  In this article we discuss how one can systematically construct the point
particle theories that realize the vanishing one-loop cosmological constant
without the bose-fermi cancellation. Our construction is based on the
asymmetric (or non-geometric) orbifolds of supersymmetric string vacua. Using
the building blocks of their partition functions and their modular properties,
we construct the theories which would be naturally identified with certain
point particle theories including infinite mass spectra, but not with string
vacua. They are obviously non-supersymmetric due to the mismatch of the bosonic
and fermionic degrees of freedom at each mass level. Nevertheless, it is found
that the one-loop cosmological constant vanishes, after removing the parameter
effectively playing the role of the UV cut-off. As concrete examples we
demonstrate the constructions of the models based on the toroidal asymmetric
orbifolds with the Lie algebra lattices (Englert-Neveu lattices) by making use
of the analysis given in [26].
