Mimicking the one-dimensional marginal distributions of stochastic diffusions

In the large maturity limit, we compute explicitly the Local Volatility surface for Heston, through Dupire’s formula, with Fourier pricing of the respective derivatives of the call price. Than we verify that the prices of European call options produced by the Heston model, concide with those given by the local volatility model where the Local Volatility is computed as said above.

Radio halos in a mass-selected sample of galaxy clusters

A fraction of galaxy clusters host Mpc-scale Radio Halos (RH), generated by ultrarelativistic electrons in the magnetized intra cluster medium (ICM). In the current view they trace turbulent regions in merging clusters, where relativistic particles are trapped and accelerated. This model has clear expectations about the statistical properties of RHs. To test these expectations large mass-selected samples of galaxy clusters with adequate radio and X-ray data are necessary. We used the Planck SZ cluster catalogue as suitable starting point of our investigation, selecting clusters with M500>6x10^14 Msun at 0.08sample with the NVSS for clusters at z<0.2 and with the Extended GMRT RH Survey for 0.2

Study of a new method for high energy top tagging at the ATLAS experiment

Since its discovery, top quark has represented one of the most investigated field in particle physics. The aim of this thesis is the reconstruction of hadronic top with high transverse momentum (boosted) with the Template Overlap Method (TOM). Because of the high energy, the decay products of boosted tops are partially or totally overlapped and thus they are contained in a single large radius jet (fat-jet). TOM compares the internal energy distributions of the candidate fat-jet to a sample of tops obtained by a MC simulation (template). The algorithm is based on the definition of an overlap function, which quantifies the level of agreement between the fat-jet and the template, allowing an efficient discrimination of signal from the background contributions. A working point has been decided in order to obtain a signal efficiency close to 90% and a corresponding background rejection at 70%. TOM performances have been tested on MC samples in the muon channel and compared with the previous methods present in literature. All the methods will be merged in a multivariate analysis to give a global top tagging which will be included in ttbar production differential cross section performed on the data acquired in 2012 at sqrt(s)=8 TeV in high phase space region, where new physics processes could be possible. Due to its peculiarity to increase the pT, the Template Overlap Method will play a crucial role in the next data taking at sqrt(s)=13 TeV, where the almost totality of the tops will be produced at high energy, making the standard reconstruction methods inefficient.