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Heavy quark hadronic Lagrangian for s-wave quarkonium
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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.
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PINEDA, Antonio (Pineda Ruiz) and SOTO RIERA, Joan. Heavy quark hadronic Lagrangian for s-wave quarkonium. Physical Review D. 1996. Vol. 53, num. 7, pags. 3983-3997. ISSN 0556-2821. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/12418