The higher your PSA, the more likely it is to show up on a PET scan.
Rough guidelines for men without a prostate are:
Newest PSMA PET scans need at least 0.2 to have a reasonable chance of finding something.
Most PSMA PET scans need at least 0.5 to have a reasonable chance of finding something.
Choline PET scans (most common on NHS) need at least 2 to have a reasonable chance of finding something.
These are not absolute. You might be lucky and find something at much lower PSA, but equally, you might be unlucky and not find anything even with a higher PSA.
If you have a prostate, which will be producing PSA anyway from the non-cancerous parts, I don't know what thresholds they use.