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Heavy mesons from the QCD instanton vacuum beyond the static limit

Ki-Hoon Hong ^1,*, Yongwoo Choi ^2,3,†, Nurmukhammad Rakhimov ^1,‡, and Hyun-Chul Kim ^4,1,5,§

¹Institute of Quantum Science, Inha University, Incheon 22212, Republic of Korea
²School of AIT, Hoseo University, Asan 31499, Republic of Korea
³Quantum AI Innovative Technology Institute (Q-AIT), Hoseo University, Asan 31499, Republic of Korea
⁴Department of Physics, Inha University, Incheon 22212, Republic of Korea
⁵School of Physics, Korea Institute for Advanced Study (KIAS), Seoul 02455, Republic of Korea

^*Contact author: kihoon.hong@inha.ac.kr
^†Contact author: ywchoi@hoseo.edu
^‡Contact author: n.r.rakhimov@gmail.com
^§Contact author: hchkim@inha.ac.kr

Phys. Rev. D 114, 074057 – Published 27 October, 2026

DOI: https://doi.org/10.1103/83wz-blj7

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 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 heavy-quark effective theory operators. For a representative vertex, calibrated at fixed $m_{b}^{eff} = 5.04 GeV$ to the leading-order decay constant $f_{B}^{LO} = 180.0 MeV$ and the spin-averaged mass ${\bar{m}}_{B} = 5.313 GeV$ , we obtain $δ f_{B}^{(1 / m_{Q}, partial)} = + 121.9 MeV$ and $f_{B}^{partial} = 301.9 MeV$ , $Λ = 190.7 MeV$ , $λ_{1}^{(\partial)} = - 0.773 {GeV}^{2}$ , and $ρ_{IW}^{2} = 1.153$ . The kinetic contribution yields a mass shift of order $Λ / 2$ 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.

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Phys. Rev. D 114, 074057– Published 27 October, 2026

Vol. 114, Iss. 7 — 1 October 2026

Received 30 June 2026
Accepted 30 September 2026

DOI: https://doi.org/10.1103/83wz-blj7

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Heavy mesons from the QCD instanton vacuum beyond the static limit

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