I've seen that type of browning before on LPS. Normally it's because much of the water has been expelled from the head of the LPS due to some aggravation from other tank species or just not happy. If nothing is done to correct this normally the exoskeleton will start to come through the injured part and be exposed and soon die. I would suggest doing one of two things, one is move entire piece to new location. Other would be break off the injured branch and place somewhere else relative to water column that it's currently in. Just by the look of the pic, it could be direct water flow passing directly into that head not sure, can't tell too much from the pic.