Asymptotically free four-fermion interactions and electroweak symmetry breaking

We investigate the fermions of the standard model without a Higgs scalar. Instead, we consider a non-local four-quark interaction in the tensor channel which is characterized by a single dimensionless coupling $f$. Quantization leads to a consistent perturbative expansion for small $f$. The running of $f$ is asymptotically free and therefore induces a non-perturbative scale $Λ_{ch}$, in analogy to the strong interactions. We argue that spontaneous electroweak symmetry breaking is triggered at a scale where $f$ grows large and find the top quark mass of the order of $Λ_{ch}$. We also present a first estimate of the effective Yukawa coupling of a composite Higgs scalar to the top quark, as well as the associated mass ratio between the top quark and the W boson.

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