Measurements of the CKM Angle α at BaBar

Transcription

1 Proceedings of the DPF-9 Conference, Detroit, MI, July 7-3, 9 SLAC-PUB-493 Measurements of the CKM Angle α at BaBar S. Stracka on behalf of the BaBar Collaboration Università degli Studi di Milano and INFN, Sezione di Milano - I-33 Milano, Italy We present improved measurements of the branching fractions and CP-asymmetries in the B π + π, B π π, and B + ρ + ρ decays, which impact the determination of α. We find for B ππ decays, and S ππ + =.68 ±. ±.3 C ππ + =.5 ±.8 ±. Cππ =.43 ±.6 ±.5 B(B π π ) = (.83 ±. ±.3) 6 B(B + ρ + ρ ) = (3.7 ±.4 ±.4) 6 f L (ρ + ρ ) =.95 ±.5 ±.6 α ρρ = ( ) for B ρρ decays. The combined branching fractions of B K (7)π and B K (4)π decays are measured for the first time and allow a novel determination of α in the B a (6) ± π decay channel. We obtain B(B K (7) + π + K (4) + π ) = ( ) 5 B(B + K (7) π + + K (4) π + ) = ( ) 5 α a π = (79 ± 7 ± ). These measurements are performed using the final dataset collected by the BaBar detector at the PEP-II B-factory.. Introduction in B a (6) ± π decays. The primary goal of the experiments based at the B factories is to test the Cabibbo-Kobayashi-Maskawa (CKM) picture of CP violation in the standard model of electroweak interactions []. This can be achieved by measuring the angles and sides of the Unitarity Triangle in a redundant way. An effective value α eff for the CKM phase α arg( V td Vtb /V ud V ub ) can be extracted from the timedependent analysis of B meson decays dominated by tree-level b uūd amplitudes, such as B π + π, B ρ + ρ, B ρ ± π, and B a (6) ± π. The current average values of α, α = (9 ± 7) [] and α = ( ) [3], obtained with different statistical techniques, are based solely on the analysis of B ππ, B ρρ, and B ρπ decays. The measurement of the angle α has witnessed significant progress over the past year. The following sections are organized as follows: a brief introduction on the experimental technique is given in Sec. ; the summer 8 update of the measurement of the time-dependent CP-violating asymmetries in B π + π decays and of the branching fractions (BFs) of B π π decays is reported in Sec. 3; Sec. 4 describes the 9 update of the BF measurement of B + ρ + ρ decays, and its impact on the precision of the determination of α; in Sec. 5, we introduce the first measurement of B K (7)π and B K (4)π decays and a new determination of α. Experimental techniques The interference between the direct tree decay (which carries the weak phase γ) and decay after B B mixing (which carries a weak phase β) results in a time-dependent decay-rate asymmetry that is sensitive to the angle β + γ = π α. At the asymmetric-energy e + e B-factory PEP-II, running at a center of momentum (CM) energy of.58 GeV, a B B pair is coherently produced in the decay of a Υ(4S) resonance. The resulting B B system has a boost βγ.56 with respect to the laboratory frame. By means of this experimental device it is possible to measure the decay vertex displacement z of the two B mesons in the event, and hence their proper-time difference t meas z βγc. One of the B mesons (B rec ) is fully reconstructed according to the final state of interest. In order to study the time-dependence of the decay rates, it is necessary to measure the proper-time difference t between the two B mesons in the event and to identify the flavor of the other B-meson (B tag ). The flavor and the decay vertex position of B tag are therefore identified from its decay products. The decay-rate distribution for B ( B ) decays to Work supported in part by US Department of Energy contract DE-AC-76SF55. SLAC National Accelerator Laboratory, Menlo Park, CA 945

2 Proceedings of the DPF-9 Conference, Detroit, MI, July 7-3, 9 a CP-eigenstate, such as π + π, is given by: dn d t = e t /τ 4τ { q tag [ C cos( m d t) () ]} S sin( m d t), where τ = (.536±.4)ps [4] is the mean B lifetime, m d = (.5 ±.7)ps is the B B mixing frequency [4], and q tag = + ( ) if the B tag decays as a B ( B ). The parameters S and C describe mixinginduced and direct CP-violation, respectively, and are defined as: S = Imλ + λ, C = λ + λ, with λ = q Ā p A, where q/p is related to the B B mixing, and A (Ā) is the amplitude of the decay of a B (B ) to the final state under study. If only the tree amplitude contributes to the decay, S = sin(α) and C =. However, b uūd transitions receive sizeable contributions from penguin (loop) amplitudes, which carry different strong and weak phases. This contribution can result in non-zero direct CP-violation C and modifies S into S = sin(α eff ) C. () The angle α eff coincides with α in the limit of vanishing penguin contributions. In order to constrain α α α eff, techniques based on the SU() isospin symmetry (for decays to a CP-eigenstate, such as B π + π, ρ + ρ ) or the SU(3) approximate flavor symmetry (for decays to a non CP-eigenstate, such as B ρ ± π, a (6) ± π ) have been