Answer: Burning bushes have a tough constitution, so I would expect them to survive assuming they were well rooted. They grow slowly, so it make take some time to see regrowth and regain the lost size. They may grow back even thicker than they were originally.
In the meantime, keep the soil evenly moist like a wrung out sponge, and mulch around them with several inches of organic mulch. (Do not allow it to touch the plants.) You might also want to mark their locations to prevent them being accidently cut again. You could give them a top dressing of good quality compost as well.
Good luck with your burning bushes!
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