http://health.discovery.com/encyclopedias/2966.html
- quick google with term "local anesthesia"
- note the "inability to feel pain" in first sentence

When you say "physical pain", I assume you refer to pain felt after something physical is done to the body. That would be physical pain, as opposed to other pain (mental, spiritual, social health and whatnot). However, humans can cause pain to not be felt even though the physical cause is there (think surgery and anesthesia, getting cut up but no pain). Of course, [I don't believe that] we have ways of causing physical pain without a physical cause (opposite of anesthesia), but in the make anime world of Naruto, Itachi can, with his technique. It is debatable, however, if the pain from the technique is mental or physical. However, if a mind feels there is physical pain, there are certain measures it takes, which could then lead to actual pain, because the measures are being taken when nothing is wrong.

edit: random grammar mistakes