Measurement of angle β with time-dependent CP asymmetry in. Emanuele Di Marco Università di Roma La Sapienza and INFN Roma December,

Transcription

1 Measurement of angle β with time-dependent CP asymmetry in B 0 K + K - K 0 decays Emanuele Di Marco Università di Roma La Sapienza and INFN Roma December,

2 b d CP violation in B 0 φk 0 and K + K - K 0 The decay is described by a penguin diagram B 0 u, c, t g W s s s d φ K S SM penguin: measure S=sin2β Also new particles, whose masses are at the NP scale, can enter, because they are off-shell in the loop: ~ ~ b s In a NP scenario: 1. NP can be favored by coupling (strong vs. weak) 2. The new particles couplings can be complex: new sources of CPV b ~ g b ~ g g ~ b s ~ s ~ g NP g s (for example SUSY) S sin(2β) would be a (indirect) modelindependent way of detect NP (destructive approach) Emanuele Di Marco 2 Determine from deviations S-sin(2β) constraints on NP (constructive approach)

3 CP content in B 0 K + K - K 0 Complication for measurement of CPV - CP depends on angular momentum L between K + and K - - (K + K - )K S can be both CP-even and CP-odd * K + L =L L=even CP(K + K - K S ) = +1 *[ CP(K + K - K S )= - CP(K + K - K L ) ] -sin2β K S B 0 K L L=odd CP(K + K - K S ) = -1 Dilution if both CP present!! +sin2β -> (2f odd -1) sin2β Need to analyze the angular momentum composition! Two strategies: 1. Quasi-2-body (BABAR 2004, Belle 2006): Measure the average CP in separate regions: low - high K + K - mass Measure the dilution with angular/isospin analysis to get sin2β 2. Dalitz plot analysis: get CP simultaneously to angular composition in the full phase space (BABAR 2006). Includes interference effects! NEW! Emanuele Di Marco 3

4 Isospin analysis Neglecting b u and b dg amplitudes, b sg is isospin conserving. B 0 K + K - K 0 and B + K + K 0 K 0 have: same partial widths (Γ) same decay dynamics Bose-Einstein: K 0 K 0 symmetric CP-even L=even: K S K S, K L K L (in equal proportions) L=odd: K S K L Reconstructing B 0 K + K - K S and B + K + K S K S (isospin) f CP-even =+0.86±0.18±0.09 Belle: PRD 69, [2004] Most of K + K - K S events out of φ is CP-even (φk S is CP-odd) Use f CP-even as dilution to get sin2β eff Emanuele Di Marco 4

5 Angular moment analysis - Describe K + K - amplitude as a sum of S-wave and P-wave A = A S + e i" A P - Decay rate in terms of moments of Legendre polynomials: " =! L L ( cos ) P P # - Moments <P L > computed using splots - in full B 0 K + K - K S phase space - in B+ K + K - K + in φ region f P = 5 4 P 2 P 0 Emanuele Di Marco 5 L f P =0.29 ± 0.03 (all DP) f P =0.89 ± 0.01 (φ region) f P =0.89 ± 0.08 ± 0.06 (non φ region) H [Phys.Rev.D71:091102,2005.] A P 2 From 879±36 K + K - K S (π + π ) decays [BABAR-CONF-06/040] Fraction of P-wave f P From 624±30 K + K + K - decays <m(K + K - )< GeV/c 2

6 The K + K - K 0 Dalitz Plot (DP) K + K - K 0 Dalitz plot composition: NEW! Resonant K + K - K 0 K - R K + K 0 Non-resonant K 0 B 0 K 0 B 0 K + B 0 K - B 0 K + R R K - eg.: R=φ,f 0 (980), etc. eg.: R=D +,D s + B 0 K + K - K 0 amplitude in the Isobar Model: f r =resonant amplitudes, NR c r =complex isobar coefficients cosθ H φ(1020) X 0 (1550) N.R. χ c0 D + the f r s interfere! m K+K- (GeV) Emanuele Di Marco 6

7 The B 0 K + K - K 0 decay amplitude Dalitz Plot variables: Invariant mass m K+K- & helicity angle θ H Proper decay time difference between B 0 and B 0 K S! H K K + K + K - CMS flavor tag 1. From Re(AA * ): sin(2β eff ) 2. From Im(AA * ): cos(2β eff ) trigonometrical ambiguity removed! Measure direct CPV ( C ) # m( A * f A f e $ 2i! ) = $% e( A * f A f )" sin(2! ) + # m( A * f A f )" cos(2! ) both real and imaginary because of CP-even, -odd interferences (->2β) real in Quasi-2-Body analyses (->sin2β) Emanuele Di Marco 7

