Database
[{_id:"t1",email:"abc@testmail.com",refId:["ref1","ref2","ref3","ref4","ref5"],deleted:false},{_id:"t2",email:"xyz@testmail.com",refId:["ref1","ref2","ref5","ref82"],deleted:false},{_id:"t3",email:"qwe@testmail.com",refId:["ref2","ref5","ref77"],deleted:false},{_id:4,email:"pou@nowhere.com",refId:["ref0"],deleted:false}]
Query
db.collection.aggregate([{"$match":{"email":{"$in":["abc@testmail.com","xyz@testmail.com","qwe@testmail.com"]},"deleted":false}},{$group:{_id:null,refId_arrays:{$push:"$refId"},first_array:{$first:"$refId"}}},{$project:{_id:0,common_refId:{$reduce:{input:"$refId_arrays",initialValue:"$first_array",in:{$setIntersection:["$$this","$$value"]}}}}}])