B737-800
Air Traffic Control Developmental
Troubleshooting; Workload; Confusion; Distraction; Training / Qualification
ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Separated Traffic; Air Traffic Control Provided Assistance; Air Traffic Control Issued New Clearance
Weather; Procedure
I was working the D-side of two combined sectors.  The traffic volume wasn't too bad and then it increased significantly due to an increase in ZZZ arrivals and overflights.  We probably had about 25 or more aircraft on frequency.  Ride conditions were mainly scattered light chop with areas of moderate; so there were a lot of questions about the rides from pilots.  I became focused on a conflict of three airplanes tied up at FL340 pretty close to our boundary.  While fixing that situation I believe I wasn't paying enough attention to the rest of the sector.  The operational error occurred about 3-5 minutes before the conflict I was taking care of would have occurred had I not fixed it.  I had no alerts on the EDST of the two airplanes that we had the operational error with.  Aircraft Y was an overflight at FL310 going across our arrival stream.  Aircraft X was going to ZZZ at FL320 on the [specified] arrival.  The Radar Controller gave Aircraft X a pilots discretion descent to FL270 and handed him off to the sector below.  [The Controller] then shipped Aircraft X to the next sector.  We both missed the overflight traffic; Aircraft Y at FL310.  The error occurred about 6 minutes from this point.  Again I believe I was in the process of fixing the other three way tie situation when the aircraft was descended and shipped.  Aircraft X started his descent when he was about 2.5-3 miles from Aircraft Y.  There was no conflict alert until the two airplanes were already within 5 miles of one another.  At this point we were not talking to either of the airplanes so the next Sector Controller tried to fix the situation but it was already too late to save it.Not to say that changing RNAV STARS was a big factor in this occurrence but it would be nice if we were not constantly changing ZZZ arrivals to different STARS because of the airport configuration always changing.  I was on flight deck training and that was the biggest complaint from the pilots.  They all said ZZZ Airport has too many STARS and it needs to be fixed.  In busy situations it takes too much time to have to issue new routing for the pilots.  As for me; being a Developmental just beginning my Radar Sectors; I need to pick up my scan and not get tunnel vision.
ZDV ARTCC Controller stated sector was busy with traffic and receiving ride reports.  While doing other duties D-Side Controller does not hear Radar Controller descend arrival into enroute traffic and loses separation.