Photon emission from weakly magnetized neutral pions

TL;DR

This paper derives an explicit expression for photon emission from neutral pions in weak magnetic fields using a hadronic approach, revealing modest suppression of decay rates and anisotropic emission patterns that could be observed in heavy-ion collisions.

Contribution

The work provides a hadronic-level calculation of photon emission from neutral pions in magnetic fields, offering an alternative to quark-based models and analyzing decay rate modifications and anisotropy.

Findings

Magnetic field slightly suppresses the pion decay rate.

Photon emission exhibits angular anisotropy in magnetic fields.

Modification of decay rate scales as |eB|^2/m_P^4.

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 $\pi^0$-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 $|eB|\simeq m_\pi^2$. 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 $\pi^0 \to \gamma\gamma$ rate is parametrically small, scaling as $|eB|^2/m_P^4$, where $m_P$ is the proton mass. Nevertheless, under favorable conditions, the resulting angular anisotropy could lead to observable signatures in heavy-ion collisions.