Commercial Fixed Wing
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Communication Breakdown; Confusion
ATC Issue All Types; Deviation - Altitude Undershoot; Deviation - Altitude Crossing Restriction Not Met; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Human Factors; Procedure
I was the PM on Aircraft X from ZZZ1 to ZZZ.  Our arrival was as planned per the PDC.  As we approached ZZZZZ (the transition fix); the ATC controller said; 'Aircraft X; cleared the ZZZZZX   arrival for the ZZZZZY VISUAL RWY XX'.  I acknowledged ATC and then asked the CA if he heard 'descend via'?  The CA and I agreed that we did not hear 'descend via' and therefore stayed at FL310 until I could query the Controller.  We had 27.6 NM to the next altitude constraint (approximately four minutes) and the radios were busy with constant chatter.  I was finally able to query the Controller approximately 7 NM prior to ZZZZZ2 with an altitude constraint of FL280-240.  ATC said that he expected us to have descended; then cleared us direct to ZZZZZ3 to resume the arrival with published altitudes and speeds. The CA started to descend; there were no further questions or issues with the clearance; and we had an uneventful arrival/approach/landing.  The Controller was not mad; nor did he ask us to call him after we landed.  Lastly; there were no traffic concerns; nor was safety an issue.Both the CA and I had not flown in two or more months so we were being extra vigilant with a heightened awareness.  A definite causal factor was the busy radio which made it hard to communicate with ATC in a timely fashion before losing a 3:1 descent profile and causing a more aggressive descent to meet the published altitudes on the ZZZZZX RNAV Arrival.  More importantly; the #1 causal factor was the lack of proper vertical clearance verbiage by ATC.  Both the CA and I expected to hear; 'descend via' but that was not stated.  There was no clearance to descend out of FL310; only 'cleared the ZZZZZX ARRIVAL'.  After reviewing the FOM Section XXXX; we executed correctly.FOM Section XXXX Standard Terminal Arrival Route (STAR) ClearancesSource: AIM & INFO 12003 An ATC arrival clearance using the phraseology 'Cleared arrival <name>.' (i.e.;'Cleared PULLMAN FOUR ARRIVAL.') authorizes a pilot to navigate laterally on theSTAR; however; the pilot must maintain the last assigned altitude until receivingauthorization to descend.See also paragraph XXXY Climb/Descend Via for additional guidance on STARclearances.I would say that if there are ATC sectors that have trends of reports filed for STARs related to issues meeting vertical clearances due to the clearance verbiage by the ATC controllers; then I'd recommend a message go out to ATC controllers for review of the proper clearance verbiage so as not to confuse/question pilots.  This could also be a quarterly review for both pilots and controllers.
Air carrier Captain reported being unsure if they were supposed to descend on the approach clearance received from ATC resulting in an altitude deviation.