数値的方法に拠る量子色力学の研究

点击翻译按钮获取中文摘要

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).