Prompt Gamma-Ray Burst Neutrinos: The Stacking Fluence Bound Against the Waxman-Bahcall Expectation

Gamma-ray bursts were the original predicted source of high-energy neutrinos, with a clean argument tying their neutrino output to the cosmic-ray energy budget. Stacked searches at IceCube have now limited the prompt neutrino emission of hundreds of bursts to about 1 per cent of the diffuse flux. This paper converts both the classic expectation and the stacking limit into the same per-burst currency. The classic expectation corresponds to an average per-burst E-squared fluence of 0.0113 GeV per square centimetre; the stacking limit corresponds to 1.416e-04 GeV per square centimetre. The ratio of limit to expectation is 0.0125 — the data sit a factor of 80 below the classic prediction. Either bursts load far fewer baryons than the classic picture assumed, or their protons reach lower energies, or the prompt phase is not where their neutrinos are made. The classic model in its original form is excluded by a wide margin. The study is computed from stated assumptions, not measured.