CONNECTION BETWEEN THE STRING TENSION, LIGHT-MESON REGGE TRAJECTORIES, AND THE QCD SCALE PARAMETER

We compare the radial excitation spectrum of an S-wave solitonlike system containing an infinitely heavy quark and a massless scalar antiquark (Qq»), 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)=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 MS (where MS denotes the modified minimal-subtraction scheme), and the effective "string tension" . We find =(1.475MS)2 [(1.912MS)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 N1, UNr2N12=3QEvac, where Q=43 and Evac 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)=r. We then introduce a commonly used two-body Klein-Gordon equation that allows us to smoothly interpolate (for a given string tension) between the Qq regime, where we found the connection between MS and , and the qq regime (massless quark and antiquark), where we can make contact with the measured Regge slope. We obtain in this way a novel connection between and , =1(8). This allows us to estimate MS in terms of the measured value (1GeV)-2. We find MS240 MeV (185 MeV) in the log (log-log) model. © 1990 The American Physical Society.