GZK cutoff: E_th = (m_Δ² − m_p²)/(4·E_CMB) ≈ 5·10¹⁹ eV via p + γ_CMB → Δ⁺ → pπ⁰

Layer 1 — Physicsin the astroparticle-physics subtree

Greisen-Zatsepin-Kuzmin (1966) cutoff: ultra-high-energy protons travelling through the CMB photon bath (T = 2.725 K, typical ω ≈ 6·10⁻⁴ eV) undergo photopion production p + γ_CMB → Δ⁺(1232) → pπ⁰ (or nπ⁺) above threshold energy E_th =…

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Cosmic microwave background

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