Spectator Effects in Inclusive Decays of Beauty Hadrons

We evaluate the matrix elements of the four-quark operators which contribute to the lifetimes of $B$-mesons and the $\Lambda_b$-baryon. We find that the spectator effects are not responsible for the discrepancy between the theoretical prediction and experimental measurement of the ratio of lifetimes $\tau(\Lambda_b)/\tau(B)$.Comment: LATTICE98. 3 pages, no figure

An Exploratory Lattice Study of Spectator Effects in Inclusive Decays of the Lambda_b Baryon

A possible explanation of the apparent disrepency between the theoretical prediction and experimental measurement of the ratio of lifetimes $\tau(\Lambda_b)/\tau(B_d)$ is that ``spectator effects'', which appear at $O(1/m_b^3)$ in the heavy quark expansion, contribute significantly. We investigate this possibility by computing the corresponding operator matrix elements in a lattice simulation. We find that spectator effects are indeed significant, but do not appear to be sufficiently large to account for the full discrepency. We stress, however, that this is an exploratory study, and it is important to check our conclusions on a larger lattice and using a larger sample of gluon configurations.Comment: 12 pages, Latex. One correction: in the original version of the paper, in eqs.10, 11, 12 and 39, the values of the pion masses appeared interchange

Cancellation of Renormalon Ambiguities in the Heavy Quark Effective Theory

Recently, it has been shown that the concept of the pole mass of a heavy quark becomes ambiguous beyond perturbation theory, because of the presence of infrared renormalons. We argue that the predictions of heavy quark effective theory, whose construction is based on the pole mass, are free of such ambiguities. In the $1/m_Q$ expansion of physical quantities, infrared and ultraviolet renormalons compensate each other between coefficient functions and matrix elements. We trace the appearance of these compensations for current-induced exclusive heavy-to-heavy and heavy-to-light transitions, and for inclusive decays of heavy hadrons. In particular, we show that the structure of the heavy quark expansion is not obscured by renormalons, and none of the predictions of heavy quark effective theory are invalidated.Comment: 26 pages LaTeX (a4), 3 figures available in separate file figures.uu, CERN-TH.7312/9

Lattice flavourdynamics

I present a selection of recent lattice results in flavourdynamics, including the status of the calculation of quark masses and a variety of weak matrix elements relevant for the determination of CKM matrix elements. Recent improvements in the momentum resolution of lattice computations and progress towards precise computations of K decay amplitudes are also reviewed

Finite-volume effects in moving frames

We determine the quantization condition for the energy levels of two interacting particles in a finite box in a "moving frame", i.e. one in which the total momentum of pions is non-zero. This condition is valid up to corrections which fall exponentially withe the box size, and holds only below the inelastic threshold. It is derived using field theoretic methods, using a generalization of previous summation formulae relating sums and integrals over momenta. The result agrees with that obtained earlier by Rummakainen and Gottlieb using a relativistic quantum mechanical approach. Technically, we expand the finite-volume four-point Green function in terms of the infinite-volume Bethe-Salpeter kernel, and determine the position of the poles. The final result is written in terms of the two-pion scattering phase shift. Our result can be used to facilitate the determination of the scattering phase shift, and can be used to generalize the Lellouch-Lüscher formula relating finite-volume two-particle matrix elements to those in infinite volume