arXiv 2008.020242020-08hep-lathep-ph

格点量子色动力学张量流的重整化和$J/ψ$张量衰变常数

Renormalisation of the tensor current in lattice QCD and the $J/ψ$ tensor decay constant

D. Hatton, C. T. H. Davies, G. P. Lepage, A. T. Lytle

备注：: 12 pages, version accepted for publication in PRD
发表信息：: Phys. Rev. D 102, 094509 (2020)
DOI：: 10.1103/PhysRevD.102.094509

摘要：

格点量子色动力学计算罕见的标准模型过程，如$B \to K \ell^+ \ell^-$的形状因子使用张量电流，需要重整化。这些重正化因子$Z_T$通常是在微扰理论中计算的，并且来自缺失高阶项的估计不确定性是显著的。在这里，我们研究张量电流重整化使用晶格实现的动量减法计划。这样的方案可能更精确，但具有来自非微扰伪影的系统误差。为了确定和去除这些凝聚贡献，我们计算基态粲偶素张量衰变常数，$f_{J/ψ}^T$，这也是超越标准模型研究的兴趣。我们获得了$f_{J/ψ}^T(\bar{\text{MS}}, 2\ \mathrm{GeV})=0.3927(27)$ GeV，与矢量衰变常数之比为0.9569（52），明显低于1。我们还给出了$Z_T$因素，转换为$\bar{\mathrm{MS}}$计划，冷凝水污染校正。这种污染在2 GeV的重正化标度（在优选的RI-S方案中）达到1.5%，因此必须去除以获得准确的结果。

英文摘要：

Lattice QCD calculations of form factors for rare Standard Model processes such as $B \to K \ell^+ \ell^-$ use tensor currents that require renormalisation. These renormalisation factors, $Z_T$, have typically been calculated within perturbation theory and the estimated uncertainties from missing higher order terms are significant. Here we study tensor current renormalisation using lattice implementations of momentum-subtraction schemes. Such schemes are potentially more accurate but have systematic errors from nonperturbative artefacts. To determine and remove these condensate contributions we calculate the ground-state charmonium tensor decay constant, $f_{J/ψ}^T$, which is also of interest in beyond the Standard Model studies. We obtain $f_{J/ψ}^T(\bar{\text{MS}}, 2\ \mathrm{GeV})=0.3927(27)$ GeV, with ratio to the vector decay constant of 0.9569(52), significantly below 1. We also give $Z_T$ factors, converted to the $\bar{\mathrm{MS}}$ scheme, corrected for condensate contamination. This contamination reaches 1.5\% at a renormalisation scale of 2 GeV (in the preferred RI-SMOM scheme) and so must be removed for accurate results.

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