Diquark properties from full QCD lattice simulations

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.