devised, and are discussed in the remaining of this paper. A neural network based tagging algorithm [5] is used to determine whether the B tag is a B or a B. Events are separated according to the particle content of the B tag final state into events where there are leptons, kaons and pions, for a total of seven mutually exclusive categories. The performance of the tagging algorithm is characterized by the efficiency ǫ tag in the determination of the flavor of B tag and by the mistag probability ω, and depends on the tagging category. The t distribution of Eq. is convolved with a detector resolution function, which differs for signal and background, and is parameterized as a triple Gaussian. Dilution from incorrect assignment of the flavor of B tag is also taken into account: dn d t meas = e t /τ 4τ q tag ( ω) R( t meas t), { q tag ω (3) [ C cos( m d t) ]} S sin( m d t) where ( ω) is the dilution factor, ω is the difference in mistag probabilities ω ω B ω B and R is the resolution function. The parameters of the resolution function are obtained from a fit to a large sample of fully reconstructed B decays, as in [5], and are free to differ between tagging categories. The analyses of the two-body and quasi-two-body decays described in the remaining of this paper rely on a common strategy for the suppression of the continuum e + e q q background (q = u, d, s, c), which represents the most abundant source of background. Two kinematic variables, the energy substituted mass m ES = s/4 p B and the energy difference E = E B s/, where s is the e + e CM energy and the four-momentum (E B, p B ) of the B meson is defined in the CM frame, allow to discriminate correctly reconstructed B candidates (for which the distribution of m ES peaks at the B-meson mass and that of E peaks at zero) and fake candidates resulting from random combination of particles (for which m ES follows a phase-space distribution and E is approximately flat). Topological variables provide further distinction between the jet-like shape of continuum events and the more isotropic B decays, and can be combined into multivariate classifiers, such as neural network and Fisher discriminant, to enhance the discriminating power. The signal and background yields and CP asymmetries are extracted via an extended unbinned maximum-likelihood (ML) fit to the data. 3. Isospin analysis of B ππ decays 3.. B π + π In the ππ system the penguin pollution is greatest. The tree (T) and penguin (P) amplitudes each contribute, with different weak (φ) and strong (δ) phases, with comparable magnitude. Direct CP violation, which is given by A CP = sinφsin δ/( T/P + P/T + cos φ cos δ), can, therefore, be within observational reach. B π + π decays are analyzed with the full BaBar dataset of 467 ± 5 million BB pairs [6]. A simultaneous ML fit to the π + π, π + K, K + π, and K + K final states is performed. K π separation is obtained by particle-identification (PID) observables (the Cherenkov angle Θ C in the DIRC [7] and ionization-energy loss de/dx in the tracking devices [8]). Additional separation between the final states under study is achieved from E: since the B meson is reconstructed from two oppositely charged tracks that are both given the pion mass hypothesis, each charged K in the final state results in a E displacement of about 45 MeV. We extract 394 ± 54 signal events. From the time distribution of B π + π decays a non-zero mixing-induced

3 Proceedings of the DPF-9 Conference, Detroit, MI, July 7-3, 9 3 C ππ.5 BABAR Preliminary the B + π + π mode in a model-independent isospin analysis [9]. Under the isospin symmetry, B ππ amplitudes can be decomposed in isospin I = (A ) and I = (A ) amplitudes. By virtue of Bose statistics, I = contributions are forbidden. The following relations hold [9]: - -C.L. = (/ )A + = A A, (4) A = A + A, A + = 3A, (5) S ππ Figure : S ππ + and C ππ + in B π + π : the central values, errors, and confidence-level (CL) contours, calculated from the square root of the change in the value of ln L compared with its value at the minimum [6]. The systematic errors are included. The measured value is 6.7σ from the point of no CP violation (S ππ + = and C ππ + = ). CP violation asymmetry S ππ + =.68 ±. ±.3 is observed with significance 6.3σ [6], as shown in Fig.. A non-zero direct CP violation asymmetry C ππ + =.5 ±.8 ±. is also extracted with significance 3.σ [6]. 