It's a non-normalized F-distribution.
The F-distribution (on rare occasions called the Beta distribution of the second kind) is usually defined as that of the quotient $ \frac{\sum_{i=1}^n X_i^2/n}{\sum_{i=1}^m Y_i^2/m} $ where $n$ and $m$ are called the numbers of degrees of freedom in the numerator and the denominator, and the $X$s and $Y$s are independent and distributed as $\mathcal{N}(0,1)$.
"Non-normalized" means only that the divisions by $n$ and $m$ are not done. It just re-scales the thing.
There is an immense literature on these, and they are introduced in any statistics textbook that discusses ANOVA.