Precision electromagnetic structure of decuplet baryons in the chiral regime

The electromagnetic properties of the baryon decuplet are calculated in quenched QCD on a 20^3 x 40 lattice with a lattice spacing of 0.128 fm using the fat-link irrelevant clover (FLIC) fermion action with quark masses providing a pion mass as low as 300 MeV. Magnetic moments and charge radii are extracted from the electric and magnetic form factors for each individual quark sector. From these, the corresponding baryon properties are constructed. We present results for the higher order moments of the spin-3/2 baryons, including the electric quadrupole moment E2 and the magnetic octupole moment M3. The world's first determination of a non-zero M3 form factor for the Delta baryon is presented. With these results we provide a conclusive analysis which shows that decuplet baryons are deformed. We compare the decuplet baryon results from a similar lattice calculation of the octet baryons. We establish that the environment sensitivity is far less pronounced in the case of the decuplet baryons compared to that in the octet baryons. A surprising result is that the charge radii of the decuplet baryons are generally smaller than that of the octet baryons. The magnetic moment of the Delta^+ reveals a turn over in the low quark mass region, making it smaller than the proton magnetic moment. These results are consistent with the expectations of quenched chiral perturbation theory. A similar turn over is also noticed in the magnetic moment of the Sigma^*0, but not for Xi^* where only kaon loops can appear in quenched QCD. The electric quadrupole moment of the Omega^- baryon is positive when the negative charge factor is included, and is equal to 0.86 +- 0.12 x 10^-2 fm^2, indicating an oblate shape.Comment: 30 pages, 32 figure

Random division of an interval

The well-known relation between random division of an interval and the Poisson process is interpreted as a Laplace transformation. With the use of this interpretation a number of (in part known) results is derived very easily

The Circular Polarization of Saggitarius A* at Submillimeter Wavelengths

We report the first detections of circularly polarized emission at submillimeter wavelengths from the compact radio source and supermassive black hole candidate Sgr A* at a level of 1.2\pm0.3% at 1.3 mm wavelength (230 GHz) and 1.6\pm0.3% at 860 microns (345 GHz) with the same handedness as observed at lower frequencies (1.4-15 GHz). The observations, taken with the Submillimeter Array in multiple epochs, also show simultaneous linear polarization (LP) at both wavelengths of about 6%. These properties differ sharply from those at wavelengths longer than 1 cm (frequencies below 30 GHz), where weak circular polarization (CP) (~ 0.5%) dominates over LP, which is not detected at similar fractional limits. We describe an extensive set of tests to ensure the accuracy of our measurements. We find no CP in any other source, including the bright quasar 1924-292, which traces the same path on the sky as Sgr A* and therefore should be subject to identical systematic errors originating in the instrument frame. Since a relativistic synchrotron plasma is expected to produce little CP, the observed CP is probably generated close to the event horizon by the Faraday conversion process. We use a simple model to show that the phase shift associated with Faraday conversion can be nearly independent of frequency, a sufficient condition to make the handedness of CP independent of frequency. Because the size of the tau=1-surface changes by more than an order of magnitude between 1.4 and 345 GHz, the magnetic field must be coherent over such scales to consistently produce left CP.Astronom

Random Topologies and the emergence of cooperation: the role of short-cuts

We study in detail the role of short-cuts in promoting the emergence of cooperation in a network of agents playing the Prisoner's Dilemma Game (PDG). We introduce a model whose topology interpolates between the one-dimensional euclidean lattice (a ring) and the complete graph by changing the value of one parameter (the probability p to add a link between two nodes not already connected in the euclidean configuration). We show that there is a region of values of p in which cooperation is largely enhanced, whilst for smaller values of p only a few cooperators are present in the final state, and for p \rightarrow 1- cooperation is totally suppressed. We present analytical arguments that provide a very plausible interpretation of the simulation results, thus unveiling the mechanism by which short-cuts contribute to promote (or suppress) cooperation