3.. B π π The B π π decay is formed from pairs of π γγ candidates, where one of the photons can eventually be reconstructed from two tracks coming from a photon conversion γ e + e inside the electromagnetic calorimeter. The yield and the flavor tag- and time-integrated CP asymmetry A CP = C ππ are obtained from a ML fit to the kinematic variables E and m ES and the output of a neural network NN computed from event-shape variables, as well as the output of the B- flavor tagging algorithm. The background model accounts for correlations between NN and m ES. We observe 47±9 signal events (corresponding to B(B π π ) = (.83 ±. ±.3) 6 ) and extracts Cππ =.43±.6±.5 [6]. Since no reliable vertex information is extracted, Sππ can not be determined Isospin analysis of B ππ decays The rates and CP asymmetries of B π + π and B π π decays are combined with the results for where A ij (A ij ) are the amplitudes of B (B) decays to the π i π j final state. This yields the complex triangle relations: A + = A + A, (6) A + = A A. (7) Tree amplitudes receive contributions from both A and A, while gluonic penguin diagrams are pure I = amplitudes and do not contribute to B + π + π amplitudes. Possible contributions from electroweak penguins (EWP), which do not obey SU() isospin symmetry, are assumed to be negligible and are therefore ignored. Under this assumption, A + = A (a sizeable contribution from EWPs would result in A + A and would be signalled by an evidence of direct CP violation in B + π + π decays). If A + and A are aligned with a suitable choice of phases, the relations (6) and (7) can be represented in the complex plane by two triangles (Fig. ), and the phase difference between A + and A + is α. A + ~ A A + + A, A ~ ~ A Figure : Triangles in the complex plane describing the isospin relations Eq.(6) and Eq.(7). Constraints on the CKM angle α and on the penguin contribution α are obtained from a confidence level (CL) scan over the parameters of interest, α and α. Assuming the isospin-triangle relations (6) and (7) and the expression (), a χ for the five amplitudes (A +, A +, A, A +, A ) is calculated from

4 4 Proceedings of the DPF-9 Conference, Detroit, MI, July 7-3, 9 Table I Summary of the input to the isospin analysis of the ππ system [6, ]. Mode B( 6 ) C π + π 5.5 ±.4 ±.3.5 ±.8 ±. π + π 5. ±.46 ±.9 (.3 ±.8 ±.) π π.83 ±. ±.3.43 ±.6 ±.5 the measurements summarized in Table I, and minimized with respect to the parameters that don t enter the scan. The CL values are then calculated from the probability of the minimized χ. The results of the isospin analysis are shown in Fig. 3 and Fig. 4. α is extracted with a four-fold ambiguity, which can be graphically represented as a flip of either triangle around A +. An additional two-fold ambiguity arises from the trigonometric relation S ππ + = sin(α eff ) C ππ +. This results in a global eight-fold ambiguity in the range [, 8] on the extraction of α. A value α < 43 at 9% CL is obtained, which dominates the uncertainty on α [6]. Considering only the solution consistent with the results of global CKM fits, α is in the range [7, 9] at the 68% CL [6]. The limiting factor in the extraction of α is the knowledge of A and A, which is severely limited by the available statistics. A significant increase in statistics is therefore required in order to perform a precision measurement of α in this channel. A measurement of Sππ, which would aid resolving some ambiguities on α, can only be addressed with Super B factory luminosities []. 4. Isospin analysis of B ρρ decays With respect to B ππ decays, B ρρ decays have a more favourable penguin to tree amplitude ratio. Moreover, the BF for B ρ + ρ decays is greater than that for B π + π decays by a factor of 5 []. Finally, the B ρ ρ decay can be reconstructed from a final state consisting of all charged tracks, with enough efficiency to allow for a measurement of Sρρ with the present statistics [3]. Despite these many advantages with respect to the isospin analysis of ππ decays, the ρρ system exhibits some potential complications. In B ρ + ρ transitions, a pseudo-scalar particle decays into two vector mesons. Three helicity states (H =, ±), with different CP transformation properties, can therefore contribute to the decay [4]. The H = state corresponds to longitudinal polarization and is CP-even, while the transverse polarization states H = + and H = (which are superpositions of S-, P-, and D-wave amplitudes) have not a definite CP-eigenvalue. Isospin relations similar to Eq. (6) and (7) hold separately for each polarization state. The analysis of the angular distribution of B ρ + ρ decays allows to determine the longitudinal polarization fraction f L : d Γ 4f L cos θ cos θ Γ d cosθ d cosθ +( f L )sin θ sin θ, (8) where θ (θ ) is the angle between the daughter π and the direction opposite to the B direction in the ρ + (ρ ) rest frame, as shown in Fig. 5. Since experimental measurements have shown the decay to be dominated by the longitudinal, CP-even polarization, it is not necessary to separate the definite-cp contributions of the transverse polarization by means of a full angular analysis. A second complication arises because the ρ mesons have finite width, thus allowing for the two ρ mesons - C.L BABAR Preliminary α - α eff (degrees) - C.L α (degrees) Figure 3: Projection of the CL scan on α for the ππ system [6]. Figure 4: Projection of the CL scan on α for the ππ system [6].

