A renormalization group invariant line and an infrared attractive top-Higgs mass relation

The renormalization group equations (RGEs) of the standard model at one loop in terms of the gauge couplings g1,2,3, the top Yukawa coupling gt and the scalar self coupling λ are reexamined. For g1,2=0, the general solution of the RGEs is obtained analytically in terms of an interesting special solution for the ratio λ/g2t as function of the ratio g2t/g23 which (i) represents a RG invariant line which is strongly infrared attractive, (ii) interpolates all known quasi-fixed points, and (iii) is finite for large g2t/g23 (ultraviolet limit). All essential features survive for g1,2≠0. The invariant line translates into an infrared attractive top-Higgs mass relation, which e.g. associates to the top masses mt = 130/145/200 GeV the Higgs masses mH ≅ 68−90/103−115/ 207 GeV, respectively