We discuss the possibility of unifying in a simple and economical manner the Yukawa couplings of third generation fermions in a non-supersymmetric SO(10) model with an intermediate symmetry breaking, focusing on two possible patterns with intermediate Pati-Salam and minimal left-right groups. For this purpose, we assume a minimal Yukawa sector at high energy, starting with two Higgs bi-doublets at the intermediate scale which then simply reduce to a two Higgs doublet model at the electroweak scale. We first enforce gauge coupling unification at the two-loop level by including the threshold corrections in the renormalization group running which are generated by the heavy fields that appear at the intermediate symmetry breaking scale. We then study the running of the Yukawa couplings of the top quark, bottom quark and tau lepton at two-loops in these two breaking schemes, when the appropriate matching conditions are imposed. We find that the unification of the third family Yukawa couplings can be achieved while retaining a viable spectrum, provided that the ratio of the vacuum expectation values of the two Higgs doublet fields is large, $\tan \beta \approx 60$.

我们讨论了在具有中间对称性破坏的非超对称 SO(10) 模型中以简单且经济的方式统一第三代费米子的 Yukawa 耦合的可能性，重点关注具有中间 Pati-Salam 和最小左右对称的两种可能模式组。为此，我们假设在高能量下有一个最小的汤川扇区，从中间尺度的两个希格斯双峰开始，然后简单地减少到电弱尺度上的两个希格斯双峰模型。我们首先通过在重整化组运行中包含阈值校正来在双循环级别强制规范耦合统一，这些校正是由出现在中间对称破坏尺度的重场生成的。然后我们研究顶夸克的汤川耦合的运行，当施加适当的匹配条件时，这两种破坏方案中的底夸克和 tau 轻子在两个循环中。我们发现，只要两个希格斯双重场的真空期望值之比大，就可以在保留可行光谱的同时实现第三族汤川耦合的统一，$\mathrm{棕褐色}\beta \approx 60$.