2D-Oide effect

The Oide effect considers the synchrotron radiation in the final focusing quadrupole and it sets a lower limit on the vertical beam size at the Interaction Point, particularly relevant for high energy linear colliders. The theory of the Oide effect was derived considering only the radiation in the focusing plane of the magnet. This article addresses the theoretical calculation of the radiation effect on the beam size consider- ing both focusing and defocusing planes of the quadrupole, refered to as 2D-Oide. The CLIC 3 TeV final quadrupole (QD0) and beam parameters are used to compare the theoretical results from the Oide effect and the 2D-Oide effect with particle tracking in PLACET. The 2D-oide demonstrates to be important as it increases by 17% the contribution to the beam size. Further insight into the aberrations induced by the synchrotron radiation opens the possibility to partially correct the 2D-Oide effect with octupole mag

Parabolic bundles and representations of the fundamental group

Let X be as smooth complex projective variety with Neron-Severi group isomorphic to Z, and D an irreducible divisor with normal crossing singularities. Assume r is equal to 2 or 3. We prove that if the fundamental group of X doesn't have irreducible PU(r) representations, then the fundamental group of X-D doesn't have irreducible U(r) representations. The proof uses the non-existence of certain stable parabolic bundles. We also obtain a similar result for GL(2) when D is smooth and X is a complex surface.Comment: 13 pages, 1 figure, LaTeX2

Calculation of nuclear matrix elements in neutrinoless double electron capture

We compute nuclear matrix elements for neutrinoless double electron capture on $^{152}$Gd, $^{164}$Er and $^{180}$W nuclei. Recent precise mass measurements for these nuclei have shown a large resonance enhancement factor that makes them the most promising candidates for observing this decay mode. We use an advanced energy density functional method which includes beyond mean-field effects such as symmetry restoration and shape mixing. Our calculations reproduce experimental charge radii and $B(E2)$ values predicting a large deformation for all these nuclei. This fact reduces significantly the values of the NMEs leading to half-lives larger than $10^{29}$ years for the three candidates