Pseudoscalar decay constant in heavy light systems

When investigating the physics of the heavy light mesonic system within the frame work of non-relativistic QCD (NRQCD), the action and observables are expanded in powers of ΛQCD/MQ, MQ denoting the heavy quark mass. If the regularisation, in our case the lattice cutoff, would be removed, divergences will arise in the matrix elements and coefficients of the expansion. To circumvent this, we keep the cutoff finite and use an improved action to minimise residual effects on physical results. Large residual divergences would become obvious as scaling violations of the contributing matrix elements. We use 278 quenched 12 × 24 configurations with β = 5.7, generously provided by UKQCD. For the light quarks the tadpole improved clover action with κ = 0.1400 has been used. This is slightly lighter than the strange quark mass as determined from the K meson, κs|K = 0.1398 [1]. At β = 6.0 [2] such a mismatch leads to a shift of 1% in fPS which is negligible compared to other errors in our calculation. Frommρ one gets a −1 = 1.103(11)(50) GeV [3]. For the heavy quarks we used a tadpole improved action corrected up to order O(1/M) in the bare heavy quark mass, details on which can be found in [4]. We use heavy quark masses in the range 20 ≥ aM ≥ 0.6, which ranges from heavy quarks much heavier than the b and slightly lighter than the c quark. All results presented are preliminary.