Measuring α with the B-factories. Adrian Bevan SCIPP 17 th Feb 04

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1 Measuring α with the B-factories Adrian Bevan SCIPP 17 th Feb 4

2 Outline CP Violation in Meson Decay & measuring α Experiments and Techniques measurements in the B meson system: B ππ from Belle and BaBar prospects from B ρρ Conclusions

3 Why is CP Violation interesting? The universe is matter dominated! Cosmology requires C and CP Violation Known levels of CP Violation in K and B decays is O(9) orders of magnitude too small to explain matter dominance! New Physics to discover Need B factories to study CP Violation in B meson decay Precision tests of the SM and search for new physics Work towards a deeper understanding of CP Violation mechanism

4 CP Violation in meson decay Diagrams of interest for CP Violation have interactions of the form W + qi = u, c, t V ij q j = d, s, b The couplings, V ij, form a 3 3 matrix: The CKM Matrix

5 V Single Complex Phase Describing CP Violation in meson decay Unitarity gives Vud Vu s Vub = Vcd Vcs Vcb + Vtd Vt s V tb Aλ (1 ρ iη ) Aλ 1 CP Violating phase present VV = V V = λ /2 λ Aλ ( ρ iη) λ 1 λ /2 Aλ O( λ ) 3 2 Orthogonality of V gives 6 closed triangles λ ~.22 A ~.8 ρ ~.2.27 η ~.28.37

6 The Unitarity Triangle 2 triangles have all sides with the same order in λ kaon system is not one of these interesting one for the B d/u system is The Unitarity Triangle V V + V V + V V = * * * ud ub cd cb td tb BB mixing VV * B D π DK Kπ,... * ub ud * b VcdV = R cb,, (,) B ππ, ρπ, ρρ γ (η,ρ) * VV td tb α * cd cb V V = R β t (1,) V = V e td td V = V e ub ub B J ψ K S DD * * /,, ϕk,... iβ iγ

7 Neutral Meson Phenomenology For neutral mesons; K, B, D strong eigenstates are not CP eigenstates 1 1 B = ( BH + BL ), B = ( BH BL ) 2p 2q mass eigenstates are an admixture of different strong eigenstates mass eigenstates=cp eigenstates CP even B = pb + qb if no CP Violation in mixing (q/p=1) H CP odd B = pb qb L particle antiparticle (mixing), f = 2 p q = 1 m= M M Γ = Γ B B H H Γ B L B L if q/p 1 have CP Violation in mixing; e.g. ε K =2.3x1-3 (mixing is very suppressed in the Standard Model for D mesons)

8 CP Violation at the B-factories Υ(4s) run at 1.58GeV CMS to produce B pairs (on-peak) Correlated B pair decay into charged and neutral B mesons f f ~ B B BB.11.1 ± (PDG 22) Run 4 MeV below the Υ(4s) O(12%) of the time to characterise continuum (light quark: u,d,s,c) background from e + e - collisions. Need asymmetric beam energies for CP violation study

9 BaBar 9GeV e - on 3.1GeV e + Υ(4S) boost: βγ=.56 Peak Lumi: run 4 run 3 run 2 run 1 Performance snapshot from 1 th Feb 4

10 Belle Total Lumi: /fb Peak Lumi: Estimate 35/fb by July 5 Performance snapshot from 1 th Feb 4

11 Observing CP violation at the Υ(4S) B Three interference effects: B f CP CP violation in mixing ( q/p 1) Pr( B B ) Pr( B B ) time dependent effect -- m (direct) CP violation in decay ( A/A 1) Pr( B f) Pr( B f) time integrated effect number counting CP violation in interference of mixing and decay (Imλ ) time dependent effect -- m

12 Analyse time evolution of B B system (assume Γ=): phys Γ Γ t CP 4 S f C d f d f ( B f, t) = e 1+ sin( m t) cos( m t) CP CP f Γ Γ t ( B phys fcp, t) = 4 e 1 S f sin( md t) + C f cos( md t) CP CP C f CP f CP λ f S = 2Imλ CP 1 λ 2 f CP f = CP 1 + λ f 2 CP λ f CP Indirect CP violation S Direct CP violation C q A = p A f f CP CP

