Electromagnetic (and adiabatic) energy losses of $\pi$’s and $\mu$’s modify the flavor ratio (measured at Earth) of neutrinos produced by $\pi$ decay in astrophysical sources, ${\Phi }_{{\nu }_e}:{\Phi }_{{\nu }_{\mu }}:{\Phi }_{{\nu }_{\tau }}$, from $1:1:1$ at low energy to $1:1.8:1.8$ at high energy. The transition occurs over 1–2 decades of $\nu$ energy, and is correlated with a modification of the neutrino spectrum. For $\gamma$-ray bursts, e.g., the transition is expected at $\sim 100\mathrm{TeV}$ and may be detected by km-scale $\nu$ telescopes. Measurements of the transition energy and energy width will provide unique probes of the physics of the sources. $\pi$ and $\mu$ energy losses also affect the ratio of ${\overline{\nu }}_e$ flux to total $\nu$ flux, which may be measured at the $W$ resonance (6.3 PeV): It is modified from $1/6$ ($1/15$) at low energy to $1/9$ (practically 0) at high energy for neutrinos produced in $pp$ ($p\gamma$) interactions.

• Received 27 July 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.181101