Infrared fixed points and fixed lines in the top-bottom-tau sector in supersymmetric grand unification

The two-loop “top-down” renormalization group flow for the top, bottom and tau Yukawa couplings, from μ = MGUT ⋍ O(1016GeV) to μ ⋍ mt, 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 mtpole −tan β plane is performed and ii) the extent to which these imply approximate Yukawa unification is determined. In the mtpole −tan β 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, mtpole ⋍ 168–180GeV (close to the experimental value), for the large interval 2.5 ≲ tan β ≲ 55; it realizes tau-bottom Yukawa unification at MGUT approximately. The less attractive fixed line as well as the fixed point at mtpole ⋍ 170 GeV, tan β ⋍ 55 implement approximate top-bottom Yukawa unification at all scales μ. 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 mtpole ⋍ O(200 GeV) sin β.