5 Proceedings of the DPF-9 Conference, Detroit, MI, July 7-3, 9 5 φ ρ π θ -CL π θ + ρ π +.5 π Figure 5: Definition of the θ and θ angles in B ρρ decays []. in the decay to have different masses. Since the Bose- Einstein symmetry does not hold, the wave function of the ρρ system can be anti-symmetric, and isospin I = amplitudes are allowed, breaking the isospin relations Eq.(6) and (7) [5]. The stability of the fitted CP-violation parameters against the restriction of the ππ invariant mass window used to select the ρ candidates shows however that possible isospin violation effects are below the current sensitivity. - =α-α (deg) α eff Figure 6: Projection of the CL scan on α for the ρρ system [6]. -CL 4.. B + ρ + ρ The B + ρ + ρ decay analysis has been updated using the final BaBar dataset of 44 fb [6], superseding the previous analysis based on fb [7]. An analysis of the angular distributions of B + ρ + ρ decays is performed. The signal yield and longitudinal polarization fraction is extracted via a ML fit to the kinematic quantities m ES, E, the output of a neural network N N based on event-shape variables, the mass of the ρ + and ρ candidates, and the cosines of the helicity angles θ ρ + and θ ρ, where θ ρ + (θ ρ ) is the angle between the daughter π (π ) and the direction opposite to the B direction in the ρ + (ρ ) rest frame. Improvements have been introduced on the charged particle reconstruction and on the background model, which takes into account correlations between N N, the cosine of the helicity angle, and the ππ invariant mass for each ρ meson in the final state. The measured BF increases from (8. ± 3.) 6 [7] up to (3.7 ±.4 ±.4) 6 [6]. The longitudinal polarization fraction is f L =.95 ±.5 ±.6 [6]. The measured direct CP-violation asymmetry A CP Γ(B ρ ρ ) Γ(B + ρ + ρ ) Γ(B ρ ρ )+Γ(B + ρ + ρ ) is A CP =.54 ±.55 ±., which is consistent with. This result indicates that the contribution from EWPs is negligible, and the isospin analysis holds within an uncertainty of [8]..5 CL=68% CL=9% 5 5 α (deg) Figure 7: Projection of the CL scan on α for the ρρ system [6]. The BFs, longitudinal polarization fractions, direct and mixing-induced CP violation asymmetries for B ρρ decays are used as input to the isospin analysis, and are summarized in Table II. The BF s of B + ρ + ρ and B ρ + ρ are now very similar and much higher than that for the B ρ ρ penguin transition. As a consequence, the isospin triangles do not close, i.e. A + / + A < A +. This results in a degeneracy of the eight-fold ambiguity on α into a four-fold ambiguity, corresponding to peaks in the vicinity of, 9 (two degenerate peaks), 8, as shown in Fig. 6 and Fig. 7. A value

6 6 Proceedings of the DPF-9 Conference, Detroit, MI, July 7-3, 9 Table II Summary of the input to the isospin analysis of the ρρ system [, 3, 6]. Mode B( 6 ) f L C S ρ + ρ 5.5 ± ± ±.5 ±.6.7 ± ρ + ρ 3.7 ±.4 ±.4.95 ±.4 ±.6 (.54 ±.55 ±.) - ρ ρ.9 ±.3 ± ±.4. ±.8 ±.3.3 ±.7 ±..8 < α < 6.7 at 68% CL is obtained. Considering only the solution consistent with the results of global CKM fits, α = The precision on α is now at the level of 5%. 5. B a (6) ± π It is possible to extract α from B decays to final states that are not CP-eigenstates [9], such as B a (6) ± π decays. The relevant amplitudes are: A + A(B a + π ), A + A( B a π+ ), (9) A A(B a π+ ), A A( B a + π ).() The time distribution for this decay mode is given by: dn a± π d t meas = ( ± A CP ) e t /τ 4τ q tag ( ω) R( t meas t), { q tag ω + [ (S ± S)sin( m d t) ]} (C ± C)cos( m d t) where A CP is the time- and flavor-integrated charge asymmetry, and S ± S Im ( ) e iβ A A ±, () A ± + A C ± C A ± A A ± + A. () The measured CP-violation parameters for B a (6) ± π decays are summarized in Table III []. Table III Values of the CP-violation parameters used as input to the calculation of the bounds on α []. A CP.7 ±.7 ±. S.37 ±. ±.7 S.4 ±. ±.6 C. ±.5 ±.9 C.6 ±.5 ±.7 In analogy to the π + π case, where α eff = arg [ e iβ A( B π + π )A (B π + π ) ], it