We study the triply heavy baryons in the QCD sum rules by performing the first calculation of the next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Compared with the leading order (LO) result, the NLO contribution is found to be very important to the . This is because the NLO not only results in a large correction but also reduces the parameter dependence, making the Borel platform more distinct, especially for the in the scheme, where the platform appears only at NLO but not at LO. Particularly, owing to the inclusion of the NLO contribution, the renormalization schemes ( and On-Shell) dependence and the scale dependence are significantly reduced. Consequently, after including the NLO contribution to the perturbative part in the QCD sum rules, the masses are estimated to be GeV for and GeV for , where the results are obtained at with errors including those from the variation of the renormalization scale μ in the range . A careful study of the μ dependence in a wider range is further performed, which shows that the LO results are very sensitive to the choice of μ whereas the NLO results are considerably better. In addition to the result, a more stable value, (4.75-4.80) GeV, for the mass is found in the range of , which should be viewed as a more relevant prediction in our NLO approach because of dependence.

我们 通过对相关函数的微扰 QCD 部分进行次前导阶 (NLO) 贡献的第一次计算来研究 QCD 和规则中的三重重子。与领先顺序 (LO) 结果相比，发现 NLO 贡献对. 这是因为NLO不仅导致大的修正，但也降低了参数的依赖，使依波路平台更加明显，尤其是对在方案，其中该平台只出现在非线性光学但不是在LO。特别是，由于包含 NLO 贡献，重整化方案（和 On-Shell) 依赖性和规模依赖性显着降低。因此，在 QCD 求和规则中包括 NLO 对微扰部分的贡献后，质量估计为GeV for和GeV for ，其中获得的结果具有误差，包括来自范围内重整化尺度μ变化的误差. 进一步对更广泛范围内的μ依赖性进行了仔细研究，这表明 LO 结果对μ的选择非常敏感，而 NLO 结果要好得多。除了结果之外，还发现质量更稳定的值 (4.75-4.80) GeV范围为，由于依赖性，这应该被视为我们 NLO 方法中更相关的预测。