The Infrared Fixed Point of the Top Quark Mass and its Implications within the MSSM

We analyse the general features of the Higgs and supersymmetric particle spectrum associated with the infrared fixed point solution of the top quark mass in the Minimal Supersymmetric Standard Model. We consider the constraints on the mass parameters, which are derived from the condition of a proper radiative electroweak symmetry breaking in the low and moderate $\tan \beta$ regime. In the case of universal soft supersymmetry breaking parameters at the high energy scale, the radiative $SU(2{)}_L\times U(1{)}_Y$ breaking, together with the top quark Yukawa fixed point structure imply that, for any given value of the top quark mass, the Higgs and supersymmetric particle spectrum is fully determined as a function of only two supersymmetry breaking parameters. We show that, for the interesting range of top quark mass values $M_t\simeq 175\pm 10$ GeV, both a light chargino and a light stop may be present in the spectrum. In addition, for a given top quark mass, the infrared fixed point solution of the top quark Yukawa coupling minimizes the value of the lightest CP-even Higgs mass $m_h$. The resulting upper bounds on $m_h$ read $m_h \leq 90 ;(105) ;(120)$GeVfor$M_t \leq 165 ;(175) ;(185)$ GeV.