{'fraction_non_alphanumeric': 0.048689636823200745, 'fraction_numerical': 0.015963815351869096, 'mean_word_length': 4.013783903957314, 'pattern_counts': {'":': 0, '<': 4, '<?xml version=': 0, '>': 3, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 23, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Measurement of Time-Dependent CP Asymmetries and the CP-odd Fraction in the Decay B^0 -->D^{*+}D^{*-}

We present a measurement of time-dependent CP asymmetries and an updated determination of the CP-odd fraction in the decay B^0 -->D^{*+}D^{*-}. The measurements are derived from a data sample of 88 times 10^{6} B bar{B} pairs collected by the BaBar detector at the PEP-II energy asymmetric B Factory at SLAC. All results are preliminary.


Introduction
The symmetry for combined charge conjugation (C) and parity (P) transformations is violated in B decays. Measurements of CP asymmetries by the BABAR [1] and BELLE [2] collaborations established this effect and are compatible with the Standard Model expectation based on the current knowledge of the Cabibbo-Kobayashi-Maskawa [3] quark-mixing matrix elements.
As a result of the interference between direct B decay, expected to be dominated by the tree decay diagram, and decay after flavor change, a CP -violating asymmetry is expected in the time evolution of the decays 4 B 0 → D * + D * − , within the framework of the Standard Model [4]. Up to corrections due to theoretically uncertain penguin diagram contributions [5], this CP asymmetry is related to sin2β (β ≡ arg [ −V cd V * cb /V td V * tb ]). Penguin-induced corrections are predicted to be small in models based on the factorization approximation and heavy quark symmetry; an effect of about 2% is predicted by Ref. [6]. A comparison of measurements of sin2β [7] from charmoniumcontaining b → ccs modes such as B 0 → J/ψK 0 S , with that obtained in B 0 → D * + D * − is an important test of these models and the consistency of the Standard Model.
The B 0 → D * + D * − mode is a pseudoscalar decay to a vector-vector final state, with contributions from three partial waves with different CP parities: even for the S-and D-waves, odd for the P -wave. In the model described in Ref. [8] the P -wave contribution is predicted to be about 11%. The angular distribution of the decay products can be used to measure the CP parameters of the CP -even and CP -odd components [9].
Following our initial results on this channel [10], we present here an updated determination of the CP -odd fraction R ⊥ in the decay B 0 → D * + D * − in BABAR, based on a projected onedimensional time-integrated angular analysis. We also present a preliminary measurement of the time-dependent CP asymmetry, obtained from a combined analysis of the time dependence of flavor-tagged decays and the one-dimensional angular distribution of decay products.

The BABAR Detector and Dataset
The data used in this analysis were collected with the BABAR detector at the PEP-II storage ring. The data sample used for the time-dependent CP -asymmetry measurement corresponds to 88.0 × 10 6 e + e − → Υ (4S) → BB events and the sample used for the R ⊥ measurement corresponds to 84.4 × 10 6 BB pairs. The collider is operated with asymmetric beam energies, producing a boost (βγ = 0.55) of the Υ (4S) along the collision axis.
BABAR is a solenoidal detector optimized for the asymmetric beam configuration at PEP-II, and is described in detail elsewhere [11]. Charged particle (track) momenta are measured in a tracking system consisting of a 5-layer, double-sided, silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH) filled with a gas mixture of helium and isobutane, both operating within a 1.5 T superconducting solenoidal magnet. Photon candidates are selected as local maxima of deposited energy in an electromagnetic calorimeter (EMC) consisting of 6580 CsI(Tl) crystals arranged in barrel and forward endcap subdetectors. In this analysis, tracks are identified as pions or kaons by the Cherenkov angle θ c , measured using a detector of internally reflected Cherenkov light (DIRC), and by the energy deposition, dE/dx, in the tracking system. The flux return of the magnet is instrumented with resistive plate chambers interspersed with iron (IFR) for the identification of muons and long-lived neutral hadrons.

