My Edgeworthia chrysantha (Oriental Paper Bush) has branches without leaves (see pics).
The plant is 6-7 years old. It never had problems. It had never experience this.

Are those branches dead ? What could I do ? Cut them ? Wait more time ?

It's fairly common for this bush to lose limbs... It's an aggressive grower that won't miss them after they get removed.

I hate and despise edgeworthia... When you attempt gardening near this bush while it's flowering... You will see what I mean. The smell... Ew.

It's not uncommon for trees and shrubs to lose branches after a stressing summer and/or winter. If they haven't leafed out a few weeks after the initial growth, they propably won't anymore, so you're good to prune them.