A distracted air carrier Captain reported giving ZLA an incomplete clearance readback to SLC and flying the PDC arrival. After a track deviation; ZLC correct the arrival and crew acknowledged an error.

Narrative

While in cruise to SLC; ZLA Center gave us a clearance to proceed 'direct Bryce Canyon and the [xxx] arrival to Salt Lake.' As pilot monitoring; I was operating the radios and read back to ATC; 'Ok; cleared via direct Bryce Canyon and the arrival to Salt Lake.' I was unsure that ATC had actually stated the name of the arrival or not; so I had just figured they meant to clear us direct to BCE (Bryce Canyon) and then proceed with the arrival we received in our flight plan PDC; which was the DELTA5. ATC did not respond to my readback with any clarification. I programmed the FMS for us to proceed direct to BCE; which gave us a very minor course 'cut'; the pilot flying verified it; and I executed the mod. About 1/2 way between BCE and DTA (Delta) we were called by ATC (now ZLC Center); 'XXX are you flying the QUENN arrival into SLC.' I responded; 'Negative; we are on the DELTA arrival.' ATC corrected us; 'Uh; you were supposed to do the QUENN arrival after Bryce Canyon.' I apologized for the error; and ATC gave us a course correction to join the QUENN arrival. The remainder of the flight was uneventful. The event/nav error occurred because I did not verify the ATC clearance appropriately when I thought I may have mis-heard it. Contributing to this error; we had a jumpseater and we were conversing when ZLA's re-route clearance had been given. Furthermore; when I did not readback the re-route properly to ZLA; the controller did not correct me.