13 CP Asymmetries & Observables Direct CP Violation A CP Br( B f ) Br( B f ) = Br( B f ) + Br( B f ) Time integrated CP asymmetry (e.g. charged B decay) Interesting Observable: A CP Direct and Indirect CP Violation A CP () t ( Bphys( t) f ) ( Bphys( t) f ) ( Bphys( t) f ) ( Bphys( t) f ) Γ Γ = Γ +Γ = Ssin( m t) Ccos( m t) Interesting Observables: S, C Time dependent CP asymmetry (e.g. neutral B decay)

14 Ingredients of a CP analysis: 1) Event Selection: Select events: discriminate against any B background and continuum background from e + e - qq 2) Flavour Tagging Determine the flavour of the selected B candidate is it a B or a B? Issues: Use the other B in the event tagging efficiency: signal, B background mis-tag probability Dilution asymmetry in tag efficiency for continuum background 3) Vertex Reconstruction Need to determine proper time difference between the tag B, B TAG, and the reconstructed CP B, B CP. (B CP is not always a CP eigenstate) Need good understanding of detector resolution for t=t CP -t TAG

15 B Flavour Tagging b c s K - Tagging algorithm with physics-based neural networks Inputs include leptons, kaons, slow-π (from D*), and high-momentum tracks Outputs combined and categorized by mistag probability (w) 5 mutually exclusive hierarchical categories: Lepton isolated high-momentum leptons cleaner signal Kaon I high quality kaons or correlated K + and slow-π - Kaon II lower quality kaons, or slow-π larger mistag prob Inclusive unidentified leptons, poor-quality kaons, high-momentum tracks Untagged no flavour information is used

16 efficiency mistag probability Q = ε(1-2w) 2 = (28.4 ±.7)% 66% of events have some flavour information

17 Tagging: example of rare B decay: h + h - Tagging efficiency is very different for signal and background Strong bkg suppression in categories with the lowest mistag prob (Lepton/Kaon) plots shown are for h + h -, a rare decay with significant backgrounds. 81/fb B h + h - sample split by tagging category Lepton 4 Kaon I m ES (GeV/c 2 ) m ES (GeV/c 2 ) m ES (GeV/c 2 ) 5 Kaon II Inclusive m ES (GeV/c 2 )

18 t Beam spot Interaction Point z z βγ 1 c B CP Vertex B TAG Vertex Vertex Reconstruction Exclusive B CP reconstruction B CP daughters B TAG direction z resolution dominated by tag side (other B) Average z resolution ~18µm Average z ~26 µm Example in B ππ e + e - qq TAG tracks, V s Resolution function parameters obtained from data for both signal and background Signal from sample of fully reconstructed B decays to flavour eigenstates: D * (π, ρ, a 1 ) Background from data sideband sampe (or float in fit) without the boost would have z~3µm B ππ e.g. CLEO t (ps)

19 The CKM Angle α Interesting modes to measure α B B B ππ ρπ ρρ need to perform an Isospin analysis of branching ratios of B and B to 2π final states to determine shift in α due to the presence of penguin (loop) diagrams 2α eff = 2α + κ ππ doing a quasi 2 body analysis will eventually have to analyse the whole Dalitz plot thus enabling the extraction of α. In analogy to these modes one needs to analyse the time dependence of this decay and extract α from an isospin analysis of each of the three partial waves (L=,1,2) in the final state (full angular analysis not required) the time evolution of π + π gives the shifted value of α The shift in α from penguin diagrams is better constrained than in ππ!

20 Tree (T) Level: mixing λ ππ = λ C S ππ ππ ππ VV V = = CP Violation in B π + π * * tb td ud * tbvtd ud 2 α e i V V V V = sin(2α ) ub * ub + + B π π & B decay π π With Penguins (P): λ C S ππ ππ ππ iδ iγ 2iα 1+ P / T e e = e iδ iγ = 1+ P / T e sin( δ ) 1 C 2 ππ e sin(2α Need to measure the weak phase α W u,c,t eff penguins are significant: P/T~.3 ) can use isospin relations to extract shift

21 The Isospin Analysis: illustration using B ππ α α = φ φ eff Established Measurements Need to measure decay of B and B to π ± π, π ± π, π π final states in order to determine the shift A= A( B f), A = CP( A) = A( B f ) Recently Observed φ φ Measure φ (φ ) for B(B) from Br( π π ) + 2 Br( π π ) Br( π cosφ = Br( π π ) Br( π π ) π ) Can bound the shift on α using BR(B ± π ± π ) and BR(B π π ) 2 sin ( αeff α) Br Br ( B π π ) + ( B + π π ) Grossman Quinn bound

