Octet and decuplet contribution to the proton self energy

Abstract

Within the hadronic language of Chiral Perturbation Theory we present the full leading-order octet-baryon$-$meson and decuplet-baryon$-$meson contribution to the proton self energy and thus to its wave function renormalization factor $Z$. By Fock-expanding the physical proton state into its bare and hadron-cloud part, we show how each individual baryon-meson probability depend on the average momenta of the particles in the fluctuation. We present how the results depend on the choice of the form factor involved in the regularization (Gaussian or Besselian) and how they depend on the cut-off parameter. We also show how the results vary with respect to a variation of the decuplet coupling constant $h_A$. The momentum distributions of the fluctuations are given and the fluctuations' relative probabilities are presented. We show that for reasonable values of the cut-off parameter, the Delta-pion fluctuation is of the same strength as the nucleon-pion fluctuation.