Effective Action in M-Theory: $(DF)^4$ Superinvariants

We construct superinvariants in M-theory via local supersymmetry, which include $(DF)^4$ terms and fermionic bilinear terms with mass dimension eight. The bases of the $(DF)^4$ and the fermionic bilinear terms are classified and the variations under the local supersymmetry are evaluated by using the Mathematica codes. By imposing the local supersymmetry, we find that 24 independent terms of $(DF)^4$ are governed by 10 parameters. The result is consistent with the effective action obtained by analyzing scattering amplitudes of superparticles or supermembranes.