Lattice QCD studies on baryon interactions from Lüscher's finite volume method and HAL QCD method

Abstract

A comparative study between the Lüscher's finite volume method and the time-dependent HAL QCD method is given for the $\Xi \Xi$(${}^1{\mathrm{S}}_0$) interaction as an illustrative example. By employing the smeared source and the wall source for the interpolating operators, we show that the effective energy shifts $\Delta E_{\mathrm{eff}}(t)$ in Lüscher's method do not agree between different sources, yet both exhibit fake plateaux. On the other hand, the interaction kernels $V(\vec{r})$ obtained from the two sources in the HAL QCD method agree with each other already for modest values of $t$. We show that the energy eigenvalues $\Delta E(L)$ in finite lattice volumes ($L^3$) calculated by $V(\vec{r})$ indicate that there is no bound state in the $\Xi \Xi {(}^1{\mathrm{S}}_0)$ channel at $m_{\pi }=0.51$ GeV in 2+1 flavor QCD.

Comments: 7 pages, 5 figures, and 2 tables, Proceedings for the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe, Japan. Minor corrections