98,873 research outputs found
A metric property of umbilic points
In the space of cubic forms of surfaces, regarded as a
-space and endowed with a natural invariant metric, the ratio of the volumes
of those representing umbilic points with negative to those with positive
indexes is evaluated in terms of the asymmetry of the metric, defined here. A
connection of this ratio with that reported by Berry and Hannay (1977) in the
domain of Statistical Physics, is discussed.Comment: 8 pages, 1 figur
Sigma pole position and errors of a once and twice subtracted dispersive analysis of pi-pi scattering data
We show how the new precise data on kaon decays together with forward
dispersion relations, sum rules and once- and twice-subtracted
Roy's equations allow for a precise determination of the sigma meson pole
position. We present a comparison and a study of the different sources of
uncertainties when using either once- or twice-subtracted Roy's equations to
analyze the data. Finally we present a preliminary determination of the sigma
pole from the constrained dispersive data analysis.Comment: 4 pages, 6 figures. Contribution to the proceedings of the QCD08 14th
International QCD Conference. 7-12th July 2008 Montpellier (France); one
reference removed, changed errors in Eqs (4), (5) and (7
New dispersion relations in the description of scattering amplitudes
We present a set of once subtracted dispersion relations which implement
crossing symmetry conditions for the scattering amplitudes below 1
GeV. We compare and discuss the results obtained for the once and twice
subtracted dispersion relations, known as Roy's equations, for three
partial JI waves, S0, P and S2. We also show that once subtracted dispersion
relations provide a stringent test of crossing and analyticity for
partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where
the resulting uncertainties are significantly smaller than those coming from
standard Roy's equations, given the same input.Comment: 8 pages, 2 figures, to appear in the Proceedings of the Meson 2008
conference, June 6-10, 2008, Cracow, Polan
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