  We present results from a new calculation of two- and three-body decays of
the gravitino including all possible Feynman graphs. The work is done in the
R-parity conserving Minimal Supersymmetric Standard Model, assuming that the
gravitino is unstable. We calculate the full width for the three-body decay
process Gravitino -> \chi_1 X Y, where \chi_1 is the lightest neutralino that
plays the role of the lightest supersymmetric particle, and X, Y are standard
model particles. For calculating the squared amplitudes we use the packages
FeynArts and FormCalc, with appropriate extensions to accommodate the gravitino
with spin 3/2. Our code treats automatically the intermediate exchanged
particles that are on their mass shell, using the narrow width approximation.
This method considerably simplifies the complexity of the evaluation of the
total gravitino width and stabilizes it numerically. At various points of the
supersymmetric parameter space, we compare the full two-body and the three-body
results with approximations used in the past. In addition, we discuss the
relative sizes of the full two-body and the three-body gravitino decay widths.
Our results are obtained using the package GravitinoPack, that will be publicly
available soon, including various handy features.