8 The Dalitz Plot isobar model RBW: Relativistic Breit Wigner Flatte : coupled Breit Wigner (f 0 KK and f 0 ππ) K + K - P-wave K + K - S-wave + small NR P-wave K ± K 0 resonances NIG: non-interfering Gaussians BABAR B + K + K - K + Dalitz plot (230M BB) (2394 ± 63 signal events) [PRD72, (2006)] Emanuele Di Marco 8

9 B 0 K + K - K 0 event yields Rare decay: BF(B 0 K + K - K 0 ) excl.φ =24.7x10-6 ; BF(B 0 φk 0 )=8.6x10-6 reconstruct all sub-modes K + K - K K + K - K S (π 0 π 0 S (π + π ) [*] ) [*] K + K - K [**] L 879±36 138±17 499±52 840±34 BABAR: 347 M BB pairs Belle: 535 M BB pairs ΔE after a constraint m B 0 rec = mb 0 PDG Belle φk S excluded [*Signal weighted: M. Pivk, F. R. Diberder, Nucl. Instr. Meth. A 555, 356 (2005)] [**Likelihood enhanced] Emanuele Di Marco 9

10 Dalitz Plot results Fit to cleanest B 0 K + K - K S (π + π - ): Fit Fraction F r : for interference φ (1020) Branching fraction: X 0 (1550) χ c0 In m K+K- < 1.1 GeV/c 2 : m K+K- (GeV) cosθ H Emanuele Di Marco 10 Combined fit with the other sub-modes for CP fit

11 f 0 (980) parameters Plot (less correlated) variables 2m K -m 0 and g K /g π [Baru et al, Eur.Phys.J.A23, 525(2005)] e+e- experiments In chmls B-decays: BABAR uses BES Belle uses E791 E791 measures g K << g π f 0 (980) K + K - small under φ (small dilution) BES predicts very larger f 0 contribution Precise measurement of f 0 (980) couplings expected by D B-factories! BES parameters seems more consistent with other measurement Emanuele Di Marco 11

12 BABARAR vs Belle S-wave estimation _ 532M BB Belle helicity (±10 MeV under φ) [Hazumi ICHEP06 talk] BABAR B + K + K - K + (230M BB pairs) [PRD72, (2006)] BABAR B 0 K + K - K 0 (347M BB pairs) [hep-ex/ ] Belle estimation (±10 MeV) from B + K + K - K + Dalitz (140fb -1 ): P-wave (φ) + S-wave non resonant no f 0 (980) contribution f S-wave = 2.75 ± 0.14% BABAR estimation (±10 MeV): B + K + K - K + angular moments (347M BB): ~ 8 ± 1% B 0 K + K - K 0 and B + K + K - K + Dalitz: f 0 K ~ 10 ± 3% + NR ~ 3 ± 1% -> f S-wave = 13 ± 3% Emanuele Di Marco 12

13 BABAR: : CPV results for B 0 φk 0 Asymmetry B 0 B 0 B 0 φk S + Asymmetry B 0 0 φk φk L L opposite CP eigenstate wrt φk S In Standard Model: C SM =0 β SM =0.379 C(φK 0 )=-0.18 ± 0.20 ± 0.10 β(φk 0 )=0.06 ± 0.16 ± 0.05 C(f 0 (980)K 0 )=0.45 ± 0.28 ± 0.10 β(f 0 (980)K 0 )=0.18 ± 0.19 ± 0.04 [m(k + K - )<1.1 GeV/c 2 ] S < sin2β. Deviation? Agreement in ~2σ Emanuele Di Marco 13

14 BABAR: : CPV results for B 0 K + K - K 0 Measured an average CP over the DP Trigonometric reflection excluded at 4.6σ Trigonometric reflection (β eff π/2-β eff ) CPV at 4.5σ level Principal solution Δlog(L)=10.6=4.6σ B 0 K + K - K S β eff π/2 β eff first β ambiguityfree measurement with penguin modes nominal solution within 1σ from SM β(k + K - K 0 )=0.361 ± ± C(K + K - K 0 )= ± ± Emanuele Di Marco 14 In Standard Model: C SM =0 β SM =0.379

