Pion Production via Proton Synchrotron Radiation in Strong Magnetic Fields in Relativistic Field Theory: Scaling Relations and Angular Distributions

We study pion production by proton synchrotron radiation in the presence of a strong magnetic field when the Landau numbers of the initial and final protons are $n_{i,f} \sim 10^4 - 10^5$. We find in our relativistic field theory calculations that the pion decay width depends only on the field strength parameter which previously was only conjectured based upon semi-classical arguments. Moreover, we also find new results that the decay width satisfies a robust scaling relation, and that the polar angular distribution of emitted pion momenta is very narrow and can be easily obtained. This scaling implies that one can infer the decay width in more realistic magnetic fields of $10^{15}$G, where $n_{i,f} \sim 10^{12} - 10^{13}$, from the results for $n_{i,f} \sim 10^4 - 10^5$. The resultant pion intensity and angular distributions for realistic magnetic field strengths are presented and their physical implications discussed.