is possible to define two quantities α + eff and α eff : α ± eff arg [ e iβ A ± A ±], (3) which are related by the phase ˆδ arg[a + A ] to the measurable quantities: α ± eff ± ˆδ = arg [ e iβ A ± A ] (4) S S = arcsin. (5) (C C) In the limit of zero penguin amplitudes, ˆδ coincides with the strong phase difference between the tree amplitudes contributing to B a (6) + π and B a (6) π + decays. An effective value α eff for the weak( phase α is then obtained as the average α eff = α + eff + eff) α with an eight-fold ambiguity []. It is possible to apply arguments based on the approximate SU(3) flavor symmetry to set bounds on α. The following ratios of CP-averaged rates of S = and S = transitions are calculated, that involve the same SU(3) flavor multiplet as a (6) [], such as B a (6) K +, B K + A π, B + a (6) + K, and B + KA π+ : R + λ f a B(B K + A π ) f K A B(B a + π ), (6) R + + λ f a B(B + K A π+ ) f K A B(B a + π ), (7) R λ f π B(B a K+ ) f K B(B a π+ ), (8) R + λ f π B(B+ a + K ) f K B(B a π+ ). (9) The bounds are effective because the penguin contribution is CKM enhanced by /λ = V cs / V cd in S = decays with respect to S = modes. The following inequalities involving (α ± eff α) hold: cos(α ± eff α) R ± A ± CP () cos(α ± eff α) R+ ±, () A ± CP

7 Proceedings of the DPF-9 Conference, Detroit, MI, July 7-3, 9 7 where A ± CP are the direct CP asymmetries A ± CP A ± A ± A ± + A ±. () The above relations set a constraint on (α ± eff α). Bounds on α are then derived from α ( α + eff α + α eff α )/. The BFs of B a (6)π and B a (6)K decays have been measured in the last few years []. The measurement of the missing piece of input, the BFs of B K (7)π and B K (4)π decays, is described in the following section. 5.. B K (7)π, B K (4)π The K A meson (the SU(3) partner of the a (6) meson) is a nearly equal superposition of the physical states K (7) and K (4). The rates of B K A π decays, which are experimental inputs to the calculation of the bounds on α, must be derived from the measurement of the rates of B K (7)π and B K (4)π decays. The BFs for these processes have recently been measured by BaBar []. The K (7) and K (4) axial vector mesons are broad resonances with nearly equal masses. In the following, we will refer to them collectively as K. The K (7) and K (4) mesons decay to the same final state Kππ, although through different intermediate states. However, since the intermediate decays proceed almost at threshold, the available phase spaces overlap and interference effects can be sizeable. The analysis strategy relies on the reconstructed Kππ invariant mass spectrum in the [.,.8] GeV range to distinguish between K (7) and K (4), including interference effects in the signal model. A two-resonance, six-channel K-matrix model is used to describe the resonant Kππ system for the signal [3]. The production amplitude for channel i = {(K π) S wave, (K π) D wave, ρk, Kπ, f K, ωk} is given by F i = e iδi ( ikρ) ij P j, (3) j where δ i are offset phases with respect to the (K π) S channel, K ij = f aif aj M a M + f bif bj M b M, (4) and P is the production vector P i = f paf ai M a M + f pbf bi M b M. (5) The labels a and b refer to K (4) and K (7), respectively, and the indexes i and j refer to the final states of K decays. The decay constants f ai, f bi, and the K-matrix poles M a and M b are real. The elements of the diagonal phase space matrix ρ(m) for the process K 3 + 4, have been approximated with the form ρ = δ ij m m 4 M m (M m + m m 4 + i ), (6) 4 where M is the mass of K, m 4 is the mass of 4, m is the mean mass of 3 and is the half width of 3. The parameters of K and the offset phases δ i are extracted from a fit to the data collected by the WA3 experiment [3] for the intensity of the Kππ channels and the relative phases. For the fit to WA3 data a background term is included in the production vector. The decay constants for the ωk channel are fixed according to the quark model [3]. The production constants f pa and f pb