On the neutrino non-detection of GRB 130427A

The recent gamma-ray burst GRB 130427A has an isotropic electromagnetic energy $E^{iso}\sim10^{54}$ erg, suggesting an ample supply of target photons for photo-hadronic interactions, which at its low redshift of $z\sim0.34$ would appear to make it a promising candidate for neutrino detection. However, the IceCube collaboration has reported a null result based on a search during the prompt emission phase. We show that this neutrino non-detection can provide valuable information about this GRB's key physical parameters such as the emission radius $R_{d}$, the bulk Lorentz factor $\Gamma$ and the energy fraction converted into cosmic rays $\epsilon_{p}$. The results are discussed both in a model-independent way and in the specific scenarios of an internal shock model (IS), a baryonic photospheric model (BPH) and magnetic photospheric model (MPH). We find that the constraints are most stringent for the magnetic photospheric model considered, but the constraints on the internal shock and the baryonic photosphere models are fairly modest.