CP Violation in B_d \to D^+D^-, D^{*+}D^-, D^+D^{*-} and D^{*+}D^{*-} Decays

CP asymmetries in B_d \to D^+D^-, D^{*+}D^-, D^+D^{*-} and D^{*+}D^{*-} decays are investigated with the help of the factorization approximation and isospin relations. We find that the direct CP violation is governed only by the short-distance penguin mechanism, while the indirect CP asymmetries in B_d \to D^{\pm}D^{*\mp} transitions may be modified due to the final-state rescattering effect. An updated numerical analysis shows that the direct CP asymmetry in B^0_d vs \bar{B}^0_d \to D^+D^- decays can be as large as 3%. The CP-even and CP-odd contributions to the indirect CP asymmetry in B^0_d vs \bar{B}^0_d \to D^{*+}D^{*-} decays are found to have the rates 89% and 11%, respectively. Some comments on the possibilities to determine the weak phase \beta and to test the factorization hypothesis are also given.Comment: LaTex 14 pages (2 figures included). Phys. Rev. D (in printing

Measurement of branching fractions and CP-violating charge asymmetries for B-meson decays to D^(*)D^(*), and implications for the Cabibbo-Kobayashi-Maskawa angle γ

We present measurements of the branching fractions and charge asymmetries of B decays to all D^(*)D^(*) modes. Using 232×10^6 BB pairs recorded on the Υ(4S) resonance by the BABAR detector at the e^+e^- asymmetric B factory PEP-II at the Stanford Linear Accelerator Center, we measure the branching fractions B(B^0→D^(*+)D^(*-))=(8.1±0.6±1.0)×10^(-4), B(B^0→D^(*±)D^∓)=(5.7±0.7±0.7)×10^(-4), B(B^0→D^+D^-)=(2.8±0.4±0.5)×10^(-4), B(B^+→D^(*+)D^(*0))=(8.1±1.2±1.2)×10^(-4), B(B^+→D^*+D^0)=(3.6±0.5±0.4)×10^(-4), B(B^+→D^+D^(*0))=(6.3±1.4±1.0)×10^(-4), and B(B^+→D^+D^(0))=(3.8±0.6±0.5)×10^(-4), where in each case the first uncertainty is statistical and the second systematic. We also determine the limits B(B^0→D^(*0)D^(*0))<0.9×10^(-4), B(B^0→D^(*0)D^0)<2.9×10^(-4), and B(B^0→D^0D^0)<0.6×10^(-4), each at 90% confidence level. All decays above denote either member of a charge-conjugate pair. We also determine the CP-violating charge asymmetries A(B^0→D^(*±)D^∓)=0.03±0.10±0.02, A(B^+→D^(*+)D^(*0))=-0.15±0.11±0.02, A(B^+→D^(*+)D^0)=-0.06±0.13±0.02, A(B^+→D^+D^(*0))=0.13±0.18±0.04, and A(B^+→D^+D^0)=-0.13±0.14±0.02. Additionally, when we combine these results with information from time-dependent CP asymmetries in B^0→D^((*)+)D^((*)-) decays and world-averaged branching fractions of B decays to D_s^(*)D^(*) modes, we find the Cabibbo-Kobayashi-Maskawa phase γ is favored to lie in the range (0.07–2.77) radians (with a +0 or +π radians ambiguity) at 68% confidence level

Constructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifolds

Compact Riemannian 7- and 8-manifolds with holonomy G(2) arid Spin(7) were first constructed by the author in 1994-5, by resolving orbifolds T-7/Gamma and T-8/Gamma. This paper describes a new construction of compact 8-manifolds with holonomy Spin(7). We start with a Calabi-Yau 4-orbifold Y with isolated singularities of a special kind. We divide by an antiholomorphic involution a of Y to get a real 8-orbifold Z = Y/. Then we resolve tire singularities of Z to get a compact 8-manifold M, which has metrics with holonomy Spin(7). Manifolds constructed in this way typically have large fourth Betti number b(4)(M).</sigma

The warping degree of a link diagram

For an oriented link diagram D, the warping degree d(D) is the smallest number of crossing changes which are needed to obtain a monotone diagram from D. We show that d(D)+d(-D)+sr(D) is less than or equal to the crossing number of D, where -D denotes the inverse of D and sr(D) denotes the number of components which have at least one self-crossing. Moreover, we give a necessary and sufficient condition for the equality. We also consider the minimal d(D)+d(-D)+sr(D) for all diagrams D. For the warping degree and linking warping degree, we show some relations to the linking number, unknotting number, and the splitting number.Comment: 28 pages, 16 figure

Study of the Decays B0 --> D(*)+D(*)-

The decays B0 --> D*+D*-, B0 --> D*+D- and B0 --> D+D- are studied in 9.7 million Y(4S) --> BBbar decays accumulated with the CLEO detector. We determine Br(B0 --> D*+D*-) = (9.9+4.2-3.3+-1.2)e-4 and limit Br(B0 --> D*+D-) < 6.3e-4 and Br(B0 --> D+D-) < 9.4e-4 at 90% confidence level (CL). We also perform the first angular analysis of the B0 --> D*+D*- decay and determine that the CP-even fraction of the final state is greater than 0.11 at 90% CL. Future measurements of the time dependence of these decays may be useful for the investigation of CP violation in neutral B meson decays.Comment: 21 pages, 5 figures, submitted to Phys. Rev.

