Lower Bound on the Garvitino Mass $m_{3\mathrm{/}2}>O(100)$ TeV in $R$-Symmetry Breaking New Inflation

In supersymmetric theories, the $R$ symmetry plays a unique role in suppressing a constant term in the superpotential. In single chiral field models of spontaneous breaking of a discrete $R$ symmetry, an $R$-breaking field can be a good candidate for an inflaton in new inflation models. In this paper, we revisit the compatibility of the single-field $R$-breaking new inflation model with the results of the Planck experiment. As a result, we find that the model predicts a lower limit on the gravitino mass, $m_{3\mathrm{/}2}>O(100)$ TeV. This lower limit is consistent with the observed Higgs mass of 126 GeV when the masses of the stops are of order the gravitino mass scale.