数値的方法に拠る量子色力学の研究

利用数值方法研究量子色动力学

基本信息

批准号：
03640270
负责人：
FUKUGITA Masataka
金额：
$ 1.41万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1992
项目状态：
已结题

项目摘要

Spectroscopic problems of lattice QCD is studied by numerical methods. The main results are(1) Unexpectedly large finite-size effects are found in hadron spectrum calculations for full QCD. This means that a proper control is necessary over the finite lattice effect to calculate the hadron mass with an accuracy of a few %. We also found that this finite-size effect is described by a power law rather than exponential as expected in field-theoretical considerations. We ascribe its origin to a real-size of hadrons confined in a finite box.(2) The validity is examined for the perturbative prescription in extracting weak matrix elements from lattice calculations, which has been often cast a doublet. We found, at least for the case of the pion-decay matrix element and the K^0 - K^0 mixing matrix element, that the prescription is justifiable.(3) The choice of hadron operators in lattice calculation of hadron spectrum is not unique, and there is a suspicion that this may cause uncertainties in calculated hadron masses. A study on this problem is made in a systematic way and it was shown that there indeed is a significant uncertainty associated with the choice of hadron operators. We have just clarified the presence of the problem. The solution is yet to be found.(4) A new technique is developed which makes it possible to calculate the pion scattering length for all possible pipi channels. (In the past only the I = 2 amplitude was calculated).

采用数值方法研究了晶格QCD的光谱问题。主要结果是(1)在全QCD的强子谱计算中发现了意想不到的大的有限尺寸效应。这意味着需要对有限晶格效应进行适当的控制，才能以百分之几的精度计算强子质量。我们还发现，这种有限尺寸效应是由幂律描述的，而不是场论考虑中预期的指数描述。我们将其起源归因于限制在有限盒子中的实际大小的强子。（2）检查了从晶格计算中提取弱矩阵元素的微扰规定的有效性，该计算经常被铸造成双峰。我们发现，至少对于π衰变矩阵元和K^0 - K^0混合矩阵元的情况，该规定是合理的。(3)强子谱格子计算中强子算子的选择不合理。独特的，并且有人怀疑这可能会导致计算的强子质量的不确定性。对这个问题进行了系统的研究，结果表明，强子算子的选择确实存在很大的不确定性。我们刚刚澄清了问题的存在。目前尚未找到解决方案。(4) 开发了一种新技术，可以计算所有可能的 pipi 通道的 pion 散射长度。（过去仅计算 I = 2 幅度）。