  The supersymmetric standard model (SSM) contains a wealth of potential
supersymmetry anomalies, all of which occur in the renormalization of composite
operators of the theory. The coefficients of the weak-E.M. superanomalies
should be related to the Witten indices of the neutrino and photon superfields,
and the coefficients of the strong superanomalies should be related to the
Witten indices of the gluon and photon superfields. Assuming the coefficients
are non-zero, the superanomalies break supersymmetry in observable states.
However the neutral Higgs particles should remain in a supermultiplet because
the Higgs supermultiplet is not coupled to any massless superfield in the SSM.
Assuming that the overall Witten index is non-zero, supersymmetry is broken by
superanomalies and yet the vacuum remains supersymmetric. This means that the
cosmological constant is naturally zero after supersymmetry breaking, even
beyond perturbation theory.
