Occurence and Luminosity Functions of Giant Radio Halos from Magneto-Turbulent Model

We calculate the probability to form giant radio halos (~ 1 Mpc size) as a function of the mass of the host clusters by using a Statistical Magneto-Turbulent Model (Cassano & Brunetti, these proceedings). We show that the expectations of this model are in good agreement with the observations for viable values of the parameters. In particular, the abrupt increase of the probability to find radio halos in the more massive galaxy clusters (M > 2x10^{15} solar masses) can be well reproduced. We calculate the evolution with redshift of such a probability and find that giant radio halos can be powered by particle acceleration due to MHD turbulence up to z~0.5 in a LCDM cosmology. Finally, we calculate the expected Luminosity Functions of radio halos (RHLFs). At variance with previous studies, the shape of our RHLFs is characterized by the presence of a cut-off at low synchrotron powers which reflects the inefficiency of particle acceleration in the case of less massive galaxy clusters.Comment: 4 pages, to appear in a dedicated issue of the Journal of the Korean Astronomical Society (JKAS). Proceedings of the "International conference on Cosmic Rays and Magnetic Fields in Large Scale Structure", Busan, Korea, 200

Virtual Compton Scattering off the Pseudoscalar Meson Octet

We present a calculation of the virtual Compton scattering amplitude for the pseudoscalar meson octet in the framework of chiral perturbation theory at ${\cal O}(p^4)$. We calculate the electromagnetic generalized polarizabilities and compare the results in the real Compton scattering limit to available experimental values. Finally, we give predictions for the differential cross section of electron-meson bremsstrahlung.Comment: 9 pages, Latex, uses cjp3.sty (included), 4 eps figures, to be published in the proceedings of the 13th Indian-Summer School "Understanding the Structure of Hadrons," August 28 - September 1, 2000, Prague, Czech Republi

Relational reasoning via probabilistic coupling

Probabilistic coupling is a powerful tool for analyzing pairs of probabilistic processes. Roughly, coupling two processes requires finding an appropriate witness process that models both processes in the same probability space. Couplings are powerful tools proving properties about the relation between two processes, include reasoning about convergence of distributions and stochastic dominance---a probabilistic version of a monotonicity property. While the mathematical definition of coupling looks rather complex and cumbersome to manipulate, we show that the relational program logic pRHL---the logic underlying the EasyCrypt cryptographic proof assistant---already internalizes a generalization of probabilistic coupling. With this insight, constructing couplings is no harder than constructing logical proofs. We demonstrate how to express and verify classic examples of couplings in pRHL, and we mechanically verify several couplings in EasyCrypt

Measurement of triple gauge boson couplings from W⁺W⁻ production at LEP energies up to 189 GeV

A measurement of triple gauge boson couplings is presented, based on W-pair data recorded by the OPAL detector at LEP during 1998 at a centre-of-mass energy of 189 GeV with an integrated luminosity of 183 pb⁻¹. After combining with our previous measurements at centre-of-mass energies of 161–183 GeV we obtain κ = 0.97_{-0.16}^{+0.20}, g_{1}^{z} = 0.991_{-0.057}^{+0.060} and λ = -0.110_{-0.055}^{+0.058}, where the errors include both statistical and systematic uncertainties and each coupling is determined by setting the other two couplings to their Standard Model values. These results are consistent with the Standard Model expectations

Cluster Mergers, Radio Halos and Hard X-ray Tails: A Statistical Magneto-Turbulent Model

There is now firm evidence that the ICM consists of a mixture of hot plasma, magnetic fields and relativistic particles. The most important evidences for non-thermal phenomena in galaxy clusters comes from the diffuse Mpc-scale synchrotron radio emission (radio halos) observed in a growing number of massive clusters (Feretti 2003) and from hard X-ray (HXR) excess emission (detected in a few cases) which can be explained in terms of IC scattering of relativistic electrons off the cosmic microwave background photons (Fusco-Femiano et al. 2003). There are now growing evidences that giant radio halos may be naturally accounted for by synchrotron emission from relativistic electrons reaccelerated by some kind of turbulence generated in the cluster volume during merger events (Brunetti 2003). With the aim to investigate the connection between thermal and non-thermal properties of the ICM, we have developed a statistical magneto-turbulent model which describes the evolution of the thermal and non-thermal emission from clusters. We calculate the energy and spectrum of the magnetosonic waves generated during cluster mergers, the acceleration and evolution of relativistic electrons and thus the resulting synchrotron and inverse Compton spectra. Here we give a brief description of the main results, while a more detailed discussion will be presented in a forthcoming paper. Einstein-De Sitter cosmology, $H_o=50$ km $s^{-1}$$Mpc^{-1}$, $q_o=0.5$, is assumed.Comment: 3 pages, 2 figures. To appear in the proceedings of IAU Colloquium 195 - "Outskirts of galaxy clusters: intense life in the suburbs", Torino, Italy, March 12-16, 200