Symmetries of degenerate center singularities of plane vector fields

Let $D$ be a closed unit $2$-disk on the plane centered at the origin $O$, and $F$ be a smooth vector field such that $O$ is a unique singular point of $F$ and all other orbits of $F$ are simple closed curves wrapping once around $O$. Thus topologically $O$ is a "center" singularity. Let also $\mathrm{Diff}(F)$ be the group of all diffeomorphisms of $D$ which preserve orientation and orbits of $F$. In arXiv:0907.0359 the author described the homotopy type of $\mathrm{Diff}(F)$ under assumption that the $1$-jet of $F$ at $O$ is non-degenerate. In this paper degenerate case is considered. Under additional "non-degeneracy assumptions" on $F$ the path components of $\mathrm{Diff}(F)$ with respect to distinct weak topologies are described.Comment: 21 page, 3 figure

The Dirac form factor predicts the Pauli form factor in the Endpoint Model

We compute the momentum-transfer dependence of the proton Pauli form factor $F_{2}$ in the endpoint overlap model. We find the model correctly reproduces the scaling of the ratio of $F_{2}$ with the Dirac Form factor $F_{1}$ observed at the Jefferson Laboratory. The calculation uses the leading-power, leading twist Dirac structure of the quark light-cone wave function, and the same endpoint dependence previously determined from the Dirac form factor $F_{1}$. There are no parameters and no adjustable functions in the endpoint model's prediction for $F_{2}$. The model's predicted ratio $F_{2}(Q^{2})/F_{1}(Q^{2})$ is quite insensitive to the endpoint wave function, which explains why the observed ratio scales like $1/Q$ down to rather low momentum transfers. The endpoint model appears to be the only comprehensive model consistent with all form factor information as well as reproducing fixed-angle proton-proton scattering at large momentum transfer. Any one of the processes is capable of predicting the others.Comment: 12 pages, 3 figure

Beam-helicity and beam-charge asymmetries associated with deeply virtual Compton scattering on the unpolarised proton

Beam-helicity and beam-charge asymmetries in the hard exclusive leptoproduction of real photons from an unpolarised hydrogen target by a 27.6 GeV lepton beam are extracted from the HERMES data set of 2006-2007 using a missing-mass event selection technique. The asymmetry amplitudes extracted from this data set are more precise than those extracted from the earlier data set of 1996-2005 previously analysed in the same manner by HERMES. The results from the two data sets are compatible with each other. Results from these combined data sets are extracted and constitute the most precise asymmetry amplitude measurements made in the HERMES kinematic region using a missing-mass event selection technique.Comment: (minor changes only compared to arXiv version 1