GlueX amplitude model

This repository was created during PWA working group meetings for GlueX at Jefferson Lab, July 31st to August 4th, 2023. Live notes for these discussions can be found here on HackMD. Each meeting was organised like a ‘hackathon’ and the results of these programming sessions can be found on compwa.github.io/gluex-amplitude.

The main target for the week was to implement a simple intensity function for two-pseudoscalar system with photo-production:

\[I(\Omega,\Phi) = 2\kappa\sum_{k}\left( (1-P_{\gamma})\left|\sum_{l,m}[l]_{m;k}^{(-)}\Re[Z_{l}^{m}(\Omega,\Phi)]\right|^2 +(1-P_{\gamma})\left|\sum_{l,m}[l]_{m;k}^{(+)}\Im[Z_{l}^{m}(\Omega,\Phi)]\right|^2 +(1+P_{\gamma})\left|\sum_{l,m}[l]_{m;k}^{(+)}\Re[Z_{l}^{m}(\Omega,\Phi)]\right|^2 +(1+P_{\gamma})\left|\sum_{l,m}[l]_{m;k}^{(-)}\Im[Z_{l}^{m}(\Omega,\Phi)]\right|^2 \right)\]

where \(Z_{l}^{m}(\Omega,\Phi)=Y_{l}^{m}(\Omega)e^{-i\Phi}\) is a phase-rotated spherical harmonic, \(\Omega\) is the solid angle, \(\Phi\) is the angle between the production and polarization planes, \(P_{\gamma}\) is the polarization magnitude, \([l]\) are the partial wave amplitudes, \(m\) is the associated m-projection, \(k\) refers to a spin flip (\(k=1\)) or non-flip (\(k=0\)) at the nucleon vertex, and \(\kappa\) is an overall phase space factor.

The details for this model have been worked out in 10.1103/PhysRevD.100.054017 (2019).

See the repository for installation instructions.

Table of contents

• Amplitude behavior investigation