@nprofile1q... - excellent detective work: thanks very much!
They are looking at something like
$$\sqrt{x^2 + a^2 m^2}$$
and saying that in the limit ๐โ+โ it becomes close to ๐๐. Sorry, no: it becomes close to ๐|๐| if we choose the positive square root.
This doesn't matter for a positive mass ๐. But then they take ๐ to be negative. ๐