The wide degeneracy affects binary events where the planet lies at a wide separation from it’s host star, and the source’s relative trajectory crosses the planetary caustic. It was described by Sumi et al.(2016), to explain event MOA-2013-BLG-605Lb.

Lens plane plots demonstrating the wide degeneracy
Lens plane plots demonstrating the wide degeneracy. The red diamond indicates the planetary caustic and the blue line represents the source's relative trajectory. Black filled circles show the positions of the host star and planet, and the blue circles show the angular size of the source before crossing the caustic. Green curves show the critical curves. [Sumi et al.(2016), Fig.3]. The four plots show parallax models depending on alternate signs of the u0 parameter, and the wide degeneracy.

This event exhibited two degeneracies, the ecliptic degeneracy (indicated by the first model suffix) and the wide degeneracy (indicated by the second), resulting in a quartet of models resulting in similar lightcurves. The wide degeneracy is a consequence of the symmetry of the diamond-shaped central caustic in a planetary event.

Taking parallax into account results in a curved source relative trajectory when plotted in the lens plane, meaning that \(\alpha\) varies as a function of time. As a result, the value of \(\alpha\) at the \(t_{0}\) (dominated by the primary mass lens) is not the same as the value of \(\alpha\) at the time of caustic crossing.

In the case of the event MOA-2013-BLG-605Lb, the source trajectory can curve above or below the planet in the lens plane and still create the same lightcurve.