New sum rule determination of the nucleon mass and strangeness content

A new QCD calculation of the mass of the nucleon is presented. It makes use of a polynomial kernel in the dispersion integrals tailored to practically eliminate the contribution of the unknown $1/2^{+}$ and $1/2^{-}$ continuum. This approach avoids the arbitrariness and instability attached to the Borel kernel used in previous sum rules calculations. Our method yields stable results for the nucleon mass and coupling for standard values of the condensates. The prediction of the nucleon mass in the chiral limit is $m_N=(830\pm 50)$ MeV. When the nucleon sigma terms are added this gives $M_N=990\pm 50$ MeV, which leaves little room for a large strangeness content of the nucleon.

Figure 1

$P_1\left(t\right)$ is our polynomial of Eq. (9) and $P_2\left(t\right)$ is the Borel kernel of Eq. (7). Both kernels are normalized to 1 at the origin.

Figure 2

Nucleon mass in the chiral limit as a function of the radius $R$ in the FESR.