. Xing, PR D61 014010 (2000)] Still below current experimental sensitivity

Sin2beff in b → s Penguins Decays dominated by gluonic penguin diagrams Golden example: B0→fKS No tree level contributions: theoretically clean SM predicts: ACP(t) = sin2bsin(Dmt) NP SM Impact of New Physics could be significant New particles could participate in the loop → new CPV phases Measure ACP in as many b→sqq penguins as possible! φK0, K+ K− KS, η′ KS, KS π0, KS KS KS, ω KS, f0(980) KS BUT there are complications: Low branching fractions (10-5) non-penguin processes can pollute u s d b B

All “sin2b” Results Compared Will be discussed in O. Long’s talk “Rare decays and new physics studies”

b g a The Unitarity Triangle (0,0) (0,1) (r,h) Vub Vud Vcd Vcb * Vtd Vtb g a b Successfully reached the main goal of the B factory program now let’s go for more [21.7 ± 1.3]o

The CKM angle a In an ideal world we could access a from the interference of a b→u decay (g) with B0B0 mixing (b): B0B0 mixing Tree decay g a = p - b - g harder because of the lower BR B0→K+p- large Br~2x10-5 ~Pure Penguin But we do not live in the ideal world. There are penguins...

sin(2a): Overcoming Penguin Pollution Access to a from the interference of a b→u decay (g) with B0B0 mixing (b) complicated by Penguin diagram B0B0 mixing Tree decay Penguin decay  g Inc. penguin contribution now the formalism gets slightly more complicated the “C” term direct CP violation due to the interference of the T and P decays but our sin(2a) term gets also modified and the question is how can we obtain a from aeff? How can we obtain α from αeff ? T = "tree" amplitude P = "penguin" amplitude d=strong phase Time-dep. asymmetry :

How to estimate |a-aeff|: Isospin analysis Use SU(2) to relate decay rates of different pp final states p+p-, p+p0, p0p0 Important point is that pp can have I=0 or 2 but gluonic penguins only contribute to I=0 (by DI=1/2 rule) &EW penguins are negligible Need to measure several B.F.s: Da=2|aeff -a| f A(B->p p ) 0 + - 0 0 0 - - 0 =A(B->p p ) + + 0 1 2 ~ Gronau-London: PRL65, 3381 (1990) BF(B+®p+p0)=BF(B-®p-p0) since p+p0 is pure I=2, only tree amplitude not enough data but maybe we can limit a-aeff if A00 is very small… look for this decay However, for this technique to work p0p0 amplitudes must be very small or very large!

B0→p+p- 227×106 B pairs 275×106 B pairs 467±33 signal events Phys.Rev.Lett. 95 (2005) 151803 Phys.Rev.Lett. 95 (2005) 101801

B0→p+p- S = −0.67±0.16±0.06 C = −0.56±0.12±0.06 S = −0.30±0.17±0.03 So two comparable measurements of S = sin(2aeff) Measurements of direct CP asymmetry less compatible

B0→p0p0 275 x 106 BB pairs 227 x 106 BB pairs PRL 94, 181803(2005)

Using isospin in pp system PRL 94, 181802 (2005) Precision measurement of a not possible with current stats using pp

B → rr to the Rescue Pseudoscalar→ Vector Vector Nature is KIND! 3 possible ang. mom. states: S wave (L=0, CP even) P wave (L=1, CP odd) D wave (L=2, CP even) Nature is KIND! B0®r+r-~100% longitudinally polarized! Transverse component taken as 0 in analysis, essentially all CP even Large Branching Fraction! Br(B0®r+r-)=(30±4±5)x10-6 Br(B0®r+r-)~6xBr(B0®p+p-) PRL 93 (2004) 231801 r helicity angle signal bkg

B0 → r+r- BaBar (227 x 106 BB) Belle (275 x 106 BB) PRL 96, 171801 (2006) PRL 95, 041805 (2005)

But How large is B0→r0r0 ? Phys.Rev.Lett. 94 (2005) 131801 In rr system the amount of neutral decays is small Measure: B0→r0r0 events in 227 x 106 BB events Br < 1.1 x 10-6 at 90% CL. Isospin triangle for rr is flattened compared to pp k=2|aeff -a| A(B->r r ) 0 0 0 0 + - 1 2 ~ - - 0 =A(B->r r ) + + 0 Penguin Pollution Defeated!

