Answer: This is unfortunate. Depending on how old the tree is they might regrow into branches, or they may take the form of watersprouts. Usually over time these trees do lose their lower branches naturally, so in the long run it is somewhat of a moot point. I would be more concerned about the numerous cuts along the trunk which become an invitation to pest and disease. Be sure to keep the tree well watered next summer to try to make sure it stays healthy until the wounds heal over. If this is a good sized or specimen tree in your landscape I would suggest you consult on site with a professionally trained and certified arborist as well. Keep in mind also that birches have a dense and thirsty root system that tends to stay near the surface making it very difficult to plant under them. You might be able to use an undemanding groundcover such as Vinca minor but this will not help much with the view problem. I'm really sorry.
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