Understanding the e+e−→D(∗)+D(∗)−e^+e^-\to D^{(*)+}D^{(*)-} processes observed by Belle

We calculate the production cross sections for $D^{*+}D^{*-}$, $D^+D^{*-}$ and $D^+D^-$ in $e^+e^-$ annihilation through one virtual photon in the framework of perturbative QCD with constituent quarks. The calculated cross sections for $D^{*+}D^{*-}$ and $D^+D^{*-}$ production are roughly in agreement with the recent Belle data. The helicity decomposition for $D^{*}$ meson production is also calculated. The fraction of the $D^{*\pm}_LD^{*\mp}_T$ final state in $e^+e^-\to D^{*+}D^{*-}$ process is found to be 65%. The fraction of $DD^*_T$ production is 100% and $DD^*_L$ is forbidden in $e^+e^-$ annihilation through one virtual photon. We further consider $e^+e^-$ annihilation through two virtual photons, and then find the fraction of $DD^{*}_T$ in $e^+e^-\to DD^{*}$ process to be about 91%.Comment: 8 pages, 2 figure

Search for the Decays B^0 -> D^{(*)+} D^{(*)-}

Using the CLEO-II data set we have searched for the Cabibbo-suppressed decays B^0 -> D^{(*)+} D^{(*)-}. For the decay B^0 -> D^{*+} D^{*-}, we observe one candidate signal event, with an expected background of 0.022 +/- 0.011 events. This yield corresponds to a branching fraction of Br(B^0 -> D^{*+} D^{*-}) = (5.3^{+7.1}_{-3.7}(stat) +/- 1.0(syst)) x 10^{-4} and an upper limit of Br(B^0 -> D^{*+} D^{*-}) D^{*\pm} D^\mp and B^0 -> D^+ D^-, no significant excess of signal above the expected background level is seen, and we calculate the 90% CL upper limits on the branching fractions to be Br(B^0 -> D^{*\pm} D^\mp) D^+ D^-) < 1.2 x 10^{-3}.Comment: 12 page postscript file also available through http://w4.lns.cornell.edu/public/CLNS, submitted to Physical Review Letter

Measurements of Branching Fractions and Time-dependent CP Violating Asymmetries in B0→D(∗)±D∓B^{0} \to D^{(*)\pm}D^{\mp} Decays

We report measurements of branching fractions and time-dependent CP asymmetries in $B^{0} \to D^{+}D^{-}$ and $B^{0} \to D^{*\pm}D^{\mp}$ decays using a data sample that contains $(772 \pm 11)\times 10^6 B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We determine the branching fractions to be $\mathcal{B}(B^{0} \to D^{+}D^{-})=(2.12 \pm 0.16 \pm 0.18)\times 10^{-4}$ and $\mathcal{B}(B^{0} \to D^{*\pm}D^{\mp}=(6.14 \pm 0.29 \pm 0.50)\times 10^{-4}$. We measure CP asymmetry parameters $\mathcal{S}_{D^{+}D^{-}} = -1.06_{-0.14}^{+0.21} \pm 0.08$ and $\mathcal{C}_{D^{+}D^{-}} = -0.43 \pm 0.16 \pm 0.05$ in $B^{0} \to D^{+}D^{-}$ and $\mathcal{A}_{D^{*}D} = +0.06 \pm 0.05 \pm 0.02$, $\mathcal{S}_{D^{*}D} = -0.78 \pm 0.15 \pm 0.05$, $\mathcal{C}_{D^{*}D} = -0.01 \pm 0.11 \pm 0.04$, $\Delta\mathcal{S}_{D^{*}D} = -0.13 \pm 0.15 \pm 0.04$ and $\Delta\mathcal{C}_{D^{*}D} = +0.12 \pm 0.11 \pm 0.03$ in $B^{0} \to D^{*\pm}D^{\mp}$, where the first uncertainty is statistical and the second is systematic. We exclude the conservation of CP symmetry in both decays at equal to or greater than $4\sigma$ significance.Comment: 7 pages, 2 figure