Current quark masses and structure functions

Abstract

Bare quark distribution functions are constructed for valence quarks in $0^{-}$, $1^{-}$ mesons and ${\left(\mathrm{½}\right)}^{+}$, ${\left(\frac{3}{2}\right)}^{+}$ baryons. The integrated $〈x^{-1\mathrm{}}〉$ moments of these structure functions lead to five independent determinations of the bare or current quark mass scale, all giving $\hat{m}=\frac{(m_u+m_d)}{2}\approx 62$ MeV and all consistent with the current quark mass ratio $\frac{m_s}{\hat{m}}\approx 5$. Furthermore, the approach also leads to a charmed current quark mass $m_c\approx 1200$ MeV.