A Corporate jet descending on a STAR into SLC experienced a TCAS RA. ATC indicated that no radar target or alarm was observed in the ATC system. ATC reported that a hang-gliding competition was in progress near event location.

Narrative

While on a descent through 14;000 for 11;000 to SLC in smooth air on the STAR from the South East; we were approaching a turn point just east of the Provo airport we received and complied with an RA. At the time; the aircraft was in a descent at approximately 2000 FPM down; and I had initiated a speed reduction; anticipating a descent below 10;000 IAW the arrival. I was very much outside the aircraft; as the PNF was busy with ATC and completing a runway change. I could see the Provo airport ahead of us; and was especially looking for VFR traffic in that direction. There were several TCAS targets showing; and we spotted the traffic we were likely to follow easily in the nice weather. At this point; we got a TCAS CLIMB! CLIMB! message; with the green arc showing 1500 FPM UP! I immediately disconnected the autopilot and initiated a rapid pitch up; as I had been trained to do. Once I had initiated that; I managed to glance at the TCAS display. It now showed a target; which had not been there a moment before. The target was showing -400 FT; and slightly ahead and left of the airplane (in the direction of Provo). So close; it was within the angle made by the Aircraft Reference on the display. The pilot not flying gave me good support during the event; looking for the threat; notifying ATC as well as calling out altitude of the threat. About the time I established the target climb and had gone about 200 FT up; the target vanished from the display. No 'Clear of Conflict' message was heard; it simply vanished. At that point I leveled the aircraft; and returned toward the assigned altitude and back onto the arrival. ATC; a person who sounded like a supervisor; asked us several questions about the event during the remainder of the arrival. I gathered their side showed no conflict; and they did not have any aircraft in the vicinity. They mentioned there was a hang-gliding competition going on in Provo; and speculated that it could have been a hang-glider. A scary thought.