Semiclassical approximation for mesons containing one heavy and one light quark

We use the leading-logarithm-improved effective action of QCD as a starting point to describe mesons containing one very heavy and one massless quark. We find a self-consistent, static, Abelian solution to the resulting classical field equations. Our trial wave function for the light quark is obtained from solving the Dirac equation in the Coulomb field of the heavy quark with a bag boundary condition ${\overline{\psi }\psi |}_R=0\mathrm{}$. The radius $R$ of the meson is obtained by minimizing the total energy of the system. Using a parameter previously determined by Adler and Piran from a fit to heavy-quarkonia potential models, we obtain ${〈r^2〉}^{\frac{1}{2}}=0.58\mathrm{}$ fm for the ground-state meson.