DOI 10.1007/s100529800852 Eur. Phys. J. C 5, 363–367 (1998) T HE EUROPEAN P HYSICAL JOURNAL C c  Springer-Verlag 1998 Third generation Yukawa couplings unification in supersymmetric SO(10) model N. Nimai Singh, S. Biramani Singh Department of Physics, Gauhati University, Guwahati 781014, India Received: 22 September 1997 / Revised version: 22 January 1998 / Published online: 24 March 1998 Abstract. In the minimal supersymmetric standard model (MSSM) contained in SUSY SO(10), top-b-τ Yukawa unification is achieved at the intermediate mass scale MI ≃ 10 13.10 GeV using the recent world average experimental value of the top-quark mass, mtop = 175 ± 6 GeV, which has been directly established by CDF and D0 experiments at the Tevatron Collider. It is also observed that the Yukawa couplings unification scale MI can be further decreased by taking lower input values of the top-quark mass. This trend indicates the possible existence of an intermediate symmetry breaking scale in SUSY SO(10). The present finding does not agree with the earlier notion that the third generation Yukawa couplings unification should occur at the GUT scale MU . 1 Introduction The topic of Yukawa couplings unification in supersym- metric unified theory (GUT) framework motivated by SO(10) or E 6 unification, has been given considerable at- tention over the last few years [1]. Minimal supersym- metric standard model (MSSM) has been accepted as a promising theory at least on its three crucial predictions consistent with the latest experimental measurements: (i) the value of Sin 2 θ w (M Z ), (ii) the meeting of the three gauge coupling constants when extrapolated at higher en- ergy scale, and (iii) the high observed value of GUT scale M U ≃ 2 × 10 16 GeV sufficient to prevent fast proton de- cay in agreement with the present experimental bound [2]. The hypothesis that the third generation Yukawa cou- plings should meet at GUT scale (h top = h b = h τ ) is in fact related to the problem of the origin of fermion masses [3]. In all earlier works, this condition is used as a starting point to predict either the top or bottom quark mass [1, 3– 5]. Another important aspect of SUSY SO(10) is its sym- metry breaking pattern. In the conventional SUSY SO(10) employing the Higgs supermultiplets 54, 16 H + 16 H and 10 in the usual fashion, it is impossible to achieve the inter- mediate scale M I substantially lower than the unification scale. Lee and Mohapatra [7] have advocated the possibil- ity of the existence of an intermediate symmetry breaking scale around M I ≃ 10 11 –10 12 GeV corresponding to B − L symmetry breaking in SUSY GUT such as SUSY SO(10) in order to solve the strong CP problem through Peccei- Quinn mechanism and achieve small neutrino masses nec- essary to understand solar neutrino flux and/or the dark matter of the universe. This corresponds to the interme- diate symmetry group SU (2) L × SU (2) R × U (1) B−L × SU (3) C (= G 2213 ) [7, 8]. It has also been noted [6] that the intermediate symmetry SU (2) L ×SU (2) R ×SU (4) C (= Fig. 1. Running of the three gauge couplings of the minimal SUSY standard model with mass scale t = ln(μ/1 GeV) for mtop = 175 GeV G 224P ) can also be achieved at M I ≃ 5×10 12 -2×10 14 GeV, provided certain states in the adjoint representation 45 and/or 16 H + 16 H have masses near 1TeV. In the context of the precise measurements [9] of the top-quark mass by CDF and D0 experiments at the Teva- tron Collider, it is now possible to study the existence of such intermediate symmetry breaking scale through the Yukawa couplings unification scheme in SUSY SO(10), and settle the question whether top-b-τ Yukawa couplings unification can occur at the intermediate scale other than GUT scale, by solving the renormalisation group equa- tions (RGEs) of the Yukawa couplings evolving from lower scale to unification scale.