Event Selection
B 0 mesons are exclusively reconstructed by combining two charged D * candidates reconstructed in a number of D * and D decay modes. Events are pre-selected by requiring that the normalized second Fox-Wolfram moment [12] of the event be less than 0.6. We also require that the cosine of the angle between the thrust axis of the reconstructed B and the thrust axis of the rest of the event be less than 0.9. These criteria are used to reject events coming from the e + e − → cc continuum process. Backgrounds from u, d, s continuum processes are negligible in this analysis due to the presence of two charm particles in the final state.
The D 0 and D + modes reconstructed are Charged kaon candidates are required to be inconsistent with the pion hypothesis, as inferred from the Cherenkov angle measured by the DIRC and the specific ionization measured by the SVT and DCH. No particle identification requirements are made for the kaon from the decay K 0 S → π + π − candidates are required to have an invariant mass within 25 MeV/c 2 of the nominal K 0 S mass [13]. The angle between the flight direction and the momentum vector of the K 0 S candidate is required to be less than 200 mrad, and the transverse flight distance from the primary event vertex must be greater than 2 mm. A mass-constrained fit is then applied to each surviving K 0 S candidate, in order to improve the mass resolution of the K 0 S π + and K 0 S π + π − combinations. Neutral pion candidates are formed from two photons in the EMC, each with energy above 30 MeV; the invariant mass of the pair must be within 20 MeV/c 2 of the nominal π 0 mass, and their summed energy must be greater than 200 MeV. A mass-constrained fit is then applied to these π 0 candidates. The π 0 from D * + → D + π 0 decay ("soft" π 0 ), however, is required to have an invariant mass within 35 MeV/c 2 of the nominal π 0 mass and momentum in the Υ (4S) frame in the interval 70 < |p * | < 450 MeV/c, with no requirement on the photon energy sum.
D 0 and D + meson candidates are required to have an invariant mass within 20 MeV/c 2 of the nominal D 0 or D + mass. The same interval is used for all D 0 modes except K − π + π 0 , which has a looser requirement of 35 MeV/c 2 due to the momentum resolution of the π 0 . D * + mesons are reconstructed in their decays D * + → D 0 π + and D * + → D + π 0 . We include D * + D * − combinations decaying to (D 0 π + , D 0 π − ) or (D 0 π + , D − π 0 ), but not (D + π 0 , D − π 0 ) due to the smaller branching fraction and larger expected backgrounds. The D 0 and D + candidates are subjected to a mass-constrained fit and then combined with soft pion candidates. A vertex fit is performed that includes the position of the beam spot to improve the angular resolution of the soft pion.
If an event contains both a D * + and a D * − candidate, each is subjected to a mass constraint fit, and then combined to form a B candidate. B 0 candidates with well reconstructed D * and D mesons are selected by means of a mass likelihood variable, L M ass , that includes all measured D * and D masses. This variable is defined in Eq. 1: where G(x; µ, σ) is a normalized Gaussian defined with mean = µ and RMS = σ; the subscript PDG refers to the nominal value [13]. For σ m D we use errors calculated candidate-by-candidate. The parameter f core is the ratio of areas for the core and tail Gaussians. This along with σ ∆mcore and σ ∆m tail are determined from fitting the ∆m distributions in simulated signal events. The value of − ln(L M ass ) is used to select signal in preference to background, with a different requirement used for each D decay mode combination. In an event where more than one B candidate is reconstructed, the candidate with the lowest − ln(L M ass ) value is chosen. The primary variables used to distinguish signal from background are the energy-substituted mass, and the difference of the B candidate energy from beam energy, where the star indicates variables evaluated in the Υ (4S) center-of-mass frame. The fits described in the following sections are performed on events required to have |∆E| < 25 MeV and m ES > 5.2 GeV/c 2 . The requirements on − ln(L M ass ) and ∆E were chosen to optimize S 2 /(S + B), where S is the expected number of signal events and B is the expected number of background events. The optimization process was done with samples of simulated signal events and with generic BB and cc Monte Carlo simulated events. Figure 1 shows the events in the m ES projection after all selection criteria have been applied. The fit to this distribution uses a Gaussian and an ARGUS function [14] parameterization for signal and background, respectively. For the data sample corresponding to 84.4 × 10 6 BB pairs, the fitted signal yield is 126 ± 13 D * + D * − events.
