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: $(\frac{m_b}{m_t}{)}^2\simeq \frac{\alpha }{3\pi }$, provided the quadratic divergence is removed by setting the four-fermion coupling $G=4+o(\frac{m_b^2}{m_t^2})$.

Comments: 13 pages LaTex