INFRARED FIXED-POINTS AND FIXED LINES IN THE TOP-BOTTOM-TAU SECTOR IN SUPERSYMMETRIC GRAND UNIFICATION

The two-loop ''top-down'' renormalization group how for the top, bottom and tau Yukawa couplings, from mu=M(GUT)similar or equal to O(10(16) GeV) to mu similar or equal to m(t), 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 (TR) fixed lines and fixed points in the m(t)(pole)-tan beta plane is performed and ii) the extent to which these imply approximate Yukawa unification is determined. In the m(t)(pole)-tan beta plane 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, m(t)(pole)similar or equal to 168-180GeV (close to the experimental value), for the large interval 2.5 less than or similar to tan beta less than or similar to 55; it realizes tau-bottom Yukawa unification at M(GUT) approximately. The less attractive fixed line as well as the fixed point at m(t)(pole)similar or equal to 170GeV, tan beta similar or equal to 55 implement approximate top-bottom Yukawa unification at all scales mu. The renormalization group flow is attracted towards the IR fixed point by way of the more attractive IR fixed line. The fixed point and lines are distinct from the much quoted effective IR fixed point m(t)(pole)similar or equal to O(200GeV) sin beta.