Fine-tuning the low-energy physics

Abstract

In this article we discuss the problem of the extreme fine-tuning necessary to achieve the top quark mass scale $m_t$ within the dynamical symmetry breaking of the phenomenological $t \bar t$ condensate model. Inspired by the vector-like phenomenon of chiral gauge theories at short distances, we postulate that the $W^\pm$-gauge bosons possess a vector-like gauge coupling and contribute to the gap-equations of quark self-energy functions in the high-energy region. We find that the gap-equations of different charge sectors are coupled, and as a result the unnatural fine-tuning is overcome and the ratio of the top and bottom masses is related to the electric charge: $({m_b\over m_t})^2\simeq {α\over3π}$, provided the quadratic divergence is removed by setting the four-fermion coupling $G=4+o({m_b^2\over m_t^2})$.