15 Belle: : CPV results for B 0 K + K - K S Fit for: S f =(2f odd -1)sin2β eff A f =-C (BABAR definition) sin2β eff =+0.68±0.15±0.03 A f =-0.09±0.10± systematics due to the f odd fraction uncertainty sin2β(φk 0 ) Q2B = 0.50 ± 0.21 ± 0.06 SM expectation: S f =sin2β, A f =0 sin(2β)=0.674 ± [BABAR Coll.: hep-ex/ ] [Belle Coll.: hep-ex/ ] good tags (r > 0.5) Consistent within 1σ with sin2β measured in B 0 [cc]k S Emanuele Di Marco 15

16 Summary of experimental results tree Convert β S =sin(2β) Average the f 0 K 0 result with f 0 π + π Belle: B 0 φk 0 and B 0 K + K - K 0 from separate Q2B fits BABAR: all from Dalitz plot fit BABAR : Dalitz plot fit to non-φ region in preparation 2004 Q2B result used for averaging by HFAG All consistent, but there is a trend: all S < sin(2β) Emanuele Di Marco 16

17 Perspectives for the future B-factories now have collected ~1ab -1 of data. All the b s penguins measurements are statistically limited. New experimental techniques (Dalitz plot, K L -ID) made measurements of some b s penguin more precise ~100 fb -1 ~5 ab -1 Summer 2006 BaBar+Belle Assuming current world average as the true value, need ~2ab -1 to observe a discrepancy from Emanuele Di Marco 17

18 Conclusions Measured tcpv in one of the theoretically cleanest modes: BABAR B 0 φk 0 : for the first time a time-dependent Dalitz plot approach is used to measure simultaneously angular composition and CPV in the whole K + K - K 0 phase space removes dilution for final states with opposite CP model uncertainties included in the fit it is the correct way to account for interference effects! Belle uses quasi 2 body approach to estimate the CP dilution separate results for φk 0 / K + K - K 0 (non φ) CPV Both measurements are consistent with SM predictions They constraint SUSY Flavor Violating squark mixing angles in SUSY GUTS, this correspond to limits in lepton FV (ex. τ µγ decays) the right place to search for NP also during LHC! Emanuele Di Marco 18

19 More slides Emanuele Di Marco 19

20 B-meson signal box: Kinematics & event shape Energy-substituted mass m = E! p ES *2 beam *2 B (Resolution from beam energy) Energy difference "E = E * * B # E beam (Sensitive to E measurement) Event shape * = e + e - CM frame BB events e + e "! qq events Emanuele Di Marco 20

21 BABAR: : K + K - K L K L s reconstruction at BABAR: as ECAL cluster w/o associated track as cluster in µ-system 1. Constrain m ES =m B0 : Both can t measure K L s energy! Energy difference BB events 2. get p KL and compute ΔE with only ΔE higher background w.r.t. K S modes Used K L identification in the ECAL to reduce the background! e + e "! qq events Emanuele Di Marco 21

22 Non-resonant contribution Cheng-Yang NR model + resonances (line) [Cheng,Chua,Soni, PRD72:094003(2005)] overlaid with BABAR angular moments (points) [PRD71:091102(2005)] φ P-Wave (CP-odd*) S-Wave (CP-even*) 232M BB X 0 (1500) not included in model *[ CP(K + K - K S )= - CP(K + K - K L ) ] Experimental non-resonant model used in nominal fit (exponential): Cheng-Chua-Soni model: NR + wide f 0 (1530) (not in PDG) - Used for systematics Emanuele Di Marco 22

23 K L identification (I) K L s identified through nuclear interactions in the EMC or in the IFR EMC / IFR have different resolutions, different backgrounds EMC: better resolution, more background in EMC most of it made by photons Identification based on: Missing momentum (γ s energy measured, K L s not, or not completely) Signal MC background Signal MC background p T miss: missing momentum projected onto expected K L direction K L nucleus γ EMC: part of the energy is reconstructed IFR: energy is not reconstructed shower shape in the EMC: lateral extension of an EM shower is narrower w.r.t. a hadronic cascade EM shower EM shower Nucleons, K s, etc. Nucleons, K s, etc. Nucleus. EM shower EM shower hadronic cascade Emanuele Di Marco 23

24 K L identification (II) Tune 2 alorithms with 7 variables sensitive to energy spread of the shower in the EMC: a Neural Network (NN) a Boosted Decision Tree (BDT) B.P.Roe, H.J.Yang, J.Zhu, Y.Liu, I.Stancu and G.McGregor, [NIM. A 543, 577 (2005)] 1. BDT gives a better K L /γ separation wrt NN 2. K L /γ separation increases with K L energy Validation on data control sample: e + e - φ(k S K L )γ ~12000 signal events! BDT output for different K L kinematics: Weighted data - MC cosθ energy Emanuele Di Marco 24

