Second-order corrections to neutrino two-flavor oscillation parameters in the wave packet approach

We report about an analytic study involving the {\em intermediate} wave packet formalism for quantifying the physically relevant information which appear in the neutrino two-flavor conversion formula and help us to obtain more precise limits and ranges for neutrino flavor oscillation. By following the sequence of analytic approximations where we assume a strictly peaked momentum distribution and consider the second-order corrections in a power series expansion of the energy, we point out a {\em residual} time-dependent phase which, coupled with the {\em spreading/slippage} effects, can subtly modify the neutrino oscillation parameters and limits. Such second-order effects are usually ignored in the relativistic wave packet treatment, but they present an evident dependence on the propagation regime so that some small modifications to the oscillation pattern, even in the ultra-relativistic limit, can be quantified. These modifications are implemented in the confront with the neutrino oscillation parameter range (mass-squared difference $\Delta m^{\2}$ and the mixing-angle $\theta$) where we assume the same wave packet parameters previously noticed in the literature in a kind of {\em toy model} for some reactor experiments. Generically speaking, our analysis parallels the recent experimental purposes which concern with higher precision parameter measurements. To summarize, we show that the effectiveness of a more accurate determination of $\Delta m^{\2}$ and $\theta$ depends on the wave packet width $a$ and on the averaged propagating energy flux $\bar{E}$ which still correspond to open variables for some classes of experiments. \