Heavy Quark Physics and Lattice QCD

Precise knowledge onB meson decay properties plays an essential role in testing the unitarity of the CKM matrix [1,2]. The experimental status relevant to the unitarity test is now promising because experimental uncertainties are already very small or expected to be reduced well in the near future [3]. On the other hand, theoretical calculations relevant to the test are still not sufficiently accurate due to the non-perturbative effect of QCD. Lattice QCD is an ideal tool to deal with this effect and should be able to reduce the current theoretical uncertainties [4]. Apart from the asymmetric ee colliders, there are two important upcoming experiments for the unitarity test. The Tevatron Run II will produce a large number of and variety of b and chadrons, and their basic properties such as mass and lifetime will be precisely measured [5]. What is important for us is that once B s -B̄ 0 s mixing is observed the mass difference ∆MBs will be measured with a few percent accuracy. The width difference in the Bs meson system is also expected to be measured precisely. Another exciting experiment is the CLEO-c project [6]. There, charmed quarkonia, hybrid states and glueballs will be observed. In particular the leptonic and the semileptonic decays of D mesons are expected to be measured with a few percent level. Advancing lattice QCD calculations with a view to combining them with these precise experimental results is an urgent task in front of us. In this review, I will focus on new and updated calculations of hadron matrix elements. The current status and progress made in spectrum calculations and formulations are not covered, although they are very important and interesting. In particular, I will mainly discuss the lattice determination of the B-B̄ mixing amplitude and how to put a strong constraint on the poorly known CKM element |Vtd|. The other important quantities such as form factors of semi-leptonic decays will be mentioned briefly. Recently several suggestions to improve the limits on accuracy of present lattice calculations have been made in methodology. I will briefly introduce some of them before summarizing my point of view on the current status.