It has been realized that the shock wave effects play an important role in neutrino oscillations during the supernova explosion. In recent years, with the development of simulations about supernova explosion, we have a better understanding about the density profiles and the shock waves in supernovae than before. It has been shown that the appearance of shock waves not only varies with time, but is also affected by the mass of the supernova. When the mass of the supernova happens to be in a certain range (e.g. it equals 10.8 times the mass of the sun), there might be a reverse shock wave, another sudden change of density except the forward shock wave, emerging in the supernova.In addition, there are some other time-dependent changes of density profiles in different supernova models. Because of these complex density profiles, the expression of the crossing probability at the high resonance, PH , which we used previously would be no longer applicable. In order to get more accurate and reasonable results, we use the data of density profiles in three different supernova models obtained from simulations to study the variations of Ps (the survival probability of νe → νe), as well as Pc (the conversion probability of νx → νe). It is found that the mass of the supernova does make a difference on the behavior of Ps, and affects Pc at the same time. With the results of Ps and Pc, we can estimate the number of νe remained after they go through the matter in the supernova.

We study the direct CP violation in the τ ± → K ± ρ 0 (ω)ν τ → K ± π + π − ν τ decay process in the standard model. An interesting mechanism involving the charge symmetry violating mixing between ρ 0 and ω is applied to enlarge the CP asymmetry. We find that the CP-violating asymmetry can be enhanced greatly via this ρ-ω mixing mechanism when the invariant mass of the π + π − pair is in the vicinity of the ω resonance. With this mechanism, the maximum differential and localized integrated CP asymmetries can reach −(5.6 +2.9 −1.7 ) ×

An extrapolation to the physical limit for the lattice data of Λb →Λc form factors computed in the nonphysical region is made in this work through a class of fitting functions proposed by us with nonlinear dependence on derived in the chiral perturbative theory (ChPT) and the heavy quark effective theory (HQET) framework. Then the results are applied to calculate the differential and integrated Λb →Λc semileptonic decay rates. Meanwhile, a comparison between our results and those obtained through the extrapolation functions with naive linear dependence on is made. It is shown that the difference between the extrapolated central values of these two cases is about 5%. The total uncertainties (depending on the momentum transfer q2) in the linear case are about 5% ∼ 10% (caused by the uncertainties of lattice data) and those in the nonlinear case are about 10% ∼ 20% (caused by the uncertainties of both lattice data and input parameters in ChPT and HQET). More accurate lattice data and parameters in ChPT and HQET are needed to reduce the uncertainties of the extrapolated results.

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