22 AB T e e P e + iδt iγ iδp ( π π ) = ( ) + ), + iδt iγ iδp ( π π ) = ( ) + ), AB T e e P e λ Alternative: Model Dependent Constraints on the CKM angle α 1 + P/ T e 1 + P/ T e i( δ+ γ) iα ππ = e i( δ γ) convention taken from M.Gronau and J.L.Rosner Phys. Rev. D65, 9312 (22) 4 parameters S C R ππ ππ ππ = [sin 2α + 2 P/ T sin( β α)cosδ β 2 P/ T sin2 ]/ Rππ, = [2 P/ T sin( β + α)sin δ ]/ R, = 1 2 P/ T cos( β + α)cos δ + P/ T ππ 2 δ δ δ P T P/T (representative) Theory ~.3 β deg (Belle & BaBar combined) δ strong phase difference not known

23 Presented at LP 3 N N N ππ Kπ KK = ± π + π results for S and C 24. = ± 37.5 = 12.5 ± 1.4 A ππ B N B ( t) N B ( tag ) N( Btag ) ( tag ) + N( Btag ) = S sin( m t) C cos( m t) ππ d ππ d S C A ππ ππ Kπ =.4 ±.22 ±.3 =.19 ±.19 ±.5 =.17 ±.41±.13 B B pairs, 113 /fb No significant signal for CPV yet with these data

24 Belle s result on 78/fb -Cππ = +.77 ±.27(stat) ±.8(syst) +.8 Sππ = 1.23 ±.41(stat) (syst).7 Events/(1.25ps) (a) q = +1-5 t (ps) Total π + π qq + Kπ B 5 Events/(1.25ps) (b) q = 1-5 t (ps) Total π + π qq + Kπ B 5 π + π yield Asymmetry (c) q = +1 q = 1 (d) t (ps) B π + π 3.1σ Evidence for CP Violation Result slightly unphysical Errors from toy MC Model dept α assumptions on δ T-P, P/T, β t (ps) 78 α 152 PRD (23)

25 New Result From Belle: 14/fb, B -pairs Improvements in the analysis; include more efficient continuum suppression algorithm (π π ) 2D fit in E-M BC plane data set I (78fb 1 ) data set II (62fb 1 ) -C=A ππ 2 2 physical bound: S + C 1 S ππ

26 Aππ Sππ Results = +.58 ±.15(stat) ±.7(syst) = 1. ±.21(stat) ±.7(syst) Belle 14fb ev. (all LR-r regions) Observation of CP Violation in B ππ (5.2 σ) Evidence for direct CPV (3.2 σ)

27 Toy MC Confirms Result is Reasonable Input: (A ππ, S ππ ) = (,) Belle result almost impossible probability ~.1 ppm Input: (A ππ, S ππ ) = maximum likelihood point in the physical region Belle result no problem probability ~ 27% 1 7 experiments (14fb -1 each) 1 7 experiments (14fb -1 each)

28 So how do these results compare? -C=A ππ Belle BaBar Belle and BaBar moving closer together as more data added Belle nearing physical region only about 1.9σ difference Belle error now from data S 2 ππ = 1 Cππ sin(2 αeff )

29 Model Dependent constraint on α α (deg) δ (deg) P /( T + P ) Small Penguin contribution ruled out by this measurement for P/T =.45 (conservative) 9 α 146 (95.5% CL)

30 Isospin Analysis: limiting factor is B π π Small signal; BR ~2 1-6 qq and ρπ background ) 2 Events / ( 2.5 MeV/ c + 14 π π N = 46 ± 3 BR( B ππ ) = (2.1±.6±.3) m ES (a) (GeV/c 2 ) Events/1. Phys.Rev.Lett. 91 (23) (c) 1 1 Significance including systematic errors = 4.2σ δα< B pairs F bin

31 ππ Isospin analysis 4-fold ambiguity needs all 3 modes + CP asymmetry measurements needs a lot more data to get a precision measurement! B ππ 26 now Belle: B π + π -

32 B ρπ / ρk : Not A CP Eigenstate doing analysis in region near ρ Dalitz Plot analysis goal ± X t / τ ( ) = (1 ± A ) ( S ± ) sin ( m t) ( C ± C ) cos ( m t) ρ X f t e S B CP ρ X ρx ρ X ρx related to α direct CPV ρk is self tagging C ρk, S ρk, S ρk =, C ρk = ±49.2 signal events large expected: A CP (ρπ) & A CP (ρk) BB ( ρπ ) = (22.6 ± 1.8 ± 2.2) 1 ± 6 BB ( ρ K ) = (7.3 ± 1.3) 1 ± BF From Winter 3 (82/fb)

