  We study diquarks on the lattice in the background of a static quark, in a
gauge-invariant formalism with quark masses down to almost physical $m_\pi$. We
determine mass differences between diquark channels as well as diquark-quark
mass differences. The lightest and next-to-lightest diquarks have "good"
scalar, $\bar{3}_F$, $\bar{3}_c$, $J^P=0^+$, and "bad" axial vector, $6_F$,
$\bar{3}_c$, $J^P=1^+$, quantum numbers, and a bad-good mass difference for
$ud$ flavors, $198(4)~\rm{MeV}$, in excellent agreement with phenomenological
determinations. Quark-quark attraction is found only in the "good" diquark
channel. We extract a corresponding diquark size of $\sim 0.6~\rm{fm}$ and
perform a first exploration of the "good" diquark shape, which is shown to be
spherical. Our results provide quantitative support for modeling the low-lying
baryon spectrum using good light diquark effective degrees of freedom.
