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Chiral and flavor SU(2) and SU(3) symmetry breaking in quantum chromodynamics

1985; American Physical Society; Volume: 31; Issue: 11 Linguagem: Inglês

10.1103/physrevd.31.2930

1538-4500

C. A. Domínguez, M. Loewe,

High-Energy Particle Collisions Research

We calculate light-quark mass differences in the framework of the Laplace-transform QCD sum rules using an improved parametrization of the hadronic spectral functions. Our results are (m${\ifmmode\bar\else\textasciimacron\fi{}}_{s}$-m${\ifmmode\bar\else\textasciimacron\fi{}}_{u}$)${\ensuremath{\Vert}}_{1}$ GeV=185\ifmmode\pm\else\textpm\fi{}15 MeV and (m${\ifmmode\bar\else\textasciimacron\fi{}}_{d}$-m${\ifmmode\bar\else\textasciimacron\fi{}}_{u}$)${\ensuremath{\Vert}}_{1}$ GeV=4\ifmmode\pm\else\textpm\fi{}1 MeV. Using an earlier determination of the quark-mass sums based on similar techniques, these results lead to: m${\ifmmode\bar\else\textasciimacron\fi{}}_{u}$(1 GeV)=6\ifmmode\pm\else\textpm\fi{}1 MeV, m${\ifmmode\bar\else\textasciimacron\fi{}}_{d}$(1 GeV)=10\ifmmode\pm\else\textpm\fi{}1 MeV, and m${\ifmmode\bar\else\textasciimacron\fi{}}_{s}$(1 GeV)=192\ifmmode\pm\else\textpm\fi{}15 MeV. Next, we estimate the difference of the light-quark vacuum condensates in the framework of the Laplace-transform QCD sum rules. Our results are \ensuremath{\psi}${(0)}_{u}^{s}$=-(0--3.5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ ${\mathrm{GeV}}^{4}$ and \ensuremath{\psi}${(0)}_{u}^{d}$=-(0--2.4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ ${\mathrm{GeV}}^{4}$, where \ensuremath{\psi}${(0)}_{i}^{j}$ are the renormalization-group-invariant quantities \ensuremath{\psi}${(0)}_{i}^{j}$=-(m${\ifmmode\bar\else\textasciimacron\fi{}}_{j}$-m${\ifmmode\bar\else\textasciimacron\fi{}}_{i}$) 〈\ensuremath{\psi}${\ifmmode\bar\else\textasciimacron\fi{}}_{j}$${\ensuremath{\psi}}_{j}$-\ensuremath{\psi}${\ifmmode\bar\else\textasciimacron\fi{}}_{i}$${\ensuremath{\psi}}_{i}$〉. These values imply a small flavor symmetry breaking in the QCD nonperturbative vacuum, i.e., 〈s\ifmmode\bar\else\textasciimacron\fi{}s〉/〈\ifmmode \bar{u}\else \={u}\fi{}u〉=0.9\ifmmode\pm\else\textpm\fi{}0.1 and 1-〈d\ifmmode\bar\else\textasciimacron\fi{}d〉/〈\ifmmode \bar{u}\else \={u}\fi{}u〉=(0--6)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$. .AE