Variationally improved structure of heavy-light mesons at $$N^3$$LO: stiffening effects and universal form factors in the V-scheme
Year: 2026
Type: article
Abstract: We present an investigation of the structural properties of heavy-light ( $$D, D_s, B, B_s$$ D , D s , B , B s ) and heavy-heavy ( $$B_c$$ B c ) mesons by incorporating the V -scheme strong coupling constant $$\alpha _V$$ α V up to the third-loop order ( $$N^3$$ N 3 LO). The inclusion of three-loop radiative corrections is critical to achieving perturbative convergence and effectively canceling renormalon-induced instabilities. A central feature of this work is the rigorous calibration of the string tension b using the universal scaling ratio $$R_{n_f} = \Lambda _{\overline{\text {MS}}}^{(n_f)}/\sqrt{b}$$ R n f = Λ MS ¯ ( n f ) / b , matched to the non-perturbative Sommer scale $$r_0$$ r 0 from FLAG 2024 averages. By integrating these flavor-dependent $$N^3$$ N 3 LO refinements ( $$b \approx 0.1951 \pm 0.0369$$ b ≈ 0.1951 ± 0.0369 GeV $$^2$$ 2 ) into a variational Cornell potential framework, we demonstrate a systematic“stiffening”of the internal structure and a physical spatial contraction across successive loop orders. Our $$N^3$$ N 3 LO results for root-mean-square (RMS) matter radii and charge radii exhibit remarkable agreement with established benchmarks: specifically, the $$B_c$$ B c charge radius (0.191 fm) and matter radius (0.2967 fm) align closely with light-front predictions and relativistic quark model studies. Evaluation of the Isgur–Wise function reveals that while higher-order corrections primarily reshape the light-quark spectator cloud, the heavy core localization remains dominated by the constituent mass scale.
Source: The European Physical Journal C
Institution: Tezpur University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7163082561