are expressed in terms of the production parameters ζ = (ϑ, φ): f pa cosϑ, f pb sinϑe iφ, where ϑ [, π/], φ [, π]. Signal Monte Carlo (MC) samples are generated by weighting the (Kππ)π population according to the amplitude i ωk Kππ i F i, where the term Kππ i consists of a factor describing the angular distribution of the Kππ system resulting from K decay, an amplitude for the resonant ππ and Kπ systems, and isospin factors. The BF of K ωk is accounted for as a correction to the total selection efficiency. The BF and the production parameters ϑ, φ for neutral and charged B meson decays to K (7)π + K (4)π are extracted via a ML fit to the kinematic observables m ES, E, a Fisher discriminant based on event-shape quantities, the Kππ invariant mass m Kππ and an angular variable. Background from B decays to K (4)π and non-resonant B decays to K ππ and ρkπ are taken into account as separate components in the fit. The dependence of the signal probability distribution in m Kππ and selection efficiencies on the production parameters ζ is described by means of non-parametric templates P(m Kππ ϑ, φ). Each event is classified according to the invariant masses of the π + π and K + π (K S π+ ) systems in the K + (K ) decay for B (B + ) candidates: events which satisfy the requirement.846 < m Kπ <.946 GeV belong to class ( K band ); events not included in class for which.5 < m ππ <.8 GeV belong to class ( ρ band ); all other events are rejected. For the B modes a likelihood scan is performed with respect to ϑ and φ. At each point, a simultaneous fit to the event classes r =, is performed. Although for events in the ρ band the signal to background ratio is worse than that for events in the K band, MC studies have shown that including those events in the fit helps in resolving the ambiguities in the determination of the parameter φ. For the B + modes, simulations show that, due to a less favourable signal to background ratio and increased background from

8 8 Proceedings of the DPF-9 Conference, Detroit, MI, July 7-3, 9 B decays, the analysis is not sensitive to φ. A value φ = π is therefore assumed and the scan is performed only with respect to ϑ. At each point of the scan, a fit to K band events only is performed. Figure 8 shows the distribution of E, m ES and m Kππ for the signal events obtained by the background-subtraction technique splot [4]. The experimental two-dimensional likelihood L for ϑ and φ is convolved with a two-dimensional Gaussian that accounts for the systematic uncertainties. The resulting distributions in ϑ and φ are shown in Fig. 9 (the 68% and 9% probability regions are shown in dark and light shading respectively, and are defined as the regions which satisfy L(r) > L min and L(r)>L min L(ϑ, φ)dϑdφ = 68% (9%)). A combined signal for B decays to K (7) + π and K (4) + π is observed with a significance of 7.5σ, while there s evidence for B + decays to K (7) π + and K (4) π + at 3.σ. The measured BFs are B(B K + π + K + π ) = and B(B + Kπ + + K π + ) = (< 8 6 at 9% probability), including systematic uncertainties []. The probability distributions for the B K (7)π, B K (4)π, and B K A π BFs are derived by setting the production parameters (f pa, f pb ) equal to (, e iφ sinϑ), (cosϑ, ), and ( f pa cosθ, f pa sin θ), respectively, where f pa = cosϑcosθ e iφ sin ϑ sinθ and θ is the K mixing angle. A value θ = 7 is used []. Including systematic uncertainties the following values are obtained (in units of 6 ): B(B K (7) + π ) = 7 +8, B(B K (4) + π ) = , B(B K + A π ) = 4 +9, B(B+ K (7) π + ) < 4, B(B + K (4) π + ) < 39, B(B + K A π+ ) < 36, where the upper limits are evaluated at 9% probability []. 