You should also check your "System Preferences" -> "Users" -> "Login Items" and look at what exactly caused the call to "HP Product Research".
You should also view the "Activity Monitor" and view the specifics of what other "Open Files and Ports" are involved with the process. Be careful ... it maybe isn't smart even to remove other files in the "/Library/Printers/hp/Frameworks/" directory other then the .app?
its also very helpful to search your "console" and system.log file for "hp" just to see whats going on before removal... (just to see what is going on) (dont remove anything outside of "/Library/Printers/hp" and do a reboot just to make sure everything is "safe" after? Here is a picture of what a console "system.log" looks like for "HP" (special note: these "errors" are most likely caused by closing the process down while its trying to startup again...
It can be interesting to save all the details and "sample" the "HP Product Research" process and see the full "call graph" of the process?