Heavy Quark Hadronic Lagrangian for S-wave Quarkonium

Abstract

We use Heavy Quark Effective Theory (HQET) techniques to parametrize certain non-perturbative effects related to quantum fluctuations that put both heavy quark and antiquark in quarkonium almost on shell. The large off-shell momentum contributions are calculated using Coulomb type states. The almost on-shell momentum contributions are evaluated using an effective 'chiral' lagrangian which incorporates the relevant symmetries of the HQET for quarks and antiquarks. The cut-off dependence of both contributions matches perfectly. The decay constants and the matrix elements of bilinear currents at zero recoil are calculated. The new non-perturbative contributions from the on-shell region are parametrized by a single constant. They turn out to be $O(\alpha^2/\Lambda_{QCD} a_{n})$, $a_{n}$ being the Bohr radius and $\alpha$ the strong coupling constant, times the non-perturbative contribution coming from the multipole expansion (gluon condensate). We discuss the physical applications to $\Upsilon$, $J/\Psi$ and $B_{c}$ systems.