Fermion Modes in Instanton-Anti-Instanton Background in (1+0)-dimensional Model

Abstract

We evaluate the eigenvalues of Dirac operator in the background of instanton-anti-instanton configuration (I-$\bar{\rm I}$), in a simple (1+0)-dimensional model, and find that quasi-zero-mode disappears for the closely localized I-$\bar{\rm I}$ configurations. This result suggests that the configurations which are dominant at high energy in the valley method are actually non-anomalous ones and irrelevant to fermion number violation. Hence, there seems to be no theoretical basis for expecting anomalous cross section to become observable at energies of 10 Tev region in Weinberg-Salam theory.