| Summary: | Lorentz violation (LV) induced by Quantum Gravity has been tested at much lower energies than the Planck scale with more and more observational evidence. In recent studies, the time of flight difference between the TeV neutrino and MeV photon from Gamma Ray Bursts (GRBs) have been used to constrain the LV energy scale, based on the energy-dependent speed variation. Here, we performed a correlation study between the updated 7.5 year high-energy starting events (HESE), neutrino alert events detected by IceCube, and a full sample of more than 7000 GRBs, and we found six GRB-neutrino candidates, including four alerts and two track events. We obtained the first order energy scale of quantum gravity, namely <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>E</mi><mi>QG</mi></msub><mo>=</mo><msubsup><mn>8</mn><mrow><mo>−</mo><mn>5</mn></mrow><mrow><mo>+</mo><mn>15</mn></mrow></msubsup><mo>×</mo><msup><mn>10</mn><mn>17</mn></msup><mspace width="3.33333pt"></mspace><mi>GeV</mi></mrow></semantics></math></inline-formula>, which was consistent with other authors‘ work. We suggest that neutrinos and anti-neutrinos can be identified, respectively, due to the delay or advance of the observed time. For future point source search study of neutrinos, the arrival time difference of different particles may have to be taken into account.
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