Measurement of helium-3 and deuterium stopping power ratio for negative muons

The measurement method and results measuring of the stopping power ratio of helium-3 and deuterium atoms for muons slowed down in the D/$^3$He mixture are presented. Measurements were performed at four values of pure $^3$He gas target densities, $\phi_{He} = 0.0337, 0.0355, 0.0359, 0.0363$ (normalized to the liquid hydrogen density) and at a density 0.0585 of the D/$^3$He mixture. The experiment was carried out at PSI muon beam $\mu$E4 with the momentum P$\mu =34.0$ MeV/c. The measured value of the mean stopping ratio $S_{^3He/D}$ is $1.66\pm 0.04$. This value can also be interpreted as the value of mean reduced ratio of probabilities for muon capture by helium-3 and deuterium atoms.Comment: 7 pages, 6 figure

Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups

International audienceWe describe the kernel of the canonical map from the Floyd boundary of a relatively hyperbolic group to its Bowditch boundary. Using the Floyd completion we further prove that the property of relative hyperbolicity is invariant under quasi-isometric maps. If a finitely generated group H admits a quasi-isometric map ϕ into a relatively hyperbolic group G then H is itself relatively hyperbolic with respect to a system of subgroups whose image under ϕ is situated within a uniformly bounded distance of the right cosets of the parabolic subgroups of G. We then generalize the latter result to the case when ϕ is an α-isometric map for any polynomial distortion function α. As an application of our method we provide in the Appendix a new short proof of a basic theorem of Bowditch characterizing hyperbolicity

Non-finitely generated relatively hyperbolic groups and Floyd quasiconvexity

The paper consists of two parts. In the first one we show that a relatively hyperbolic group $G$ splits as a star graph of groups whose central vertex group is finitely generated and the other vertex groups are maximal parabolic subgroups. As a corollary we obtain that every group which admits 3-discontinuous and 2-cocompact action by homeomorphisms on a compactum is finitely generated with respect to a system of parabolic subgroups. The second part essentially uses the methods of topological entourages developed in the first part. Using also Floyd metrics we obtain finer properties of finitely generated relatively hyperbolic groups. We show that there is a system of "tight" curves satisfying the property of horospherical quasiconvexity. We then prove that the Floyd quasigeodesics are tight and so the parabolic subgroups of $G$ are quasiconvex with respect to the Floyd metrics. As a corollary we obtain that the preimage of a parabolic point by the Floyd map is the Floyd boundary of its stabilizer

Dispersion relations and subtractions in hard exclusive processes

We study analytical properties of the hard exclusive processes amplitudes. We found that QCD factorization for deeply virtual Compton scattering and hard exclusive vector meson production results in the subtracted dispersion relation with the subtraction constant determined by the Polyakov-Weiss $D$-term. The relation of this constant to the fixed pole contribution found by Brodsky, Close and Gunion and defined by parton distributions is proved, while its manifestation is spoiled by the small $x$ divergence. The continuation to the real photons limit is considered and the numerical correspondence between lattice simulations of $D$-term and low energy Thomson amplitude is found.Comment: 4 pages, journal versio

The role of impacting processes in the chemical evolution of the atmosphere of primordial Earth

The role of impacting processes in the chemical evolution of the atmosphere of primordial Earth is discussed. The following subject areas are covered: (1) Earth's initial atmosphere; (2) continuous degassing; (3) impact processes and the Earth's protoatmosphere; and (4) the evolution of an impact-generated atmosphere