11,089 research outputs found

### DeltaGamma_s Measurement at the Upsilon(5S) from Belle

Using the full Belle Upsilon(5S) data sample of 121 fb^-1we have measured
exclusive branching fractions for the decays B_s^0 -> D_s^(*)+D_s^(*)-.
Assuming these decay modes saturate decays to CP-even final states, the
branching fraction determines the relative width difference between the CP-odd
and -even eigenstates of the B_s.Comment: Proceedings of CKM 2012, the 7th International Workshop on the CKM
Unitarity Triangle, University of Cincinnati, USA, 28 September - 2 October
201

### Observation of $B_s^{0} \to D_s^{*-} \pi^{+}$, $B_s^{0} \to D_s^{(*)-} \rho^{+}$ and $B_s^{0} \to D_s^{(*)+} D_s^{(*)-}$ and Estimate of $\Delta \Gamma_{CP}$ at Belle

The large data sample being recorded with the Belle detector at the
$\Upsilon$(5S) energy provides a unique opportunity to study the
less-well-known $B_s^{0}$ meson decays. Following our recent measurement of
$B_s^{0}\to D_s^{-}\pi^{+}$ in a sample of 23.6 fb$^{-1}$, we extend the
analysis to include decays with photons in the final state. Using the same
sample, we report the first observation of three other dominant exclusive
$B_s^{0}$ decays, in the modes $B_s^{0}\to D_s^{*-}\pi^+$, $B_s^{0}\to
D_s^{-}\rho^+$ and $B_s^{0}\to D_s^{*-}\rho^+$. We measure their respective
branching fractions and, using helicity-angle distributions, the longitudinal
polarization fraction of the $B_s^{0}\to D_s^{*-}\rho^+$ decay.
We also present a measurement of the branching fractions for the decays
$B_s^{0} \to D_s^{(*)+}D_s^{(*)-}$. In the heavy quark limit, this branching
fraction is directly related to the width difference between the $B_s$ CP-even
and CP-odd eigenstates.Comment: 4 pages, 2 figures, To appear in the proceedings of the "35th
International Conference On High Energy Physics: ICHEP 2010", 21-28 July
2010, Paris, Franc

### Updated Measurement of ${\cal B}(B_s \to D_s^{(*)+}D_s^{(*)-})$ and Determination of $\Delta \Gamma_{s}$

Using fully reconstructed $B_{s}$ mesons, we measure exclusive branching
fractions for the decays $B_s \to D_s^{(*)+}D_s^{(*)-}$. The results are {\cal
B}(B^0_s\ra D^+_s D^-_s)=(0.58\,^{+0.11}_{-0.09}\,\pm 0.13)%, {\cal
B}(B^0_s\ra D^{*\pm}_s D^{\mp}_s)=(1.8\, \pm 0.2\,\pm 0.4)%, and {\cal
B}(B^0_s\ra D^{*+}_s D^{*-}_s)=(2.0\,\pm 0.3\,\pm 0.5)%; the sum is {\cal
B}(B^0_s\ra D^{(*)+}_s D^{(*)-}_s)=(4.3\,\pm 0.4\,\pm 1.0)%. Assuming these
decay modes saturate decays to CP-even final states, the branching fraction
determines the relative width difference between the $B_s$ CP-odd and CP-even
eigenstates. Taking \cp\ violation to be negligibly small, we obtain \dgs/\gs
= 0.090\,\pm 0.009\,{\rm(stat.)}\,\pm 0.022 \,{\rm (syst.)}, where \gs is
the mean decay width. The results are based on a data sample collected with the
Belle detector at the KEKB $e^+ e^-$ collider running at the $\Upsilon(5S)$
resonance with an integrated luminosity of 121.4 fb$^{-1}$.Comment: 5 pages, 2 figures, 3 tables, for the proceedings of the DPF-2011
conference, Providence, RI, August 9-13, 201

