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We report on a study of the decay {bar B}{sup 0} {yields} D*{sup +}{omega}{pi}{sup -} with the BABAR detector at the PEP-II B-factory at the Stanford Linear Accelerator Center. Based on a sample of 232 million B{bar B} decays, we measure the branching fraction {Beta}({bar B}{sup 0} {yields} D*{sup +}{omega}{pi}{sup -}) = (2.88 {+-} 0.21(stat.) {+-} 0.31(syst.)) x 10{sup -3}. We study the invariant mass spectrum of the {omega}{pi}{sup -} system in this decay. This spectrum is in good agreement with expectations based on factorization and the measured spectrum in {tau}{sup -} {yields} {omega}{pi}{sup -} {nu}{sub {tau}}. We also measure the polarization of the D*{sup +} as a function of the {omega}{pi}{sup -} mass. In the mass region 1.1 to 1.9 GeV we measure the fraction of longitudinal polarization of the D*{sup +} to be {Lambda}{sub L}/{Lambda} = 0.654 {+-} 0.042(stat.) {+-} 0.016(syst.). This is in agreement with the expectations from heavy-quark effective theory and factorization assuming that the decay proceeds as {bar B}{sup 0} {yields} D*{sup +}{rho}(1450), {rho}(1450) {yields} {omega}{pi}{sup -}.
Using ee− annihilation data collected by the CLEO II detector at CESR, we have observed the decay D{sub s} 2![omega][pi]+. This final state may be produced through the annihilation decay of the {sub s}+, or through final state interactions. We find a branching ratio of [Lambda](D{sub s}+ 2![omega][pi]+)/[Lambda](D{sub s}+ 2![eta][pi]+) = 0.016 ± 0.04 ± 0.03, where the first error is statistical and the second is systematic.
The authors report a Dalitz-plot analysis of the charmless hadronic decays of neutral B mesons to K{sup ±}?{sup {-+}}?°. With a sample of (231.8 ± 2.6) x 106?(4S) → B{bar B} decays collected by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC, they measure the magnitudes and phases of the intermediate resonant and nonresonant amplitudes for B° and {bar B}° decays and determine the corresponding CP-averaged branching fractions and charge asymmetries. The inclusive branching fraction and CP-violating charge asymmetry are measured to be?(B° → K?−?°) = (35.7{sub -1.5}{sup +2.6} ± 2.2) x 10−6, and?{sub CP} = -0.030{sub -0.051}{sup +0.045} ± 0.055 where the first errors are statistical and the second systematic. They observe the decay B° → K*°(892)?° with the branching fraction?(B° → K*°(892)?°) = (3.6{sub -0.8}{sup +0.7} ± 0.4) x 10−6. This measurement differs from zero by 5.6 standard deviations (including the systematic uncertainties). The selected sample also contains B° → {bar D}°?° decays where {bar D}° → K+?−, and they measure?(B° → {bar D}°?°) = (2.93 ± 0.17 {+-} 0.18) x 10−4.
Particle physicists study the smallest particles and most basic rules of their interactions in humankind's current scope. The Charm Analysis Working Group (CWG) of the BaBar Collaboration studies decays involving the charm quark. They currently study mixing in D decays, an interesting and poorly understood phenomenon in current physics models. We, as part of the CWG, investigated the plausibility of using Dalitz plots and the BaBar analysis framework to study mixing in Wrong Sign (WS) D[sup 0][yields] K[pi][pi][sup 0] decays. Others in the CWG have studied mixing in the 2-body decay, D[sup 0][yields] K[pi]. The 3-body decay analyzed with the RooFitDalitz analysis package and Dalitz plots provides more information and another way of separating Doubly Cabibbo Suppressed Decays (DCSD) from mixing--which share the same end products. Through doing many simulations, we have demonstrated the usefulness of this approach. We selected D[sup 0][yields] K[pi][pi][sup 0] events from Simulation Production run No. 4 (SP4) and BaBar's run 1 and run 2. We made Dalitz plots with this data. Now that we better understand Dalitz plots and software, we plan to select WS D[sup 0][yields] K[pi][pi][sup 0] events and perform rate fits as discussed in BaBar Analysis Document (BAD) No. 443, as well as fits for several different decay times and resonances, in order to further distinguish DCSD from mixing.
For a Riemannian manifold M, the geometry, topology and analysis are interrelated in ways that have become widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold. The eigenvalues of the Laplacian are naturally linked to the geometry of the manifold. For manifolds that admit spin structures, one obtains further information from equations involving Dirac operators and spinor fields. In the case of four-manifolds, for example, one has the remarkable Seiberg-Witten invariants. In this text, Friedrich examines the Dirac operator on Riemannian manifolds, especially its connection with the underlying geometry and topology of the manifold. The presentation includes a review of Clifford algebras, spin groups and the spin representation, as well as a review of spin structures and $\textrm{spin}mathbb{C}$ structures. With this foundation established, the Dirac operator is defined and studied, with special attention to the cases of Hermitian manifolds and symmetric spaces. Then, certain analytic properties are established, including self-adjointness and the Fredholm property. An important link between the geometry and the analysis is provided by estimates for the eigenvalues of the Dirac operator in terms of the scalar curvature and the sectional curvature. Considerations of Killing spinors and solutions of the twistor equation on M lead to results about whether M is an Einstein manifold or conformally equivalent to one. Finally, in an appendix, Friedrich gives a concise introduction to the Seiberg-Witten invariants, which are a powerful tool for the study of four-manifolds. There is also an appendix reviewing principal bundles and connections. This detailed book with elegant proofs is suitable as a text for courses in advanced differential geometry and global analysis, and can serve as an introduction for further study in these areas. This edition is translated from the German edition published by Vieweg Verlag.