The static force in background perturbation theory

Abstract

The static force $F_B(r)$ and the strong coupling ${\alpha }_F(r)$, which defines the gluon-exchange part of $F_B(r)$, are studied in QCD background perturbation theory (BPT). In the region $r\la 0.6 $ fm ${\alpha }_F(r)$ turns out to be essentially smaller than the coupling ${\alpha }_B(r)$ in the static potential. For the dimensionless function ${\Phi }_B(r)=r^2{F}_B(r)$ the characteristic values ${\Phi }_B(r_1)=1.0$ and ${\Phi }_B(r_0)=1.65$ are shown to be reached at the following $Q\bar{Q}$ separations: $r_1\sqrt{\sigma }=0.77,r_0\sqrt{\sigma }=1.09$ in quenched approximation and $r_1\sqrt{\sigma }=0.72,r_0\sqrt{\sigma }=1.04$ for $n_f=3$. The numbers obtained appear to be by only 8% smaller than those calculated in lattice QCD while the values of the couplings ${\alpha }_F(r_1)$ and ${\alpha }_F(r_0)$ in BPT are by $\sim 30$ and $50$ larger than corresponding lattice couplings. With the use of the BPT potential good description of the bottomonium spectrum is obtained.

21 pages, 1 figure. To be publised in Phys. Atom. Nucl. dedicated to the 70-th birthday of Yu.A. Simonov

References in corpus (19)

• Analytic Model for the QCD Running Coupling with Universal ${\bar{\alpha }}_s(0)$ Value
• Non-perturbative quark mass renormalization in quenched lattice QCD
• Casimir scaling of SU(3) static potentials
• Field correlators in QCD. Theory and applications
• The Running Coupling from SU(3) Lattice Gauge Theory
• Calculation of Quarkonium Spectrum and $m_b,m_c$ to Order ${\alpha }_s^4$
• Casimir scaling as a test of QCD vacuum
• On the Behavior of the Effective QCD Coupling alpha_tau(s) at Low Scales
• Light-meson orbital excitations in the QCD string approach
• The ${\eta }_c(3654)$ and hyperfine splitting in charmonium
• The restriction on the strong coupling constant in the IR region from the 1D-1P splitting in bottomonium
• Are there short distance non-perturbative contributions to the QCD static potential?
• A High Precision Study of the QQ(bar) Potential from Wilson Loops in the Regime of String Breaking
• Determination of Alpha_s(1 GeV) from the charmonium fine structure
• Zero temperature string breaking in lattice quantum chromodynamics
• Heavy Quarkonium
• String Breaking in Four Dimensional Lattice QCD
• Test of the QCD vacuum with the sources in higher representations
• Pion Rescattering in Two-Pion Decay of Heavy Quarkonia

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• The $c\bar{c}$ interaction above threshold and the radiative decay $X(3872)\to J/\psi \gamma$
• Is the remnant of GW190425 a strange quark star?
• Conformal Symmetry as a Template for QCD
• Dominant spin-orbit effects in radiative decays {${\rm Y}(3S\to \gamma {\chi }_{bJ}(1P))$}}