One-loop right-handed neutrino threshold corrections for two-loop running in supersymmetric type I seesaw models

The renormalization group (RG) running of the neutrino mass operator is required for comparing the predictions of neutrino models at high energies with the experimental data at low energies. In the type I seesaw scenario with nG right-handed neutrinos, the RG running is also performed in the effective theories above and between the thresholds given by the masses of the right-handed neutrinos. At these thresholds, the effective theories are matched. When calculating the two-loop RG running, the matching has to be performed at the one-loop level. In this work, we calculate the one-loop matching formulae in the MSSM extended by nG right-handed neutrinos using supergraph techniques. Moreover we present a general formula for one-loop matching of superpotential operators which can readily be applied to any supersymmetric theory where chiral superfields are integrated out.