Evidence for Diquarks in Lattice QCD

Diquarks may play an important role in hadron spectroscopy, baryon decays, and color superconductivity. We investigate the existence of diquark correlations in lattice QCD by considering systematically all the lowest energy diquark channels in a color gauge-invariant setup. We measure mass differences between the various channels and show that the positive parity scalar diquark is the lightest. Quark-quark correlations inside the diquark are clearly seen in this channel, and yield a diquark size of $\mathcal{O}(1)\mathrm{fm}$.

Figure 1

Effective mass difference $\Delta m_{\mathrm{eff}}$ in the various diquark channels, at $\beta =6.0$ for our lightest quarks. The arrows (from left to right) indicate the time slice of the source, of the density insertions, and of the sink.

Figure 2

Mass difference between good and bad diquarks as a function of $m_{\pi }^4$ at $\beta =5.8$ (crosses), $\beta =6.0$ (open triangles), $\beta =6.2$ (solid circles), and unquenched result (solid square). The dashed lines are fits to Eq. (4).

Figure 3

$C_{\Gamma }(r/a=7.35,\theta )$ versus $\cos (\theta )$ for $\beta =6.2$ and $\kappa =0.1520$ for the good diquark (asterisks) and the other diquark channels using the same notation as in Fig. 1. Correlators for the bad diquark have been multiplied by two and for all negative-parity channels by ten.

Figure 4

Left: $C_{\Gamma }(r/a=5.1,\theta )/C_{{\gamma }_5}(r/a=5.1,0)$ versus $\cos (\theta )$. Right: $C_{\Gamma }(r=0.5\mathrm{fm},r_{ud})/C_{{\gamma }_5}(r=0.5\mathrm{fm},0)$ versus $r_{ud}$, for the good (asterisks) and bad (solid triangles) diquarks at the lightest pion for our three lattice spacings.

Figure 5

String formation for three quarks, where one quark has been taken to the distant left. As a function of the separation between the other two quarks, the static potential rises with an effective string tension ${\sigma }_{\mathrm{eff}}=\sigma (\sqrt{3}/2)$.