Neutrino oscillation from the beam with Gaussian-like energy distribution

A recent neutrino experiment at Daya Bay gives superior data of the distribution of the prompt energy. In this paper, the energy distribution presented in the experiment is simulated by applying a Gaussian-like packet to the neutrino wave function received by the detector. We find that the wave packet of neutrinos is expanded during the propagation. As a result, the mixing angle $\theta_{13}$ is more difficult to be measured than $\theta_{12}$ and $\theta_{23}$ in long baseline experiments. Some other propagation properties, such as the time evaluation of the survival probability, the neutrino oscillation and the $CP$ violation, are also studied with the employment of the coherent state method. When the Gaussian packet width increases, the amplitude of the neutrino oscillation decreases, whereas the oscillation period increases gradually.