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According to the GADF definition (https://gamma-astro-data-formats.readthedocs.io/en/latest/general/coordinates.html#coords-fov), "FOV LON should increase with decreasing OTHER LON". As this is the coordinate system in which a background model has to be stored, it is mandatory to switch the sign of longitude angle when creating a background model.
In Gammapy, this is not solved consistent up to now (see: gammapy/gammapy#3510) for ALTAZ and RADEC alignment of the FoV coordinates. If it will be changed in Gammapy, it will also have to be changed in the creation of the background files.