Photon emission from weakly magnetized neutral pions

Abstract

Using a hadronic framework, we derive an explicit expression for photon production from neutral pions in a weak background magnetic field. Our calculation is built on the proton triangle diagram with an effective Yukawa $\ddot{I}{€}^0$-proton coupling, offering an alternative to quark-level descriptions that is advantageous when the magnetic length greatly exceeds the proton size. Corrections to the pion decay constant are computed up to second order in the magnetic-field strength, revealing that the field generally suppresses the decay rate. Quantitatively, however, the effect remains modest even for fields as strong as $|eB|\simeq m_{\ddot{I}}{€}^2$. The differential photon emission rate exhibits anisotropy, with the strongest suppression occurring when the pion momentum is perpendicular to the magnetic field. Overall, the modification of the $\ddot{I}{€}^0\to {\hat{I}}^3{\hat{I}}^3$ rate is parametrically small, scaling as $|eB{|}^2/m_P^4$, where $m_P$ is the proton mass. While the magnetic-field-induced anisotropy is conceptually interesting in principle, it is likely too small to be resolved in present heavy-ion measurements.

21 pages, 3 figures; v2: final version accepted for publication in Physical Review D, with several expanded discussions