Scaling Study of the Leptonic Decay Constants of Heavy-Light Mesons: A Consumers Report on Improvement Factors

A high statistics calculation, performed at $\beta =5.74,6.00$ and $6.26$, enables us to study the variation of the leptonic decay constants $f_P$ of heavy pseudoscalar mesons with the lattice spacing $a$. We observe only a weak $a$ dependence when the standard $\sqrt{2\kappa }$ normalization is used for the quark fields, whereas application of the Kronfeld-Mackenzie normalization induces a stronger variation with $a$. Increasing the meson mass from $1.1GeV$ to $2.3GeV$ this situation becomes even more pronounced.