The invisible renormalon

We study the structure of renormalons in the Heavy Quark Effective Theory, by expanding the heavy quark propagator in powers of 1/m_Q. We demonstrate that the way in which renormalons appear depends on the regularisation scheme used to define the effective theory. In order to investigate the relation between ultraviolet renormalons and power divergences of matrix elements of higher-dimensional operators in the heavy quark expansion, we perform calculations in dimensional regularisation and in three different cut-off regularisation schemes. In the case of the kinetic energy operator, we find that the leading ultraviolet renormalon which corresponds to a quadratic divergence, is absent in all but one (the lattice) regularisation scheme. The nature of this ``invisible renormalon'' remains unclear

An ``Improved" Lattice Study of Semi-leptonic Decays of D-Mesons

We present results of a lattice computation of the matrix elements of the vector and axial-vector currents which are relevant for the semi-leptonic decays $D \rightarrow K$ and $D \rightarrow K^*$. The computations are performed in the quenched approximation to lattice QCD on a $24^3 \times 48$ lattice at $\beta=6.2$, using an $O(a)$-improved fermionic action. In the limit of zero lepton masses the semi-leptonic decays $D \rightarrow K$ and $D \rightarrow K^*$ are described by four form factors: $f^{+}_K,V,A_1$ and $A_2$, which are functions of $q^2$, where $q^{\mu}$ is the four-momentum transferred in the process. Our results for these form factors at $q^2=0$ are: f^+_K(0)=0.67 \er{7}{8} , V(0)=1.01 \err{30}{13} , A_1(0)=0.70 \err{7}{10} , A_2(0)=0.66 \err{10}{15} , which are consistent with the most recent experimental world average values. We have also determined the $q^2$ dependence of the form factors, which we find to be reasonably well described by a simple pole-dominance model. Results for other form factors, including those relevant to the decays \dpi and \drho, are also given.Comment: 41 pages, uuencoded compressed postscript file containing 14 figures, LaTeX, Edinburgh Preprint 94/546 and Southampton Preprint SHEP 93/94-3

Applications of perturbative QCD to hard scattering processes

The author presents a survey of the ideas and techniques necessary to apply QCD to hard scattering processes. A brief review of light-cone techniques was given and corrections to asymptotic predictions of QCD for deep inelastic structure functions were discussed. Asymptotic predictions were also made for general hard scattering processes. The next-to-reading order log approximation was discussed. (89 refs)