= Photopion threshold on a photon background
{title2=$E_{\rm th}=\frac{m_\pi c^2(2m_pc^2+m_\pi c^2)}{4\epsilon}$}
For an ultrarelativistic <proton> of <energy> $E$ colliding head-on with a <photon> of <energy> $\epsilon$, the invariant squared collision <energy> is approximately $(m_pc^2)^2+4E\epsilon$. Producing a final <proton> and <neutral pion> requires at least $(m_pc^2+m_\pi c^2)^2$. Thus $E_{\rm th}=m_\pi c^2(2m_pc^2+m_\pi c^2)/(4\epsilon)$. A broad isotropic <photon> background turns this threshold into an energy-loss feature depending on the <photon> distribution and source distance, not an absolute ceiling for all arriving <protons>.
Back to article page
