Heavy Hadron Weak Decay Form Factors to Next-to-Leading Order in 1/m

Based on the short-distance expansion of currents in the heavy quark effective theory, we derive the exact expressions for the heavy-to-heavy meson and baryon weak decay form factors to order $1/m_Q$ in the heavy quark expansion, and to all orders in perturbation theory. We emphasize that the Wilson coefficients in this expansion depend on a kinematic variable $\bar w$ that is different from the velocity transfer $w=v\cdot v'$ of the hadrons. Our results generalize existing ones obtained in the leading-logarithmic approximation. Some phenomenological applications are briefly discussed.