SLC TWR CTLR WITNESSED NMAC WHEN ACFT ON FINAL EITHER FAILED TO CONTACT TWR OR APCH CTLR FAILED TO XFER ACFT IN SUFFICIENT TIME TO AVOID CONFLICT.

Narrative

I WAS WORKING LCL CTL E AND RWY 17 WAS MY RWY. I HAD CLRED SINGLE ENG CESSNA; TO LAND ON RWY 17 FROM THE DOWNWIND. IN THE MEANTIME I DID SEVERAL OTHER THINGS: MADE SEVERAL XMISSIONS; AND ENTERED A CODE OF A VFR HELI OFF OF SKYPARK ARPT INTO STARS (RADAR DATA). I WAS COORDINATING THE HELI WITH LCL CITY (VFR LCL CTLR) AND LOOKED UP TO CHK ON THE PROGRESS OF THE CESSNA. I COULD NOT SEE THE DATA TAG FOR THE ACFT AS IT WAS COVERED BY A RWY 16L IFR ARR ACFT AND SOME OTHER ACFT. IT TOOK ME A MOMENT TO REALIZE THAT THE OTHER ACFT WAS ON FINAL TO RWY 17. BECAUSE OF THE DATA TAG OVERLAP AND THE PROX OF THE ACFT; I DID NOT WANT TO CHANGE THE ALT OF EITHER THE CITATION OR THE CESSNA. I ISSUED AN IMMEDIATE L TURN; FLY EBOUND TO THE CESSNA AS THE CITATION FINALLY ATTEMPTED TO CHK IN ON MY FREQ. THE FREQ HAD NOT BEEN BUSY BEFORE THIS; THE CITATION HAD EITHER NOT BEEN SWITCHED BY APCH OR CHOSE NOT TO CALL UNTIL HE WAS 1 - 1 1/2 MI FINAL AT TWICE THE SPD OF THE CESSNA WHO WAS ABOUT A 1 MI FINAL. BY THE TIME I COULD SEE THE CALL SIGN OF THE CITATION AND CLR HIM TO LAND; HE WAS OVER THE THRESHOLD. THE CESSNA HAD TURNED; AS INSTRUCTED; AND I BROUGHT HIM BACK AROUND TO LAND; AND APOLOGIZED. I DO NOT KNOW HOW CLOSE THEY GOT. I HAD BEEN LOOKING THROUGH MY BINOCULARS EARLIER AS IT WAS HAZY AND THE ACFT WERE HARD TO SEE. ANOTHER CTLR SAID THAT THE CITATION HAD FLOWN A NONSTANDARD PATTERN FROM ABOUT THE FAF OF THE W RWY TO THE NUMBERS OF RWY 17. HE WAS TWICE THE SPD OF THE CESSNA AND NOT TALKING TO ME. I TOLD THE SUPVR AND HE ASKED IF I LOST SEPARATION. I SAID THAT THEY DID NOT HIT BECAUSE OF THE DATA TAG OVERLAP. I DO NOT KNOW HOW CLOSE THEY GOT.