Heavy Quark Effective Fields as Operator-valued Distributions

We look at effective fields defined in the heavy-quark effective theory as operator-valued generalized functions on Minkowski space-time to be averaged with physically suitable smoothing functions (Gaussians of typical width the hadronic size) leading to operator-valued distributions in Hilbert space. One-heavy-quark states are thus represented by normalizable wave packets displaying a particle-like behaviour at the characteristic hadronic time ${\mathrm{\Lambda }}_{QCD}^{-1}$. We examine some consequences relative to the average kinetic energy of heavy quarks in hadrons to avoid inconsistences within this formalism.