What was found
AT REDUCTION OF RT ENGINE POWER DURING DESCENT FROM FL 45,000 FT IN CLEAR AND VISIBLE MOISTURE FREE CONDITION WHILE PASSING THROUGH FL 43,000 FT THE RT ENGINE BEGAN TO DECREASE N1 RPM UNTIL SHUTDOWN. ALL CORRESPONDING ENGINE RELATED INDICATIONS ADVISORY WARNING LIGHT CAME ON. THE PILOTS RAN THE IN-FLIGHT EMERGENCY CHECK LIST AND SECURED THE ENGINE. THE PILOT FOLLOW THE PROCEDURES FOR IN-FLIGHT ENGINE RESTART IN 3 OCCATIONS AND THE ENGINE DID NOT START. CONTACTED ENG MFG AND CONCLUDED THAT THE ENGINE FLAME OUT WS CAUSED BY THE FUEL DELIVERY UNIT.