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Desingularizing -symplectic structures
A -dimensional Poisson manifold is said to be -symplectic
if it is symplectic on the complement of a hypersurface and has a simple
Darboux canonical form at points of which we will describe below. In this
paper we will discuss a desingularization procedure which, for even,
converts into a family of symplectic forms having the
property that is equal to the -symplectic form dual to
outside an -neighborhood of and, in addition, converges to
this form as tends to zero in a sense that will be made precise in
the theorem below. We will then use this construction to show that a number of
somewhat mysterious properties of -manifolds can be more clearly
understood by viewing them as limits of analogous properties of the
's. We will also prove versions of these results for
odd; however, in the odd case the family has to be replaced
by a family of folded symplectic forms.Comment: new version, 13 pages, 3 figures, final version accepted at IMRN,
International Mathematics Research Notice
B Physics on the Lattice: , , , , mixing, \fb and all that
We present a short review of our most recent high statistics lattice
determinations in the HQET of the following important parameters in B physics:
the B--meson binding energy, and the kinetic energy of the
b quark in the B meson, , which due to the presence of power
divergences require a non--perturbative renormalization to be defined; the
running mass of the b quark,
; the -- mass splitting, whose
value in the HQET is determined by the matrix element of the chromo--magnetic
operator between B meson states, ; the B parameter of the
-- mixing, , and the decay constant of the B meson,
. All these quantities have been computed using a sample of gauge
field configurations on a lattice at . For
and , we obtain our
estimates by combining results from three independent lattice simulations at
, and on the same volume.Comment: 3 latex pages, uses espcrc2.sty (included). Talk presented at
LATTICE96(heavy quarks
Splitting from Nonrelativistic Renormalization Group
We compute the hyperfine splitting in a heavy quarkonium composed of
different flavors in next-to-leading logarithmic approximation using the
nonrelativistic renormalization group. We predict the mass difference of the
vector and pseudoscalar charm-bottom mesons to be MeV.Comment: Eq.(22) and Appendix corrected, numerical results slightly changed.
arXiv admin note: text overlap with arXiv:hep-ph/031208
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