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Hopping Parameter Expansion for Heavy-Light Systems UKQCD Collaboration

We present a technique which permits the calculation of two-point functions of operators containing one heavy quark and an arbitrary number of light quarks as analytic functions of the heavy-quark mass. It is based on the standard Jacobi linear solver used for the calculation of quark propagators. Results for the heavy-light pseudoscalar and vector meson masses are obtained on 163 × 48 lattices at β = 6.2 using the Wilson fermion action, and agree with published data. The incorporation of smeared operators and O(a)improved actions presents no problems. Introduction There is much interest at present in studying systems involving both heavy and light quarks on the lattice. The reasons for this are twofold. Firstly, the values of quantities such as the decay constants of the D and B mesons and the form of the IsgurWise function [1] are currently of great interest to both the experimental and theoretical communities. These are, in principle, calculable on the lattice. Secondly, it is expected that discretisation errors are relatively large for states containing heavy quarks and such systems provide an arena in which to look for gains from the use of improved actions [2]. Although nature has so far only revealed two heavy quarks, charm and bottom, with masses of approximately 1.5 and 5 GeV respectively, it is not always sufficient to perform lattice simulations solely at these two points. Regarding the evaluation of the Isgur-Wise function ξ(v .v ), it is essential to know when (and if) the heavy-quark effective theory is valid. Once this has been determined, it is necessary to perform measurements at many different heavyquark velocities to map out the form of ξ(v .v ). Since the lattice quantises the allowed values of momenta, this can only be done in a continuous fashion by varying the quark mass. In order to study lattice artifacts we need to have results at many heavy-quark masses to discover when and how the discretisation errors manifest themselves and to decide when to trust the lattice results. In this letter, we use the standard Wilson fermion action S F = ∑