B±→r±r0 New result with 231 x 106 BB events Previous BaBar/Belle HFAG average hep−ex/0603003 New result is better match to isospin model Moriond QCD 2006 Smaller uncertainty on |aeff−a| compared to pp mode

B0 → (rp)0 Analysis B0 → (rp)0 →p+p−p0 is not a CP eigenstate 6 decays to disentangle: Tried by BaBar and Belle for just r± phase space Did not set limits on a Can use a Dalitz plot analysis to get a from decays Snyder & Quinn: Phys. Rev. D48, 2139 (1993) r0p0 r+p- r-p+ Convert to a square Dalitz plot Mostly resonant decays Move signal away from edges Simplifies analysis MC q0=r helicty angle m0=invariant mass of charged tracks

B0 → (rp)0 Dalitz plot analysis Dalitz plot analysis yields CP asymmetries and strong phases of decays Using 213 x 106 BB events hep-ex/0408099 1184±58 B→p+p-p0 Signal events Blue histos are different types of backgrounds m’ and q’ are variables for a square Daltiz plot Analysis provides a weak determination of a: However, useful for resolving ambiguities…..

Combined constraints on a rr gives single best measurement rp resolves 2-fold ambiguity from rr World Average: Global CKM Fit (w/o a): Dms

a g b The Unitarity Triangle (0,0) (0,1) (r,h) Vub Vud Vcd Vcb * Vtd Vtb g b [99 ± 11]o a being able to measure 2 angles is already a surprise but let’s go for 3 [21.7 ± 1.3]o

Summary and Outlook BABAR & Belle measure sin2b in ccK0 modes to 5% precision sin2bcharmonium=0.687±0.032 Comparison with sin2beff in b s penguin modes could reveal new physics effects BUT need to carefully evaluate SM contributions sin2beff measurements are statistically limited, can add new modes, beat 1/√L scaling Extraction of a depends crucially on penguin contributions B→r0r0/r+r0 Theory Û experimental feedback is helpful Expected precision Vs time reference +1s sin2b in penguins reference (current r0r0 Br) reference -1s from rr Luminosity (ab-1)

Putting it all together As of today the complex phase in the CKM matrix correctly describes CP Violation in the B meson system! h this is a confusing plot because it combines 30 years worth of information. Consistent But not enough r More to come from BABAR/Belle, CDF/D0, and LHCb Will they find CKM violation????

Extra Slides

Adding Theoretical Uncertainties size of possible discrepancies Δsin2β have been evaluated for some modes: estimates of deviations based on QCD-motivated specific models; some have difficulties to reconcile with measured B.R. Beneke at al, NPB675 Ciuchini at al, hep-ph/0407073 Cheng et al, hep-ph/0502235 Buras et al, NPB697 Charles et al, hep-ph/0406184 model independent upper limits based on SU(3) flavor symmetry and measured b d,sqq B.R. [Grossman et al, PRD58; Grossman et al, PRD68; Gronau, Rosner, PLB564; Gronau et al, PLB579; Gronau et al, PLB596; Chiang et al, PRD70] 2xΔsin2β ‘naive’ upper limit based on final state quark content, CKM (λ2) and loop/tree (= 0.2-0.3) suppression factors [Kirkby,Nir, PLB592; Hoecker, hep-ex/0410069]

There is a problem B0  p+p- B0  K+p- B0p+p- 157  19 q pp Kp B0  p+p- B0  K+p- B0p+p- 157  19 (4.7  0.6  0.2) x 10-6 B0K+p- 589  30 (17.90.9 0.7) x 10-6 Penguin/Tree ~ 30%