Parity projection of QCD sum rules for the nucleon

Abstract

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. First, we rederive the parity projected sum rules for baryons using ``old-fashioned'' correlation functions. Doing this, the method is generalized so that higher order operator product expansion terms can be calculated unambiguously. We then apply this approach to the nucleon channel taking into account all known first order ${\ensuremath{\alpha}}_{s}$ corrections to the Wilson coefficients of the operator product expansion. As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. Simultaneously, this phase rotation strongly suppresses the continuum contribution and improves the convergence of the operator product expansion. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive- and negative-parity states.