Connect the Lorentz Violation to the Glashow Resonance Event

The recent reported Glashow resonance (GR) event shows a promising prospect in the test of the Lorentz violation (LV) by the high-energy astrophysical neutrinos (HANs) around the resonant energy. However, since the production source and the energy spectra of HANs are uncertain at present, moderate LV effects may be concealed at the TeV energy-scale. In this paper, we propose the LV Hamiltonian of a special texture which can lead to the decoupling of $\nu_{\mu}$ ($\bar{\nu}_{\mu}$). On the base of the decoupling, a noticeable damping of the GR event rate is shown for the HANs from the source dominated by $\bar{\nu}_{\mu}$, irrespective of the energy spectra of the HANs at Earth. Accordingly, the observation of GR events may bring stringent constraints on the LV and the production mechanism of HANs.