Accurate nucleon electromagnetic form factors from dispersively improved chiral effective field theory

We present a theoretical parametrization of the nucleon electromagnetic form factors (FFs) based on a combination of chiral effective field theory and dispersion analysis. The isovector spectral functions on the two-pion cut are computed using elastic unitarity, chiral pion-nucleon amplitudes, and timelike pion FF data. Higher-mass isovector and isoscalar t-channel states are described by effective poles, whose strength is fixed by sum rules (charges, radii). Excellent agreement with the spacelike proton and neutron FF data is achieved up to Q^2 \sim 1 GeV^2. Our parametrization provides proper analyticity and theoretical uncertainty estimates and can be used for low-Q^2 FF studies and proton radius extraction.Comment: 5 pages, 3 figures, 2 table

Harmonic mappings and conformal minimal immersions of Riemann surfaces into RN

We prove that for any open Riemann surface N, natural number N ≥ 3, non-constant harmonic map h:N→R N−2 and holomorphic 2-form H on N , there exists a weakly complete harmonic map X=(Xj)j=1,…,\scN:N→R\scN with Hopf differential H and (Xj)j=3,…,\scN=h. In particular, there exists a complete conformal minimal immersion Y=(Yj)j=1,…,\scN:N→R\scN such that (Yj)j=3,…,\scN=h . As some consequences of these results (1) there exist complete full non-decomposable minimal surfaces with arbitrary conformal structure and whose generalized Gauss map is non-degenerate and fails to intersect N hyperplanes of CP\scN−1 in general position. (2) There exist complete non-proper embedded minimal surfaces in R\scN, ∀\scN>3.Ministerio de Ciencia y Tecnología MTM2007-61775Ministerio de Ciencia y Tecnología MTM2007-64504Junta de Andalucía P09-FQM-508

Complete minimal surfaces and harmonic functions

We prove that for any open Riemann surface N and any non constant harmonic function h : N → R, there exists a complete conformal minimal immersion X : N → R3 whose third coordinate function coincides with h. As a consequence, completeminimal surfaceswith arbitrary conformal structure andwhose Gauss map misses two points are constructed.Ministerio de Educación y Ciencia MTM2007-61775Ministerio de Educación y Ciencia MTM2007-64504Junta de Andalucía P06-FQM-01642