Tree problems

My neighbor recently hired a tree company to cut back trees on his property. They also severely cut back three of my large trees at the property line. The branches that were over my neighbors yard I understand, but they ended up cutting well over the property line and 2 large maples are left with branches just on my side.
The question is can the tree company and my neighbor cut my trees without my permission. I'm afraid that if two trees are weakened or die because of this severe trimming ,I will need to have them totally cut down. These were healthy trees .

[able1]

Based on what you say here, you could file suit against both of them --the company and the neighbor--(or at least threaten to do so) in small claims court or in regular court; filing in small claims court is easier and requires no attorney...you could try to collect all of the costs and damages that you suffered due to their behavior...