In this section we present a one-dimensional angular analysis to determine the fraction, R ⊥ , of the P -wave CP -odd component in the vector-vector final state of the B 0 → D * + D * − decay. In the transversity basis [9] the following three angles involving decay products are defined (see Fig. 2): • the polar angle θ 1 between the momentum of the π − in the D * − rest frame, and the direction of flight of the D * − in the B rest frame, • the polar angle θ tr between the normal, z, to the D * − decay plane and the π + line of flight in the D * + rest frame, and • the corresponding azimuthal angle φ tr .  Figure 2: Representation of the "Transversity Frame" for the decay B 0 → D * + D * − . The momenta of the D * − decay products are represented in the B 0 rest frame, while the momenta of the D * + decay products are represented in the D * + rest frame. The x direction is defined by the direction of flight of the D * + in the B 0 rest frame. The (x, y) plane is defined by the momenta of the D * − decay products in the B 0 rest frame. The "transversity" axis, z, is orthogonal to the (x, y) plane.
The time-dependent angular distribution of decay products in the transversity frame for the mode B 0 → D * + D * − is given by [15] where A 0 , A , A ⊥ are the time-dependent decay amplitudes in the transversity basis. For the B 0 decayĀ ⊥ = −A ⊥ , under the assumption there is no direct CP violation.
In principle, 11 unknown parameters can be extracted from a full angular, time, and B-flavor dependent analysis. These parameters are: M i ≡ |A i (t = 0)|, 2 relative phases, and the complex CP parameters λ i = (q/p)(Ā i /A i ), with i = , 0, ⊥, resulting from the interference of mixing (q/p) and decay amplitudes (A i ). Considering the size of the current data sample, a simplified strategy is adopted to extract only the CP -odd component from the cos θ tr distribution.
Ignoring the B flavor and integrating over time, θ 1 , and φ tr results in the one-dimensional differential decay rate: with: The measurement of R ⊥ is based on an unbinned maximum likelihood fit of the cos θ tr distribution, with a simultaneous fit to the m ES distribution. The probability density function for the m ES distribution is given by the sum of normalized ARGUS [14] and Gaussian functions; the relative weight of each function is given by a signal fraction f sig , which is allowed to float in the likelihood fit. The likelihood is defined as: where n is the number of selected events in the m ES distribution, F sig m ES is the signal Gaussian for the m ES distribution and F bkg m ES is the background ARGUS function with shape parameter κ. F R ⊥ refers to the probability density function for signal events, given by Eq. 3. The background shape is modeled by a polynomial in cos θ tr : where N is the normalization factor. We categorize our events in three types: D * + D * − → (D 0 π + , D 0 π − ), (D 0 π + , D − π 0 ), and (D + π 0 , D 0 π − ). We distinguish these three types of events because events with a neutral slow pion and events with a charged slow pion have different background levels and cos θ tr resolution (note: θ tr is the angle between the slow pion from the D * + and the transversity axis).
We allow different signal fractions for each event type. Thus, the parameters floating in the likelihood fit are: 3 signal fractions, the background parameter b 2 , 3 m ES parameters (σ and mean of Gaussian fit, and κ from ARGUS shape), and R ⊥ .
A fit to the dataset yields a value of R ⊥ = 0.096 ± 0.060(stat), neglecting possible biases from angular resolution in θ tr and detector acceptance.  The experimental resolution of θ tr biases the measurement of R ⊥ ; the simulated distribution of residuals on θ tr is seen to have significant tails caused by mis-reconstructed events. The presence of these tails distorts the cos θ tr distribution, and thus produces a bias on R ⊥ . A smaller bias on R ⊥ is produced by the transverse momentum dependence of the detector reconstruction efficiency. The presence of the two slow pions from the D * decays makes this analysis susceptible to this effect. The net bias from these two effects was estimated from a study on simulated data, and is found to be +0.028. This was determined using simulated events with a generated value of R ⊥ very similar to the value measured in data. The corresponding systematic error incurred for this correction is taken conservatively to be the full size of the correction, namely 0.028. The next largest systematic uncertainty affecting the R ⊥ measurement arises from the background parameterization (0.005). The total systematic uncertainty on R ⊥ is determined to be 0.03, giving as a preliminary result the final corrected value: R ⊥ = 0.07 ± 0.06(stat) ± 0.03(syst). (7) This is an update to a previous BABAR measurement [10], with a factor of three reduction in the statistical error (R ⊥ dependent).

