We investigate the possibility of constructing a renormalizable standard model with purely fermionic matter content. The Higgs scalar is replaced by pointlike fermionic self-interactions with couplings growing large at the Fermi scale. An analysis of the UV behavior in the pointlike approximation reveals a variety of non-Gaussian fixed points for the fermion couplings. If real, such fixed points would imply nonperturbative renormalizability and avoid the triviality of the Higgs sector. For pointlike fermionic self-interactions and weak gauge couplings, one encounters a hierarchy problem similar to that for a fundamental Higgs scalar.

• Received 25 December 2003

DOI:https://doi.org/10.1103/PhysRevD.69.105008