Rational concordance of double twist knots

Double twist knots $K_{m, n}$ are known to be rationally slice if $mn = 0$, $n = -m\pm 1$, or $n = -m$. In this paper, we prove the converse. It is done by showing that infinitely many prime power-fold cyclic branched covers of the other cases do not bound a rational ball. Our rational ball obstruction is based on Donaldson's diagonalization theorem.