Reti neurali per determinazione di shape functions in B -> Xu l nu

We present a new technique for the determination of shape functions in inclusive semileptonic B decay. These non-perturbative form factors arise in the partial decay rate due to experimental cuts, that are needed to isolate the charmless mode but introduce sensitivity to the Fermi motion of the b quark in the hadron. They cannot be computed from first principles and an unbiased determination is possible using neural networks, a robust tool that is largely used in particle physics, but has never been applied in this context. Our technique represents an improvement with respect to previous methods used to determine shape functions in semileptonic B decay, based on the assumption of a functional form. The use of neural networks trained with available theoretical constraints through order (1/mb)^3 in the heavy quark expansion, allows us to predict the shape of these unknown functions without bias and to compute the decay rate with cuts. We illustrate in detail how the value of the CKM matrix element |Vub| can be extracted, comparing the theoretical predictions with measured branching fractions. An analysis of the uncertainty of the result due to the used technique is also presented. Finally, the interest in applying the neural networks parameterization for shape functions does not restrict to the application presented in this thesis. The methodology that has been first tested here, has a future potential use for a more accurate study of shape functions when direct experimental information on various kinematical distributions will be available from Belle II experiment. Experimental constraints can probably be implemented more easily in the neural networks framework than other methods and will allow us to perform a simulta- neous fit to the shape functions parameters and the |Vub| value.