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 $\varphi (\vec{p})$, 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 $\Lambda$ and the residue-normalized meson-quark coupling, from which we evaluate the decay constant and the spin-independent kinetic matrix element including the retained $1/m_Q$ derivative and kinetic contributions. The Isgur-Wise function is evaluated separately in the static heavy-quark limit, and its zero-recoil slope is extracted by using the same residue-normalized heavy-light vertex. The subleading calculation is restricted to the kinetic (derivative) part of the HQET operators. For a representative vertex, calibrated at fixed $m_b^{\mathrm{eff}}=5.04\mathrm{GeV}$ to the leading-order decay constant $f_B^{\mathrm{LO}}=180.0\mathrm{MeV}$ and the spin-averaged mass ${\bar{m}}_B=5.313\mathrm{GeV}$, we obtain $\delta f_B^{(1/m_Q,\mathrm{partial})}=+121.9\mathrm{MeV}$ and $f_B^{\mathrm{partial}}=301.9\mathrm{MeV}$, $\Lambda =190.7\mathrm{MeV}$, ${\lambda }_1^{(\partial )}=-0.773{\mathrm{GeV}}^2$, and ${\rho }_{\mathrm{IW}}^2=1.153$. The kinetic contribution yields a mass shift of order $\Lambda /2$ and a sizable partial $1/m_Q$ correction, indicating that the spin-independent nonperturbative $1/m_Q$ sector is a sensitive probe of the finite-mass heavy-light vertex.

arXiv comment16 pages, 2 figures