Photon emission from weakly magnetized neutral pions

TL;DR

This work analyzes how a weak background magnetic field alters the anomalous decay $\pi^0 \rightarrow \gamma\gamma$ using a hadronic description based on the proton triangle with a Yukawa $\pi^0$–proton coupling. A weak-field expansion shows the linear magnetic corrections cancel, and the leading effect scales as $|eB|^2/m_P^4$, introducing a small suppression of the total decay rate while also generating an anisotropy in the angular distribution of emitted photons that depends on the angle $\beta$ between the pion momentum and the field. In CM and SP limits, explicit expressions show the suppression is numerically tiny for realistic fields (e.g., $|eB|\sim m_\pi^2$ gives ~0.02%), but the anisotropy is enhanced when the pion travels perpendicular to $\mathbf{B}$. The findings offer a controlled framework for weak-field effects on anomalous decays and hint at possible observable directional photon correlations in heavy-ion collisions, with extensions to strong-field or medium-influenced regimes to be explored.

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 $π^0$-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 $|eB|\simeq m_π^2$. 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 $π^0 \to γγ$ 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.

Figures (3)

• Figure 1: Triangular one-loop Feynman diagrams contributing to the anomalous decay of the neutral pion into two photons.
• Figure 2: Field-strength dependence of the absolute value of the field-induced correction to the pion decay rate in a general frame. The different curves correspond to various pion momenta, ranging from $p_\pi = 0$ to $p_\pi = 5~\text{GeV}$. Results are shown for two fixed angles: $\beta=\pi/4$ (left) and $\beta=\pi/2$ (right).
• Figure 3: Absolute value of the field-induced correction to the pion decay rate in a general frame as a function of the angle between the pion momentum and the magnetic field. The different curves correspond to various pion momenta, ranging from $p_\pi = 0$ to $p_\pi = 5~\text{GeV}$. Results are shown for two fixed magnetic-field strengths: $|eB|=m_\pi^2/2$ (left) and $|eB|=2m_\pi^2$ (right).