Study of the effect of neutrino oscillations on the supernova neutrino signal in the LVD detector

The LVD detector, located in the INFN Gran Sasso National Laboratory (Italy), studies supernova neutrinos through the interactions with protons and carbon nuclei in the liquid scintillator and interactions with the iron nuclei of the support structure. We investigate the effect of neutrino oscillations in the signal expected in the LVD detector. The MSW effect has been studied in detail for neutrinos travelling through the collapsing star and the Earth. We show that the expected number of events and their energy spectrum are sensitive to the oscillation parameters, in particular to the mass hierarchy and the value of $\theta_{13}$, presently unknown. Finally we discuss the astrophysical uncertainties, showing their importance and comparing it with the effect of neutrino oscillations on the expected signal.