Measurement of the Time-Dependent
In this section we present a determination of the time-dependent CP asymmetry in B 0 → D * + D * − . We perform a combined analysis of the cos θ tr distribution of all selected events and the time dependence of those with a flavor tag. The inclusion of the angular dependence enables us to fit for the CP asymmetries of the CP -even and CP -odd components separately.
Although factorization models predict a small penguin contamination of the weak phase difference Im(λ f ) = − sin 2β [6], a sizeable penguin diagram contribution cannot a priori be excluded. Thus, the value of λ f = q pĀ (f ) A(f ) can be different for the three transversity amplitudes because of possible different penguin-to-tree ratios. These contributions are explicitly included in the parameterization of the flavor-tagged decay rates described here.
The decay rate, f + (f − ), for a neutral B meson tagged as a B 0 (B 0 ) can be obtained from Eq. 2 as: where ∆t = t rec − t tag is the difference between the proper decay time of the reconstructed B meson (B rec ) and the proper decay time of the tagging B meson (B tag ), τ B 0 is the B 0 lifetime, and ∆m d is the mass difference determined from the B 0 -B 0 oscillation frequency. The dilution factor, D, describes the effect of incorrect tags, with ∆D accounting for possible differences in the mis-tag probability between B 0 and B 0 . The O, C and S coefficients are defined as: These coefficients contain the explicit dependence on the transversity angle θ tr defined in the previous section, which provides a separation between the CP -odd (cos 2 θ tr ) and CP -even (sin 2 θ tr ) components.
The CP -even parameters, |λ + | and Im(λ + ), are related to λ and λ 0 by: Table 1: Efficiencies ǫ i , average mis-tag fractions w i , mis-tag fraction differences ∆w i = w i (B 0 ) − w i (B 0 ), and Q extracted for each tagging category i by using the B flav sample. Category ε (%) w (%) ∆w (%) Q (%) It should be noted that this formulation does not take into account detector acceptance. Therefore, a combined fit to the ∆t and cos θ tr dependence of the data will give an "effective" value of R ⊥ , which is not necessarily identical to the acceptance-corrected value from the time-integrated measurement. A measurement of CP asymmetries requires a determination of the experimental ∆t resolution and the fraction of events in which the tag assignment is incorrect. A mis-tag fraction w reduces the observed CP asymmetry by a factor D = 1 − 2w. The mis-tag fractions and ∆t resolution functions are determined from a sample, B flav , of neutral B decays to flavor eigenstates (D ( * )− h + (h + = π + , ρ + , and a + 1 ) and J/ψ K * 0 (K * 0 → K + π − )) as for the sin2β measurement using charmonium decays, described in detail elsewhere [7].
We use multivariate algorithms to identify signatures of B decays that determine the flavor of B tag . Primary leptons from semileptonic B decays are selected from identified electrons, muons, and isolated energetic tracks. We use the charges of the best kaon candidates to define a kaon tag. Soft pions from D * + decays are selected on the basis of their momentum and direction with respect to the thrust axis of B tag . A neural network, which combines the outputs of these algorithms, takes into account correlations between different sources of flavor information and provides an estimate of the mis-tag probability for each event.
Using the outputs of the algorithms and the estimated mis-tag probability, each event is assigned to one of four hierarchical, mutually exclusive tagging categories. The Lepton category contains events with an identified lepton, and a supporting kaon tag if present. Events with a kaon candidate and soft pion with opposite charge and similar flight direction are assigned to the Kaon I category. Events with only a kaon tag are assigned to the Kaon I or Kaon II category depending on the estimated mis-tag probability. The Kaon II category also contains the remaining events with a soft pion. All other events are assigned to the Inclusive category or excluded from further analysis based on the estimated mis-tag probability. The tagging efficiencies ε i for the four tagging categories are measured from data and summarized in Table 1. The figure of merit for tagging is the effective tagging efficiency Q ≡ i ε i (1 − 2w i ) 2 . This algorithm improves Q by about 7% (relative) over the algorithm used in Ref. [16].
