Radiative electroweak symmetry breaking and the infrared fixed point of the top quark mass

The infrared quasi fixed point solution for the top quark mass in the Minimal Supersymmetric Standard Model explains in a natural way large values of the top quark mass and appears as a prediction in many interesting theoretical schemes. Moreover, as has been recently pointed out, for moderate values of $\tan\beta$, in order to achieve gauge and bottom-tau Yukawa coupling unification, the top quark mass must be within $10 \%$ of its fixed point value. In this work we show that the convergence of the top quark mass to its fixed point value has relevant consequences for the (assumed) universal soft supersymmetry breaking parameters at the grand unification scale. In particular, we show that the low energy parameters do not depend on $A_0$ and $B_0$ but on the combination $\delta = B_0 - A_0/2$. Hence, there is a reduction in the number of independent parameters. Most interesting, the radiative $SU(2)_L \times U(1)_Y$ breaking condition implies strong correlations between the supersymmetric mass parameter $\mu$ and the supersymmetry breaking parameters $\delta$ and $M_{1/2}$ or $m_0$. These correlations, which become stronger for $\tan\beta < 2$, may have some fundamental origin, which would imply the need of a reformulation of the naive fine tuning criteria.