Heavy mesons from the QCD instanton vacuum beyond the static limit

Abstract

We study pseudoscalar heavy mesons in the QCD instanton vacuum beyond the static limit. Finite-mass effects in the heavy-light loop are encoded in a separable effective vertex built from a profile function $ϕ(\vec{p})$, kept distinct from the static Wilson-line form factor $F_Q^{(\infty)}(\vec{q})$ of the $m_Q\to\infty$ limit. The pseudoscalar two-point function fixes the residual mass $Λ$ and the residue-normalized meson-quark coupling, from which we evaluate the decay constant, the spin-independent kinetic matrix element, and the zero-recoil slope of the Isgur-Wise function at order $1/m_Q$. The subleading calculation is restricted to the kinetic (derivative) part of the HQET operators. For a representative vertex calibrated to the $B$-meson decay constant and the spin-averaged $B$-meson mass, we obtain $f_B = 186.8$~MeV, $Λ= 184.5$~MeV, $m_b^{\mathrm{eff}} = 5.04$~GeV, $λ_1^{(\partial)} = -0.922~\mathrm{GeV}^2$, and $ρ_{\mathrm{IW}}^2 = 1.105$. The kinetic contribution yields a mass shift of order $Λ/2$ and a sizable $1/m_Q$ current correction, indicating that the spin-independent nonperturbative $1/m_Q$ sector is a sensitive probe of the finite-mass heavy-light vertex.