### Sum-Product Type Estimates over Finite Fields

Let $\mathbb{F}_q$ denote the finite field with $q$ elements where $q=p^l$ is
a prime power. Using Fourier analytic tools with a third moment method, we
obtain sum-product type estimates for subsets of $\mathbb{F}_q$. In particular,
we prove that if $A\subset \mathbb{F}_q$, then
$|AA+A|,|A(A+A)|\gg\min\left\{q, \frac{|A|^2}{q^{\frac{1}{2}}} \right\},$ so
that if $A\ge q^{\frac{3}{4}}$, then $|AA+A|,|A(A+A)|\gg q$.Comment: Lemma 1.2 is written in a general form. I would like to thank Oliver
Roche-Newton for pointing out that the main result of the paper can be
improved by using point-line incidence theorem of Le Anh Vinh over finite
field

### Erd\H{o}s Type Problems in Modules over Cyclic Rings

In the present paper, we study various Erd\H{o}s type geometric problems in
the setting of the integers modulo $q$, where $q=p^l$ is an odd prime power.
More precisely, we prove certain results about the distribution of triangles
and triangle areas among the points of $E\subset \mathbb{Z}_q^2$. We also prove
a dot product result for $d$-fold product subsets $E=A\times \ldots \times A$
of $\mathbb{Z}_q^d$, where $A\subset \mathbb{Z}_q$

### Jets, Lifts and Dynamics

We show that complete cotangent lifts of vector fields, their decomposition
into vertical representative and holonomic part provide a geometrical framework
underlying Eulerian equations of continuum mechanics. We discuss Euler
equations for ideal incompressible fluid and Vlasov equations of plasma
dynamics in connection with the lifts of divergence-free and Hamiltonian vector
fields, respectively. As a further application, we obtain kinetic equations of
particles moving with the flow of contact vector fields both from Lie-Poisson
reductions and with the techniques of present framework

### On Geometry of Schmidt Legendre Transformation

A geometrization of Schmidt-Legendre transformation of the second order
Lagrangians is proposed by building a proper Tulczyjew's triplet. The
symplectic relation between Ostrogradsky-Legendre and Schmidt-Legendre
transformations is obtained. Several examples are presented

### Lie Algebra of Hamiltonian Vector Fields and the Poisson-Vlasov Equations

We introduce natural differential geometric structures underlying the
Poisson-Vlasov equations in momentum variables. We decompose the space of all
vector fields over particle phase space into a semi-direct product algebra of
Hamiltonian vector fields and its complement. The latter is related to dual
space of Lie algebra. Lie algebra of Hamiltonian vector fields is isomorphic to
the space of all Lagrangian submanifolds with respect to Tulczyjew symplectic
structure. This is obtained as tangent space at the identity of the group of
canonical diffeomorphisms represented as space of sections of a trivial bundle.
We obtain the momentum-Vlasov equations as vertical equivalence of complete
cotangent lift of Hamiltonian vector field generating particle motion. Vertical
representatives can be described by holonomic lift from a Whitney product to a
Tulczyjew symplectic space. A generalization of complete cotangent lift is
obtained by a Lie algebra homomorphism from the algebra of symmetric
contravariant tensor fields with Schouten concomitant to the Lie algebra of
Hamiltonian vector fields. Momentum maps for particular subalgebras result in
plasma-to-fluid map in momentum variables. We exhibit dynamical relations
between Lie algebras of Hamiltonian vector fields and of contact vector fields,
in particular; infinitesimal quantomorphisms. Gauge symmetries of particle
motion are extended to tensorial objects including complete lift of particle
motion. Poisson equation is then obtained as zero value of momentum map for the
Hamiltonian action of gauge symmetries for kinematical description

### De Donder Form for Second Order Gravity

We show that the De Donder form for second order gravity, defined in terms of
Ostrogradski's version of the Legendre transformation applied to all
independent variables, is globally defined by its local coordinate
descriptions. It is a natural differential operator applied to the
diffeomorphism invariant Lagrangian of the theory

### Lagrangian Dynamics on Matched Pairs

Given a matched pair of Lie groups, we show that the tangent bundle of the
matched pair group is isomorphic to the matched pair of the tangent groups. We
thus obtain the Euler-Lagrange equations on the trivialized matched pair of
tangent groups, as well as the Euler-Poincar\'e equations on the matched pair
of Lie algebras. We show explicitly how these equations cover those of the
semi-direct product theory. In particular, we study the trivialized, and the
reduced Lagrangian dynamics on the group $SL(2,\mathbb{C})$

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