  Pseudo-goldstinos appear in the scenario of multi-sector SUSY breaking.
Unlike the true goldstino which is massless and absorbed by the gravitino,
pseudo-goldstinos could obtain mass from radiative effects. In this note,
working in the scenario of two-sector SUSY breaking with gauge mediation, we
explicitly calculate the pseudo-goldstino mass at the leading three-loop level
and provide the analytical results. In our calculation we consider the general
case of messenger masses (not necessarily equal) and include the higher order
terms of SUSY breaking scales. Our results can reproduce the numerical value
estimated previously at the leading order of SUSY breaking scales with the
assumption of equal messenger masses. It turns out that the results are very
sensitive to the ratio of messenger masses, while the higher order terms of
SUSY breaking scales are rather small in magnitude. Depending on the ratio of
messenger masses, the pseudo-goldstino mass can be as low as ${{\cal O} (0.1)}$
GeV.
