Off-axis vortex scattering of electron-positron annihilation into a photon pair

TL;DR

This work addresses off-axis vortex scattering in the fundamental QED process $e^-e^+ \to \gamma\gamma$ by developing a formalism that uses a Bessel-Gaussian wave packet for the initial electron and Bessel vortex states for the final photons. The triple-vortex amplitude is expressed in terms of the plane-wave amplitude ${\cal A}_{\mathrm{pw}}$ and momentum-conservation constraints are systematically incorporated, yielding a differential cross section $d^4\sigma$ regularized against the non-normalizability of a pure Bessel state. Numerical studies at $E \approx 1~\textrm{MeV}$ reveal strong dependencies of the cross sections and photon-cone distributions on the scattering angle $\alpha$ and the orbital angular momenta $m$ and $m_a$, with orbital angular momentum not conserved off-axis in contrast to on-axis scattering. These results provide a framework and diagnostic patterns for detecting vortex electrons and exploring off-axis vortex QED dynamics in high-energy processes.

Abstract

The off-axis triple-vortex scattering process of $e^-e^+\toγγ$ is studied theoretically, in which the positron is in a plane-wave state and the electron and photons are in vortex states. We develop a theoretical formalism for the process, which allows us to study the effects of various vortex parameters and scattering angle. We adopt a Bessel-Gaussian type wave packet for the initial vortex electron for the purpose of normalization. Numerical calculations are performed for an electron and a positron with a moderate energy around $1~\textrm{MeV}$. Our results demonstrate strong impacts of the scattering angle and the topological charges on the cross section and distributions in the energy and cone angles of the vortex photons. This could provide insight into off-axis vortex scattering and also a possible approach to distinguishing and detecting vortex electrons by off-axis vortex scattering.

Figures (8)

• Figure 1: Scattering geometry.
• Figure 2: Comparison of $R_\sigma,~R_S$ variation in $m_1=m_2$ at fixed $\theta=\pi/6$ and $m=3/2,~21/2$.
• Figure 3: $\sigma_{\gamma}\textrm{ (b/rad)}$ is shown as a function of $m_1=m_2$ in panel (a) with fixed $\theta=\pi/6$, $m=3/2,~21/2$, and $\alpha=\pi/6,~2\pi/3$, and as a function of $\theta$ in panel (b) with fixed $m=21/2$, $m_1=m_2=10$, and $\alpha=\pi/6$.
• Figure 4: Differential cross section $G$ ($\textrm{b}/(\textrm{MeV }\textrm{rad}^2)$) in the plane $\theta_1=\theta_2=\theta_\gamma$ is shown as a density distribution in $\omega_1$ and $\theta_\gamma$. In all panels $m_{1}=m_{2}=1$ and $\theta=\pi/6$, and in panel (a,b,c,d), $(m,\alpha)=(21/2,\pi/6),~(21/2,2\pi/3),~(3/2,\pi/6),~(3/2,2\pi/3)$ respectively.
• Figure 5: Same as \ref{['2d_m1']} except that $m_1=m_2=10$.