In supersymmetric extensions of the Standard Model with a very light gravit
ino, the effective theory at the weak scale should contain not only the gol
dstino (G) over tilde, but also its supersymmetric partners, the sgoldstino
s. In the simplest case, the goldstino is a gauge-singlet and its superpart
ners are two neutral spin-0 particles, S and P. We study possible signals o
f massive sgoldstinos at hadron colliders, focusing on those that are most
relevant for the Tevatron. We show that inclusive production of sgoldstinos
, followed by their decay into two photons, can lead to observable signals
or to stringent combined bounds on the gravitino and sgoldstino masses. Sgo
ldstino decays into two gluon jets may provide a useful complementary signa
ture. (C) 2000 Elsevier Science B.V. All rights reserved.