To give perspective, I have completely supported this war all along.
BUT, if these looters are truly unarmed then killing them is wrong. There isn't anyway to justify it. I understand that this is a country that is in a state of chaos, but if these looters are not threatening the lives of the soldiers, or other people, killing them is the wrong move. Simply arrest them and place them in a jail. Let them sit there and rot until a government is set up and trials can be held. Stealing is wrong and should be punished. Killing a person who is not intending to inflict harm on anyone is also wrong and should be punished.
On the other hand, we may not be hearing the full story. The NYTimes has a decidely left slant to it. These looters may be armed and ready to fight it out. If that is the case, shoot to kill.