The algorithm for vertex reconstruction and the determination of ∆t are described in detail in Ref. [16]. The time interval ∆t between the two B decays is calculated from the measured separation ∆z between the decay vertex of the reconstructed B meson and the vertex of the flavor-tagging B meson along the collision axis. We determine the z position of the B rec vertex from the charged tracks that constitute the B rec candidate. The decay vertex of the B tag is determined by fitting the tracks not belonging to the B rec candidate to a common vertex. An additional constraint on the tagging vertex comes from a pseudotrack computed from the B rec vertex and three-momentum, the beam-spot and the Υ (4S) momentum. Events with a ∆t error of less than 2.5 ps, and a measured |∆t| < 20 ps are accepted.
We determine the parameters Im(λ + ) and |λ + | with a simultaneous unbinned maximum likelihood fit to the ∆t distributions of the B rec and B flav tagged samples (Fig. 4). The ∆t distribution of the B flav sample evolves according to the known frequency for flavor oscillations in neutral B mesons. The observed amplitudes for the CP asymmetry in the B rec sample and for flavor oscillation in the B flav sample are reduced by the same factor (1 − 2w) due to flavor mis-tags. The ∆t distributions for the B rec and B flav samples are both convolved with a common ∆t resolution function. Events are assigned signal and background probabilities based on their m ES values. Backgrounds are incorporated with an empirical description of their ∆t evolution, containing prompt (zero lifetime) and non-prompt components convolved with a separate resolution function [16].
A total of 38 parameters are varied in the fit, including the values of Im(λ + ) and |λ + | (2), the effective CP -odd fraction (1), the average mis-tag fraction w and the difference ∆w between B 0 and B 0 mis-tags for each tagging category (8), parameters for the signal ∆t resolution (9), and parameters for the background time dependence (7), ∆t resolution (3), and mis-tag fractions (8). Because the CP -odd fraction is small, the parameters |λ ⊥ | and Im(λ ⊥ ) are poorly determined. Therefore they are fixed in the fit to 1.0 and −0.741 [7] respectively. These are the values expected if direct CP violation and contributions from penguin diagrams are neglected. The changes in the fitted values of Im(λ + ) and |λ + | for different input values of Im(λ ⊥ ) (varied between −1.0 and 1.0) and |λ ⊥ | (varied between 0.7 and 1.3) are taken into account as systematic uncertainties. The preliminary results obtained from the fit (Fig. 4) are as follows: Im(λ + ) = 0.31 ± 0.43(stat) ± 0.13(syst) (11) |λ + | = 0.98 ± 0.25(stat) ± 0.09(syst).
The dominant source of systematic uncertainty comes from the variation on the value of λ ⊥ (0.09 and 0.02 respectively for Im(λ + ) and |λ + |). Other relevant sources are the angular acceptance and resolution of the detector (0.06 and 0.08), the level, composition, and CP asymmetry of the background (0.07 and 0.02), the uncertainty on the SVT internal alignment and boost (0.03 and 0.02), limited Monte Carlo simulation statistics (0.02 and 0.01), and possible differences between B flav and B rec mis-tag fractions and resolution function parameters (0.01 and 0.01). The total systematic error is 0.13 for Im(λ + ) and 0.09 for |λ + |.
If the B → D * + D * − transition proceeds only through the b → ccd tree amplitude, we expect that Im(λ + ) = − sin 2β and |λ + | = 1. To test this hypothesis, we fix Im(λ + ) = −0.741 [7] and |λ + | = 1 and repeat the fit. The observed change in the likelihood corresponds to 2.7 standard deviations (statistical error only). More data is needed to establish whether there are significant contributions from other processes, in particular, penguin diagrams.

Summary
We have reported preliminary measurements of time-dependent CP asymmetries and a measurement of the CP -odd fraction for the decay B 0 → D * + D * − . The measurement of R ⊥ represents an improvement in the statistical uncertainty by a factor of almost three compared to previous measurements. The time-dependent asymmetry measurements still have large statistical uncertainties. These should be reduced steadily in the coming years as BABAR accumulates additional data, thus allowing useful tests of the Standard Model.