Determination of the strength of vector interaction by Lattice QCD

Recently, Lattice QCD (LQCD) has become possible to provide the information of QCD phase diagram not only in the finite temperature(T) region but also in the finite quark chemical potential ($\mu_{q})$ region. For small $\mu _{q}$, say $\mu_{q}$ /T1, we can obtain the reliable physical quantities calculated by LQCD. However, it is still difficult to perform LQCD calculation in the large $\mu_{q}$ region, where physics such as neutron stars exists. On the other hand, the effective models allow us to analyze the large $\mu _{q}$ region. Especially, entanglement Polyakov-loop extended Nambu-Jona-Lasinio (EPNJL) model is useful one. But EPNJL model includes an ambiguity of the strength of vector interaction acting on quarks. This ambiguity should be eliminated by LQCD results. By using LQCD, quark number density is calculated in the $\mu_{q}$ /T1.2 region. Quark number density is sensitive to the strength of vector interaction, so we aim to determine the strength of vector interaction from the quark number density calculated by LQCD. In addition, we investigate whether our results are consistent with the observation of neutron stars with two solar mass.