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.

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.

Multivariate analysis methods in the search for the Higgs boson produced in association with top pairs at the ATLAS experiment at LHC.

The Large Hadron Collider, located at the CERN laboratories in Geneva, is the largest particle accelerator in the world. One of the main research fields at LHC is the study of the Higgs boson, the latest particle discovered at the ATLAS and CMS experiments. Due to the small production cross section for the Higgs boson, only a substantial statistics can offer the chance to study this particle properties. In order to perform these searches it is desirable to avoid the contamination of the signal signature by the number and variety of the background processes produced in pp collisions at LHC. Much account assumes the study of multivariate methods which, compared to the standard cut-based analysis, can enhance the signal selection of a Higgs boson produced in association with a top quark pair through a dileptonic final state (ttH channel). The statistics collected up to 2012 is not sufficient to supply a significant number of ttH events; however, the methods applied in this thesis will provide a powerful tool for the increasing statistics that will be collected during the next LHC data taking.