The alternative renormalizable minimal $SO(10)$ model is composed of the Yukawa couplings with $\mathbf{\text{10}}\oplus \mathbf{\text{120}}$ Higgs fields, whereas the right-handed (RH) neutrino Majorana masses are generated via the Witten mechanism. The gauge coupling unification is achieved together with a unique pattern of the fermion masses and mixing at the grand unification scale due to additional contributions of vector-like quarks to the standard model renormalization group equations. We perform the fitting of the model to the experimental data of charged fermion masses and the CKM matrix. The best fit point is obtained with large pulls for $m_c$, $m_s$, $m_b$, and $m_{\tau }$. For the modifications to the minimal model by adding either ${\mathbf{\text{10}}}^{\prime }$ or ${\mathbf{\text{120}}}^{\prime }$, a large deviation for the tau mass rules out all these models. In the case with the bottom and vector-like quark mixing, the mass matrices are well fitted the charged fermions but the bound on the light neutrino mass scale excludes this scenario. To ameliorate this deficit, we consider the two-step symmetry breaking scenario, $SO(10)\to SU(5)\to SU{(3)}_C\times SU{(2)}_L\times U{(1)}_Y$, with the $SO(10)$ breaking at the Planck scale leading to the radiatively generated RH neutrino Majorana masses being at the ordinary seesaw scale. For this case, we find the best fit point with ${\chi }^2=7.8$ consistent with experimental results including the neutrino sector. The largest deviation is 2.3σ corresponding to the strange quark mass. Hence, a more precise determination of the strange quark mass can test this model. For the best fit point, we find the effective Majorana neutrino mass of $m_{\beta \beta }=0.22$ meV and the sum of light neutrino masses as $\mathrm{\Sigma }=0.078$ eV, which are consistent with the current constraints from the search for the neutrinoless double beta decay and the CMB anisotropy measurement.

替代可重归化最小值 $\mathrm{小号}Ø（10）$ 模型由Yukawa联轴器和 $\mathbf{\text{10}}\oplus \mathbf{\text{120}}$希格斯场，而右旋（RH）中微子马里亚纳质量是通过维滕机制产生的。规范耦合统一是与费米子质量的独特模式一起实现的，并且由于矢量样夸克对标准模型重归一化组方程的其他贡献，从而在大统一尺度上进行混合。我们对带电费米子质量和CKM矩阵的实验数据进行模型拟合。大拉力可获得最佳的配合点${米}_C$， ${米}_s$， ${米}_b$和 ${米}_{\tau }$。对于最小模型的修改，可以添加${\mathbf{\text{10}}}^{\prime }$ 要么 ${\mathbf{\text{120}}}^{\prime }$，tau质量的较大偏差排除了所有这些模型。在底部和类似矢量的夸克混合的情况下，质量矩阵很好地拟合了带电的费米子，但轻中微子质量标界上的边界排除了这种情况。为了改善这一缺陷，我们考虑了两步对称破损的情况，$\mathrm{小号}Ø（10）\to \mathrm{小号}ü（5）\to \mathrm{小号}ü{（3）}_C\times \mathrm{小号}ü{（2）}_{\mathrm{大号}}\times ü{（\mathrm{1个}）}_{ÿ}$，与 $\mathrm{小号}Ø（10）$在普朗克尺度上破裂，导致辐射产生的RH中微子质量达到普通跷跷板尺度。对于这种情况，我们找到了最佳拟合点${\chi }^2=7.8$与包括中微子区域在内的实验结果一致。最大偏差为2.3σ，对应于奇怪的夸克质量。因此，对奇异夸克质量的更精确确定可以测试该模型。为了获得最佳拟合点，我们发现有效的马约拉纳中微子质量为${米}_{\beta \beta }=0.22$ meV和轻中微子质量之和为 $\mathrm{\Sigma }=0.078$ eV，与从无中微子双β衰变和CMB各向异性测量中寻找到的电流约束一致。