Infrared Fixed Points and Fixed Lines in the Top-Bottom-Tau Sector in Supersymmetric Grand Unification

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Abstract
The two-loop ``top-down'' renormalization group flow for the top, bottom and tau Yukawa couplings is explored in the framework of supersymmetric grand unification; reproduction of the physical bottom and tau masses is required. Instead of following the recent trend of implementing exact Yukawa coupling unification i) a search for infrared (IR) fixed lines and fixed points in the m(top)-tan(beta) plane is performed and ii) the extent to which these imply approximate Yukawa unification is determined. Two IR fixed lines, intersecting in an IR fixed point, are located. The more attractive fixed line has a branch of almost constant top mass, 168-180 GeV, close to the experimental value, for the large interval 2.5<tan(beta)<55; it realizes tau-bottom Yukawa unification at MGUT approximately. The fixed point at m(top)= 170 GeV, tan(beta)=55 implements approximate top-bottom Yukawa unification at all scales. The fixed point and lines are distinct from the much quoted effective IR fixed point m(top)=O(200)GeV sin(beta).

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