In Monte Carlo simulations of N = 1 supersymmetric Yang-Mills theory the mass of the unphysical adjoint pion, which is easily obtained numerically, is being used for the tuning to the limit of vanishing gluino mass. In this article we show how to define the adjoint pion in the framework of partially quenched chiral perturbation theory and we derive a relation between its mass and the mass of the gluino analogous to the Gell-MannOakes-Renner relation of QCD.

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Adding a gluino mass term to N = 1 supersymmetric Yang-Mills theory breaks supersymmetry softly. In order to approach the supersymmetric continuum limit in numerical simulations with the Wilson action, the bare gluino mass has to be tuned to the limit of vanishing renormalised gluino mass. This can be done efficiently by means of the mass of the adjoint pion, which is, however, an unphysical particle. We discuss how the adjoint pion can be defined in the framework of partially quenched chiral perturbation theory. A relation between its mass and the mass of the gluino, analogous to the Gell-Mann-Oakes-Renner relation of QCD, can be derived.