Detection of supernova neutrinos on the Earth for large theta13

Supernova (SN) neutrinos detected on the Earth are subject to the shock wave effects, the Mikheyev-Smirnov-Wolfenstein (MSW) effects, the neutrino collective effects and the Earth matter effects. Considering the recent experimental result about the large mixing angle $\theta_{13}$ ($\backsimeq8.8^{\circ}$) provided by the Daya Bay Collaboration and applying the available knowledge for the neutrino conversion probability in the high resonance of SN, $P_{H}$, which is in the form of hypergeometric function in the case of large $\theta_{13}$, we deduce the expression of $P_{H}$ taking into account the shock wave effects. It is found that $P_{H}$ is not zero in a certain range of time due to the shock wave effects. After considering all the four physical effects and scanning relevant parameters, we calculate the event numbers of SN neutrinos detected at the Daya Bay experiment. From the numerical results, it is found that the behaviors of neutrino event numbers detected on the Earth depend on the neutrino mass hierarchy and neutrino spectrum parameters including the temperature $T_{\alpha}$, the dimensionless pinching parameter $\eta_{\alpha}$ or $\beta_{\alpha}$ (where $\alpha$ refers to neutrino flavor), the average energy $< E_{\alpha}>$, and the SN neutrino luminosities $L_{\alpha}$. We also compare the results of two parametrization methods for the neutrino energy distributions and give the ranges of SN neutrino event numbers that will be detected at the Daya Bay experiment.