Periodicity and quark-antiquark static potential

Abstract

Beyond the standard model, a static potential between quark pairs is obtained phenomenologically (QCD inspired), associated with the range of strong interaction, when the virtual exchange gluon squared momentum transfer has a periodicity for periodic boundary conditions of the quark-pair system enclosed by a constant volume, in the lowest order of the effective perturbed QCD (in which the gluon propagator is replaced by the effective gluon one). This potential includes a periodicity dependent effect, characterized by a finite face value of the periodicity $N$, in addition to the periodicity independent potential (the Coulomb type plus linear one). That periodicity dependent effect, dominant at short distance, is applied to an explanation of the top quark mass $$m_t=8πm_πN^{1/2},$$ whose numerically calculated results indicate approximately both upper and lower bounds of $m_t$ $$177~\mbox{GeV} > m_t > 173 ~\mbox{GeV}$$ for the range of strong interaction $L=1.40~fm~(=m_π^{-1})$.