  Let $d\geq 4$ and let $u$ be a global solution to the focusing mass-critical
nonlinear Schr\"odinger equation $iu_t+\Delta u=-|u|^{\frac 4d}u$ with
spherically symmetric $H_x^1$ initial data and mass equal to that of the ground
state $Q$. We prove that if $u$ does not scatter then, up to phase rotation and
scaling, $u$ is the solitary wave $e^{it}Q$. Combining this result with that of
Merle \cite{merle2}, we obtain that in dimensions $d\geq 4$, the only
spherically symmetric minimal-mass blowup solutions are, up to phase rotation
and scaling, the pseudo-conformal ground state and the solitary wave.
