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- W2023220664 abstract "We compare the radial excitation spectrum of an $S$-wave solitonlike system containing an infinitely heavy quark and a massless scalar antiquark ($Qoverline{q}$), as described in a renormalization-group-improved effective-action model (EAM) of QCD (log and log-log models), to the spectrum of an analogous system obeying a Klein-Gordon equation with a Lorentz-scalar linear potential $V(r)=ensuremath{sigma}r$. We show that the two systems have the same energy spectrum for high radial excitation numbers $N$, which enables us to establish a connection between the QCD scale ${ensuremath{Lambda}}_{stackrel{-}{mathrm{MS}}}$ (where $stackrel{-}{mathrm{MS}}$ denotes the modified minimal-subtraction scheme), and the effective string tension $ensuremath{sigma}$. We find $ensuremath{sigma}={(1.475{ensuremath{Lambda}}_{stackrel{-}{mathrm{MS}}})}^{2}$ [${(1.912{ensuremath{Lambda}}_{stackrel{-}{mathrm{MS}}})}^{2}$] in the log [log-log] model. Moreover, we find for our solitonlike states that the ratio of the total energy of the system to the rms radius is, for $Nensuremath{gg}1$, $frac{{U}_{N}}{{〈{r}^{2}〉}_{N}^{frac{1}{2}}}=sqrt{3}Q{E}_{mathrm{vac}}ensuremath{simeq}ensuremath{sigma}$, where $Q=sqrt{frac{4}{3}}$ and ${E}_{mathrm{vac}}$ is the vacuum color-electric field in the EAM. This is an additional indication that the light quark in the EAM experiences to a very good approximation an effective scalar potential $V(r)=ensuremath{sigma}r$. We then introduce a commonly used two-body Klein-Gordon equation that allows us to smoothly interpolate (for a given string tension $ensuremath{sigma}$) between the $Qoverline{q}$ regime, where we found the connection between ${ensuremath{Lambda}}_{stackrel{-}{mathrm{MS}}}$ and $ensuremath{sigma}$, and the $qoverline{q}$ regime (massless quark and antiquark), where we can make contact with the measured Regge slope ${ensuremath{alpha}}^{ensuremath{'}}$. We obtain in this way a novel connection between ${ensuremath{alpha}}^{ensuremath{'}}$ and $ensuremath{sigma}$, ${ensuremath{alpha}}^{ensuremath{'}}=frac{1}{(8ensuremath{sigma})}$. This allows us to estimate ${ensuremath{Lambda}}_{stackrel{-}{mathrm{MS}}}$ in terms of the measured value ${ensuremath{alpha}}^{ensuremath{'}}ensuremath{approx}{(1 mathrm{GeV})}^{ensuremath{-}2}$. We find ${ensuremath{Lambda}}_{stackrel{-}{mathrm{MS}}}ensuremath{approx}240$ MeV (185 MeV) in the log (log-log) model." @default.
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- W2023220664 date "1990-08-01" @default.
- W2023220664 modified "2023-09-25" @default.
- W2023220664 title "Connection between the string tension, light-meson Regge trajectories, and the QCD scale parameter" @default.
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- W2023220664 doi "https://doi.org/10.1103/physrevd.42.911" @default.
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