Do you mean his right carotid (sp?) artery? That would be on the right side of his neck. You only have one aorta, not a right & left. (unless I am gravely mistaken)
Anyway, high fat diets can cause this because it increased the bad cholesterol levels. If this is the problem, then many times changes in diet & exercise can greatly reduce the risks. Also- oatmeal is a HUGE help in lowering cholesterol.
There are medicinal treatments that can be used and I'm sure the vascular surgeon will be able to help with that. He may use a dopler to help determine how occluded the artery is, or he may recommend doing some sort of x-ray (like a flouroscopy procedure) with contrast and maybe a balloon catheter to thin it out/remove it.
If it turns out that your husband is a surgical candidate, then the vascular surgeon can go over all that with you. Carotid Endarterectomies have come a very long way, and have proven to help many people.
Best wishes to you and your husband!