Research in lattice QCD via large scale numerical simulations

格点规范理论已有几个研究成果。(A)在3种不同的晶格间距下，用2个轻动力学夸克进行了格子QCD模拟，以求取物理能观的连续极限。研究发现，在连续介质极限下的强子谱，如介子质量，比在忽略动力学夸克效应的猝灭QCD中更接近相应的实验值。然后我们用2+1个动力学夸克开始了格子QCD模拟，其中2是简并的上下夸克，1是奇怪的夸克。再次对3种不同晶格间距的数据进行连续谱外推，我们证实了在连续谱极限中强子质量与实验值在误差范围内是一致的。(B)我们用在晶格上具有良好手征对称性的域壁夸克计算了K介子B参数等电弱矩阵元。我们发现，与其他非手征夸克相比，在猝灭的QCD中，B参数的标度破坏大大减小，从而得到了更可靠的B参数。此外，我们还用域壁夸克进行了2+1全QCD模拟，计算了强子谱和电弱矩阵元。(C)计算了确定Kobayashi-Maskawa矩阵所需的B介子的衰变常数和形状因子。为了估计轻动力学夸克对这些量的影响，在猝灭和全QCD模拟中都进行了计算。(D)在具有动力学夸克的QCD中，确定了在重离子碰撞实验中研究QCD相变所需的QCD状态方程。(E)我们提出了新的手征微扰理论，它包含了模拟中使用的晶格夸克场的晶格间距效应。我们通过将其预测与数值数据进行比较，验证了该公式的有效性。

There are several research results in lattice gauge theories. (a) Lattice QCD simulations with 2 light dynamical quarks have been performed at 3 different lattice spacings, in order to take the continuum limit of physical observables. It has been found that hadron spectra such as meson masses in the continuum limit become much closer to corresponding experimental values than in the quenched QCD where the dynamical quark effect is neglected. We then have started the lattice QCD simulation with 2+1 dynamical quarks, where 2 are degenerate up and down quarks and 1 is a strange quark. Again performing the continuum extrapolation form data at 3 different lattice spacings, we have confirmed that hadron masses in the continuum limit agree with experimental values within errors. (b) We have calculated electroweak matrix elements such as K meson B parameters using domain-wall quarks, which has a good chiral symmetry on the lattice. We found that the scaling violation of B parametr is much reduced in quenched QCD compared with other non-chiral quarks, so that a more reliable value of B parameter is obtained. Furthermore we have started 2+1 full QCD simulations with domain-wall quarks and calculated hadron spectra and electroweak matrix elements. (c) We have calculated decay constants and form factors of B mesons, needed to determine Kobayashi-Maskawa matrix. Calculations have been performed in both quenched and full QCD simulations, in order to estimate an effect of the light dynamical quark to these quantities. (d) The QCD equation of state, which is needed to investigate QCD phase transition at heavy ion collision experiments, has been determined in QCD with dynamical quarks. (e) We have proposed new formulation of chiral perturbation theory, which includes the lattice spacing effect of lattice quark field used in simulations. We have checked the validity of this formulation by comparing its predictions with numerical data.