[Paper Review] EeV neutrinos associated with UHECR sources

Zhuo Li, Eli Waxman|arXiv (Cornell University)|Nov 30, 2007

Noncommutative and Quantum Gravity Theories1 references3 citations

TL;DR

This paper proposes a novel mechanism for detecting EeV neutrinos from ultrahigh-energy cosmic ray (UHECR) sources such as gamma-ray bursts (GRBs), where high-energy photons from pion decay escape the source due to Klein-Nishina suppression and produce muon pairs via CMB interactions. The resulting muon decay generates high-energy neutrinos that are directionally and temporally correlated with the source, potentially reaching a few percent of the Waxman-Bahcall bound and enabling direct UHECR source identification and stringent tests of quantum gravity-induced Lorentz violation.

ABSTRACT

Electromagnetic energy losses of charged pions and muons suppress the expected high energy, >1E18 eV, neutrino emission from sources of ultrahigh energy, >1E19 eV, cosmic-rays. We show here that >1E19 eV photons produced in such sources by neutral pion decay may escape the sources, thanks to the Klein-Nishina suppression of the pair production cross section, and produce muon pairs in interactions with the cosmic microwave background. The flux of muon decay neutrinos, which are expected to be associated in time and direction with the electromagnetic emission from the sources, may reach a few percent of the Waxman-Bahcall bound. Their detection may allow one to directly identify the sources of >1E19 eV cosmic-rays, and will provide the most stringent constraints on quantum-gravity-induced Lorentz violation.

Motivation & Objective

• To identify a new, unsuppressed source of high-energy neutrinos associated with UHECR sources, overcoming limitations from pion and muon energy losses.
• To demonstrate that high-energy photons (>10^19 eV) can escape UHECR sources due to Klein-Nishina suppression of pair production.
• To show that these escaping photons can produce muon pairs in interactions with the cosmic microwave background (CMB), leading to detectable EeV neutrinos.
• To enable direct association of neutrinos with UHECR sources through time- and direction-correlation, independent of magnetic field deflections.
• To provide a pathway for testing quantum gravity-induced Lorentz violation using time-delay measurements of EeV neutrinos relative to GRB photons.

Proposed method

• Model the muon pair production cross section in interactions between high-energy photons (>10^19 eV) and CMB photons using relativistic kinematics and the center-of-momentum frame.
• Use the inverse mean free path formula (eq. 1) to calculate the muon pair production optical depth, accounting for the thermal CMB spectrum and energy-dependent cross sections.
• Apply Klein-Nishina suppression to show that photons above ~10^19 eV are optically thin in UHECR sources, enabling escape despite high radiation fields.
• Estimate the fraction of photon energy converted to muons (f_μ ≈ 0.03–0.1) and the resulting neutrino flux from muon decay, assuming ~2% of UHECR energy is converted to neutrinos.
• Account for neutrino oscillations, predicting a flavor ratio of 0.4:0.3:0.3 at Earth (ν_e:ν_μ:ν_τ), distinct from the 1:1:1 ratio from pion decay.
• Assess detectability using ARIANNA, a neutrino telescope sensitive to EeV neutrinos, and evaluate time-delay signatures for Lorentz invariance violation.

Experimental results

Research questions

• RQ1 Can high-energy photons (>10^19 eV) escape UHECR sources despite intense radiation fields, due to Klein-Nishina suppression?
• RQ2 To what extent can these escaping photons produce muon pairs via interaction with the CMB?
• RQ3 What fraction of UHECR energy can be converted into detectable EeV neutrinos through this mechanism?
• RQ4 Can the resulting neutrinos be associated in time and direction with the original source, even in the presence of intergalactic magnetic fields?
• RQ5 How sensitive are these neutrinos to testing quantum gravity-induced Lorentz violation through time-delay measurements relative to GRB photons?

Key findings

• The fraction of photon energy converted to muon pairs via CMB interactions is approximately 3–10%, with a mean free path of ~10^27 cm for muon pair production at ~10^20 eV.
• The expected neutrino flux from muon decay reaches ~2% of the Waxman-Bahcall bound, significantly higher than the suppressed flux from internal pion decay.
• The characteristic neutrino energy at Earth is ~3×10^17 eV for sources at redshift z=1, with a flux strongly suppressed below this energy.
• Neutrino flavor ratios at Earth are predicted to be 0.4:0.3:0.3 (ν_e:ν_μ:ν_τ), differing from the 1:1:1 ratio expected from pion decay due to oscillations.
• The time delay between GRB photons and EeV neutrinos is expected to be less than 1 ms for intergalactic magnetic fields <1 nG, enabling precise tests of Lorentz invariance violation.
• A single EeV neutrino detected years after a GRB would still imply association with the burst, allowing high-precision time-delay measurements for quantum gravity constraints.