Followup: Looking at this more, you are correct about the upper v. lower bound, and given the high energy levels in the paper, one expects it to be so close to the speed of light (whether the mass is real or imaginary) that the SN 1987A data isn't relevant.

It's square electron-volts, since you're measuring square of mass.

Thanks. Corrected.

Wouldn't the same logic say that if they were even a tiny bit slower than the speed of light they should have arrived much later? It gives an upper bound on the magnitude of the mass. It's the same upper bound regardless of if the mass is real or imaginary.

I'm not sure completely. My impression is that there's a lack of symmetry here but it isn't clear to me where it arises.

Second, there's reason to believe that tachyons if they existed would emit Cherenkov-like radiation.

How could they emit light? They have no electric charge.

Hence the term "Cherenkov-like". The Glashow paper shows a mechanism where something very similar to Cherenkov radition occurs with tachyons even without electric charge.