While (correlation != causation) and all that, there really is a pretty extensive research base showing the benefits of music (and the arts in general) for students.
Education these days has been very, very focused on something called convergent thinking - basically, being able to choose the right answer from a short list. We've bought into the myth that all you need to succeed in STEM fields is convergent thinking, so that's what's taught.
The arts, by contrast, develop divergent thinking. Creativity, and the ability to generate multiple possibilities for the same problem. ("Should I lay out my artwork this way or that way? What if I try improvising a new melody in this part?")
In reality, we need both. Students who are "Masters of STEM" in K-12 often run into trouble when they realize the world isn't full of convenient lists from which we have to pick the right answer.
Think about the job of the guy who has to build a bridge over a river. He isn't handed a list of four bridges, conveniently labelled A through D, and has to pick between them. No, he first needs to generate a variety of possible bridges (divergent thinking) and then sort through them to find which one is most optimal for his constraints (convergent thinking). There's often not a clear "right answer" - one bridge might be 20% more expensive, but 2% less likely to collapse in a major earthquake.
So even if you don't use the arts directly, they can be very useful for cultivating a different mindset from what we're beating into our students these days.