Tensioner pulley keeps coming loose

So, the tensioner pulley decided to leave us on Christmas Eve. It took with it the hardware holding it in place.

I bought a new pulley, also a couple M10-1.50 Nuts, and went home to find the M10-1.50 nuts did not thread onto the stud. I went back and got M10-1.25 nuts and, while I seem to have gotten one on there, it doesn't seem to be correct. The tension on the belt has loosened back up, so it appears I am still not repaired fully.

What size nut and thread do I need for this? Is there a sleeve or bushing needed (as I obviously am not getting pressure from the nut to hold the pulley in place)? Do I need to wholesale replace the tensioner assembly? (Is that possible?)

Thank you for your time!