The $\Lambda _Q\Lambda _Q$ Potential

D. Arndt (graduate student), S.R. Beane and M.J. Savage

The $\Lambda _Q\Lambda _Q$ interaction provides a useful theoretical laboratory to learn about nuclear physics from lattice QCD. As one-pion exchange does not contribute to the potential, the long-distance behavior is dominated by the same physics that provides the intermediate-range attraction between two nucleons. In the heavy-quark limit the $\Lambda _Q\Lambda _Q$ force can be unambiguously measured on the lattice. We computed the two-pion box and crossed-box diagrams that provide the leading long-distance contributions to the $\Lambda _Q\Lambda _Q$ potential in QCD and in partially-quenched QCD.

Figure 2: The left panel shows the potential between two $\Lambda _Q$'s in partially-quenched QCD, $V^{\rm PQ}(r)$, evaluated at $r=1 {\rm fm}$ as a function of the meson mass $m_{SV}$, while the right panels shows $V^{\rm PQ}(r)$ evaluated at $r=2 {\rm fm}$. The vertical axis is in units of ${\rm MeV}$. When $m_{SV}=m_\pi$ the value of $V^{\rm PQ}(r)$ is equal to $V^{\rm QCD}(r)$.