5.. Extraction of α A MC technique is used to estimate a probability region for the bound on α. The CP-averaged rates and CP-violation parameters participating in the estimation of the bounds are generated according to the experimental distributions; a summary of the experimental values used as input to this calculation is provided in Table IV. For each set of generated values, the bound on α is evaluated. The limits on α are obtained by counting the fraction of bounds within a given value and the results are α <. (3. ) at 68% (9%) probability []. The angle α is extracted with an eight-fold ambiguity in the range [, 8]. The eight solutions are α = (±7±), α = (4±7±), α = (49±7±), α = (79 ± 7 ± ), α = ( ± 7 ± ), α = (3±7±), α = (39±7±), α = (69±7±). Table IV Summary of the B a (6)π and B a (6)K branching fractions (in units of 6 ) and of the form factors (in MeV) used in the calculation of α. B(a ± π ) [] B(a K + ) [] B(a + K ) [] 33. ± 3.8 ± ±.9 ± ± 5. ± 4.4 f π [4] f K [4] f a [5] f KA [6] 3.4 ± ±.9 3 ± 8 7 ± Assuming that the strong phase ˆδ is negligible [], only two solutions are still allowed. Considering only the solution consistent with the results of global CKM fits, α = (79 ± 7 ± ). 6. Conclusion Recent updates of measurements related to the determination of α have been presented. The first measurement of the branching fraction of B K π decays, combined with the input from the analysis of the time-dependent CP-violation asymmetries in B a (6) π ± decays and of the branching fractions of B a (6)K decays, allows to measure α in the a (6)π system. This novel determination of α is independent from, and consistent with, the current averages, which are based on the analysis of the ππ, ρπ, and ρρ systems only. With the new update of the B + ρ ρ + branching fraction and longitudinal polarization fraction measurements, the determination of α in the ρρ system has reached the unprecedented precision of 7%, comparable with the 5.3% precision achieved in sin β measurements. In the ππ system, the updated measurement of CPviolating asymmetries in B π + π decays provides a 6.7σ evidence of CP violation. B π π decays branching fraction and direct CP asymmetry are input to the isospin analysis of B ππ decays that is used to constrain the effect of penguin pollution on the extraction of α. All the measurements described in this work have been performed on the final BaBar sample. Most of them are still limited by statistics, and improvement may come from next generation, very high luminosity facilities. Acknowledgments I would like to thank the organizers of DPF 9 for an interesting conference and my BaBar and PEP-II collaborators for their contributions. I m grateful to Vincenzo Lombardo and Fernando Palombo for their support and for reviewing the manuscript.

9 Proceedings of the DPF-9 Conference, Detroit, MI, July 7-3, (a) 5 (b) 6 4 (c) 5 5 Events 5 4 (d) (g) m ES (GeV) (e) -.. (h) -.. E (GeV) 3 (f) (i) m Kππ (GeV) Figure 8: splot projections of signal onto m ES (left), E (center), and m Kππ (right) for B class (top), B class (middle), and B + class (bottom) events: the points show the sums of the signal weights obtained from on-resonance data. For m ES and E the solid line is the signal fit function. For m Kππ the solid line is the sum of the fit functions of the decay modes K (7)π + K (4)π (dashed), K (4)π (dash-dotted), and K (89)ππ (dotted), and the points are obtained without using information about resonances in the fit, i.e., we use only the m ES, E, and F variables. φ (rad) 6 φ (rad) (a) (b).5 ϑ (rad).5.5 ϑ (rad).5 Figure 9: 68% (dark shaded zone) and 9% (light shaded zone) probability regions for ϑ and φ for the (a) B and (b) B + modes. References [] N. Cabibbo, Phys. Rev. Lett., 53 (963); M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 65 (973). [] M. Bona et al. (UTfit Collaboration), JHEP 63, 8 (6). [3] J. Charles et al. (CKMFitter Group), Eur. Phys. Jour. C 4, (5). [4] C. Amsler et al. (Particle Data Group), Phys. Lett. B 667, (8). [5] B. Aubert et al. (BABAR Collaboration), Phys. Rev. D 66, 33 (). [6] B. Aubert et al. (BABAR Collaboration), arxiv:87.46 [hep-ex] (8). [7] I. Adam et al. (BABAR-DIRC Collaboration), Nucl. Instr. Meth. A 538, 8 (5). [8] B. Aubert et al. (BABAR Collaboration),

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