Monday·July 25, 2016

[Submitted on 21 Jul 2016] (cross-list from hep-lat)

Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD

Takumi Iritani🇺🇸 · Takumi Doi🇯🇵 · Sinya Aoki🇯🇵 · Shinya Gongyo🇫🇷 · Tetsuo Hatsuda🇯🇵 · Yoichi Ikeda🇯🇵 · Takashi Inoue🇯🇵 · Noriyoshi Ishii🇯🇵 · Keiko Murano🇯🇵 · Hidekatsu Nemura🇯🇵 · Kenji Sasaki🇯🇵

Single state saturation of the temporal correlation function is a key condition to extract physical observables such as energies and matrix elements of hadrons from lattice QCD simulations. A method commonly employed to check the saturation is to seek for a plateau of the observables for large Euclidean time. Identifying the plateau in the cases having nearby states, however, is non-trivial and one may even be misled by a fake plateau. Such a situation takes place typically for the system with two or more baryons. In this study, we demonstrate explicitly the danger from a possible fake plateau in the temporal correlation functions mainly for two baryons ($\Xi \Xi$ and $NN$), and three and four baryons (${}^3\mathrm{He}$ and ${}^4\mathrm{He})$ as well, employing (2+1)-flavor lattice QCD at $m_{\pi }=0.51$ GeV on four lattice volumes with $L=$ 2.9, 3.6, 4.3 and 5.8 fm. Caution is given for drawing conclusion on the bound $NN$, $3N$ and $4N$ systems only based on the temporal correlation functions.