QCD Sum Rules and Hadronic Matrix Elements

在当代粒子物理研究中，人们正在深入研究含有重b夸克或c夸克的强子的独占半轻子衰变和辐射衰变，研究不同口味量子数夸克之间的基本跃迁。这些过程特别有趣，因为它们对超越粒子物理标准模型的新重粒子的虚拟效应非常敏感。在重强子衰变的研究中，理论精度必须与实验测量的高精度相匹配(在“大型强子对撞机”和未来的加速器设施，即所谓的“超级工厂”)。这里的主要挑战在于量子色动力学(QCD)中强相互作用效应的理论计算。在这个项目中，旨在解决这一问题的理论方法的组合将得到进一步的发展和应用，重点将是QCD中的所谓光锥和规则方法。基于解析计算，和规则方法结合了几个强大的理论工具：QCD中的算符-乘积展开，强子色散关系和夸克-强子对偶。QCD中的计算程序将被基于QCD的有效理论中的强子振幅的系统展开所补充，例如软共线有效理论。我们计划了求和规则技术的新应用，包括：计算末态两个伪标量介子的半轻子B介子和D介子衰变幅度，重重子的半轻子跃迁，以及与具有味变化中性流的重强子衰变相关的强子矩阵元。除了传统的光锥和规则外，还将在有效理论中得到新的和规则，以评估算符乘积展开中高阶效应恢复的影响。

In contemporary particle physics research, the fundamental transitions between quarks with different flavour quantum numbers are being intensively investigated in exclusive semileptonic and radiative decays of hadrons containing heavy b- or c-quarks. These processes are especially interesting because they are sensitive to virtual effects of new heavy particles beyond the Standard Model of particle physics. In studies of heavy hadron decays, the theoretical accuracy has to match the high precision of the experimental measurements (at the “Large Hadron Collider” and at future accelerator facilities, the so called “super-flavour factories”). Here, the main challenge lies in the theoretical computation of the strong-interaction effects in Quantum Chromodynamics (QCD). In this project, a combination of theoretical methods aimed at solving this problem will be further developed and applied.The emphasis will be on the so-called light-cone sum rule approach in QCD. Based on analytical calculations, the sum-rule method combines several powerful theory tools: the operator-product expansion in QCD, hadronic dispersion relations and quark-hadron duality. The calculational procedures in QCD will be supplemented by systematic expansions of hadronic amplitudes in QCD-based effective theories, such as the Soft-Collinear Effective Theory. We plan new applications of the sum-rule technique, including: the calculation of semileptonic B- and D-meson decay amplitudes with two pseudoscalar mesons in the final state, the semileptonic transitions of heavy baryons, and the hadronic matrix elements relevant for heavy-hadron decays with flavour-changing neutral currents. In addition to the conventional light-cone sum rules, new sum rules in the effective theories will be obtained to assess the effects of the resummation of higher-order effects in the operator-product expansion.