Vacuum Expectation Values of the Baryon Currents and Their Symmetry

Abstract

The spectral representations for the vacuum expectation value of the baryon currents are studied. A chiral symmetry between the baryon currents and axial baryon currents is assumed in the form of asymptotic symmetry. This leads to sum rules involving the spectral functions for the baryon currents. In much the same way as has been done with vector and axial-vector currents, we try to saturate the obtained sum rules with baryon resonances. Constraints on the baryon mass spectrum (with ${J}^{P}$ values ${\mathrm{\textonehalf{}}}^{\ifmmode\pm\else\textpm\fi{}}$ and ${\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}}$) are deduced. Fair agreement is obtained in two possible cases: (1) the $Y=0$, $I=1 Y_{1}^{}{}_{}{}^{*}$ system; (2) the $Y=\ensuremath{-}1$, $I=\frac{1}{2}\ensuremath{\Xi}_{\frac{1}{2}}^{}{}_{}{}^{*}$ system.