On your Payment layout:
Enter Find Mode---> clear the pause check box
Set Field [Payment_Disbursement::_fkDisbursementID ; "*" ] ---> finds all payment records that have a join record with a disbursementID
Omit Records----> changes this to an "omit" request that omits all records where the related join has a disbursementID
Set Error Capture [on]
Perform find 
But I see a problem here. You have set up a many to may relationship so there could be many records in your join table. This script will find all payment records that either have no join table records or that have at least one join table record with an empty disbursementID record.
That may or may not be what you actually want.
The above script uses methods found in this thread of scripted find examples: Scripted Find Examples
Thank you, and thank you for the link. Very helpful!
I do have this set up as a many-to-many, and the results you describe are exactly what I want. Thanks again.