33 LP 3 result (113 /fb) ~ B pairs + A ρπ 2.4σ C cos( m t) + S sin( m t) + A Difficult to relate to α without DP analysis ρπ ρπ ρπ

34 The Future for α α from B ππ is limited by theoretical interpretation - isospin analysis needs a Super B Factory - But can still get model dependent constraint B ρπ need a Dalitz plot analysis to really understand what is going on B ρρ - the new kid on the block By the end of the current generation of the B-factories we should expect to see combinations of measurements from these modes

35 B ρ + ρ final state is dominated by CP even helicity amplitude 2 mv fl 1 2 mb smaller penguin pollution than ππ or ρπ! expect now experimentally confirmed Assume Grossman Quinn Bound (ignores possible I=1 amplitudes) f ( B ρ ρ) ( B ρ ρ ) < Br > 2 ρρ, L L sin ( αef f α) = 16 (9% C.L.) f + L Br + + larger BF than ππ: (e.g. factorisation predicts 2.5 larger) promising alternative to ππ and ρπ for getting a precise measure of α

36 Measuring α with B ρρ Problems: Angular analysis Gluonic penguin pollution: δα Electro-Weak longitudinal Penguins polarisation is O(1) simplifies measurement Isospin Symmetry Breaking Interference Grossman Quinn Bound: δα 13 (68% C.L.) Current expectation O(5 ) theoretical uncertainty will improve See: Ciuchini, CKM Planning slac Fall 3 Not yet estimated Similar precision to α eff as for ππ (see BaBar physics book) Model free measurement of α soon!

37 BaBar Method: Optimised analysis for longitudinal polarisation component So have to work on reducing B and continuum background for large cosθ H only have to fit time dependence for longitudinal polarisation but deal with transverse and longitudinal Consider exclusive charmless and inclusive charm B backgrounds (~3K events) (about 16% of total background) large continuum background (~22K events) can fit shape on data so don t need to rely on MC

38 Likelihood Fit: B Background We use 7 distinct PDFs for the 7 main modes (with an asterisk and arrow in table). The fraction of b c decays is determined with the generic B B and B + B - MC. For the Five-body decays we use the JetSet estimation (from charmless cocktail). The BF of the other modes are measured or estimated from isospin symmetries. 38

39 Time Dependence is: t / τ Long e f ( t) = (1 ± S sin( ) cos( )) B ( B ) Long m t CLong m t 4τ t / τ Tran e f ( t) = (1 ± S sin( ) cos( )) B ( B ) Tran m t CTran m t 4τ (simplified form also have tagging dilution factor and resolution to consider) For now vary S and C for transverse component between ±1 as systematic main systematics: CPV in background (dominates) PDF shapes in likelihood SVT Local Alignment currently working on 82/fb plan to update to run1-3 soon Analysis in final stage of review journal draft in preparation expect a hep-ex soon

40 Blind Projections Assume that α~11 degrees (near the CKM best fit result) Project current sensitivity by 2.4 and 6 in stats Blind Plot 26 CL =.317 summer 4 Caveats: I=1 amplitudes could contribute at the level of 5% (see Falk et al; PRD ) Interference needs to be treated properly. Electroweak penguins could give up to a 5 degree correction on this Thanks to Andreas Höcker & Lydia Roos for plots

41 Can also get rid of some ambiguity: Isospin Analysis has 4 fold ambiguity inputs: BF, BF, BF, C, S, C, S Same as ππ I-spin analysis CPV in interference unique to ρρ I-spin analysis If BF is small Grossman Quinn bound; limit δα If BF is large do isospin analysis: measure S and C & resolve 2 solutions δα S constrains this angle

42 Conclusions α will ultimately be measured to O(5-1 ) at B factories Belle s new result established CPV in B ππ and is our best indication of direct CPV outside of the kaon system! isospin analysis of ππ limited by knowledge of penguin diagrams δα<5 as of now can get model dependent limits on α 9 α 146 (95.5% CL) [Belle] focus moving to ρπ and ρρ for longer term at current machines (theoretically cleaner) expect measurement from ρρ analysis soon watch hep-ex

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