We report the measurement of the branching fraction, the polarization and the parameters of the time dependent CP-violation for B⁰ → D ^*+ D^*- decays using the full data sample of 772 million BB-pairs, collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e⁺e^- collider.

B⁰ mesons are reconstructed in the following decay chains
B⁰ → D^*+ ( → D⁺ π⁰ ) D^*- ( → D⁰ π^- )
B⁰ → D^*+ ( → D⁰ π⁺ ) D^*- ( → D^- π⁰ )
B⁰ → D^*+ ( → D⁰ π⁺ ) D^*- ( → D⁰ π^- )
where 4 D⁺ and 5 D⁰ decay modes are reconstructed.
Since this is a decay of a scalar meson to two vector mesons, the final state is a mixture of multiple CP-eigenstates and therefore an angular analysis has to be performed to determine the fraction of CP-even decays. This is done using two of three possible angles of the transversity base which are denoted as cos θ_tr and cos θ₁. The relation between the amplitudes A_i and the CP-eigenvalue is given in the table below and the angular distribution is given by:

1/Γ (d²Γ(B⁰→ D^*+D^*-))/(dcos θ_tr dcos θ₁) = 9/16 (2|A₀|² cos² θ₁ sin² θ_tr +2|A_⊥|² sin² θ₁ cos² θ_tr +|A_\\|² sin² θ₁ sin² θ_tr)

Table 1 : Relation between relative angular momentum and the amplitudes in the transversity basis

 

Illustration of transversity basis.

The number of signal events is extracted with a two dimensional extended unbinned maximum likelihood fit on M_bc and ΔE. The shapes of the signal distribution are determined using simulated signal events and in the fit on the reconstructed data sample the position, the width and the fraction of the signal distribution as well as the parameters of the background description are free.

The fitted number of signal events is 1225 ± 59.
The reconstructed efficiencies are determined for each combination of D-decay channels separately using simulated signal events and corrected according to known differences between measured data and simulated events.
The resulting branching fraction is Bf(B⁰ → D^*+ D^*-) = (7.82 ± 0.38 ± 0.60) × 10^-4

Fitted M_bc and ΔE distribution projected in the signal range of the other variable

These two measurements are performed simultaneously with a five dimensional fit on M_bc, ΔE, two of the three angles of the transversity base and Δt. The signal shapes for the angles cos θ_tr and cos θ₁ are determined for each of the three polarizations independently using simulated signal events.
The signal PDF for the Δt distribution is

P_B⁰ ( Δt ) = 1/4 τ_B⁰ e^-|Δt|/τ_B0 (1 - q Δw + q(1 - 2 w) ( (1 - 2 P_odd(cos θ_tr, cos θ₁ ))S sin (Δm Δt) + A cos (Δm Δt)) ),

where P_odd is the probability of an event to be CP-odd.

The preliminary results are:

Projections of the angular distributions in the signal range of ΔE and M_bc. The black (green, red) line shows the total (signal, background) pdf, while orange, blue and cyan show the signal contribution for each polarization: 0, ⊥, \\

Δt distribution and raw asymmetry for good tags (r > 0.5) in the signal region of ΔE and M_bc, red corresponds to positive tags, black to negative ones and the dashed curve to the fitted background.