25 electron βγ=0.56 Time-dependent CPV (tcpv( tcpv) ϒ(4S) resonance B 1 positron B 2 "t # "z $% c B 0 _ B 0 CP-side π -K+ µ + Flavor tag and vertex reconstruction 1. Fully reconstruct one B-meson which decays to CP eigenstate (es. J/ψK S ) 2. Tag-side determines its flavor (effective efficiency = 30%) 3. Proper time (Δt) is measured from decay-vertex difference (Δz) ν µ Δz ~ 200µm 0 D µ + µ - π - J/ψ K S/L Emanuele Di Marco 25

26 tcpv: : resolution & tagging quality S = 0.65 C = 0.00 _B 0 tag B 0 tag B _ 0 tag B 0 tag P 1 4#! t " ( q = ± 1,! t) = e # [ 1± ( S sin! m! t + Acos! m! t) ] Asymmetry in B D*lν: determine Δm, w on data Δt (ps) ( 1! 2w)! R R : detector resolution ω : wrong tag fraction (misidentification of flavor) (1-2ω) quality of flavor tagging They are well determined by using data control samples D * lν, D (*) π etc Emanuele Di Marco 26

27 Systematic uncertainties The DP model is the largest one for the full DP fit fix the X 0 (1500) to f 0 (1500) of PDG vary the other resonances parameters use the Cheng-Chua-Soni model for the NR The NR and X 0 (1500) contributions in m(k + K - )<1.1 GeV are negligible: for this fit the DP model systematic is highly reduced DP resolution: neglected in the nominal fit (<resonances width) included for systematics CP of BB background, vertexing and tagging Possible biases in the fit Double-Cabibbo-Suppressed-Decays tag side interference Emanuele Di Marco 27

28 Interpreting results: the MSSM The measurements show agreement with SM. Can they be used to constraint New Physics parameters? In the MSSM, introduce a SUSY partner of each SM particle. ~ g Assume that the gauge couplings of the SUSY particles have the same flavor of the SM partners In the basis where the quark mass matrix is diagonal, squarks mass is not diagonal (super-ckm basis) b ~ b ~ s g s The down-type squark mass matrix: A new ~ kind of interaction : ~ the b s mass insertion Assuming Δ s small and squarks nearly degenerate, use the Mass Insertion Approximation (MIA): Dimensionless, complex quantity Emanuele Di Marco 28 A (B)=helicity of the initial (final) state Mean squark mass

29 Constraining δ ij s The phases Im(δ ij s) can produce further CPV δ 12 and δ 13 already highly constrained from s d and b d transitions (~0) b s transitions is the less constrained sector. Use these decays to constraint δ 23. Experimental inputs from: BR(B X s γ, E cut =1.8 GeV)=(3.51 ± 0.43)x10-4 A CP (B X s γ)=0.004 ± BR(B X s l + l -, low)=(1.59 ± 0.49)x10-6 BR(B X s l + l -, high)=(4.34 ± 1.15)x10-7 Im(δ d 23 ) LL [V. Porretti, L. Silvestrini] Im(δ d 23 ) RR A CP (B X s l + l - )=-0.22 ± 0.26 Δm s =17.77 ± 0.12 ps -1 These measurements favour SM solution: [Re,Im](δ ij )=0 Im(δ d 23 ) LR Re(δ d 23 ) LL Im(δ d 23 ) RL Re(δ d 23 ) RR How are they related with CPV in b s? Re(δ d 23 ) LR Re(δ d 23 ) RL Emanuele Di Marco 29

30 New physics phases constraints Off diagonal elements of squark mass matrix Initial, final helicity mean squark mass Agreement with SM favors S φk = sin2β and C φk =0 δ LR and δ RL allow smaller values of S S φk M. Ciuchini et al., PRD 68: , [2003] S φk Intriguing trend S < sin2β! (SM estimations predict S > sin2β) b d! W tree c c s d S φk SM: S=sin2β=0.674 ± C=0 C φk S φk C φk Penguin naïve average: sin2β eff =0.52 ± 0.05 SM theoretical predictions (QCD factorization) (penguin-tree) Emanuele Di Marco 30 BABAR measurement: S φk =0.12±0.31±0.10 C φk =0.18±0.20±0.10 C φk C φk