Higher Order Corrections to Nonleptonic and Rare Decays

重介子的非轻子独占衰变在定量CP违逆量中起决定性作用，这是风味物理中最微妙的现象。为了与当前和未来的对撞机设备的精确测量相竞争，理论方面的精确预测对于我们理解标准模型（SM）的夸克部分，甚至可能寻找新物理学的线索都是必不可少的。本项目的目的是将有效的理论方法与衰变拓扑和风味对称关系的分析结合起来，提高底(B)和粲(D)介子的二体和三体非轻子衰变的预测振幅的精度。对于二体衰变，重点是在定量上达到新的精度水平。为此，我们采取两种方法。一方面，对分解定理的修正将在有效理论框架中计算，特别是在软共线有效理论中阐述的QCD分解。除了高阶微扰（多环）修正外，我们将重点关注相对于重夸克质量逆的功率抑制的贡献。另一方面，我们将利用风味的对称性和它们的破坏。通过风味对称性的群论参数化，我们将推导振幅关系，该关系将用于这些衰变中的可观测值的模型独立描述。其中一个主要目标是量化二体非轻子b衰变的最终态重散射相。三体衰变为在微分分布中寻找CP违背提供了理想的机会。因此，主要的努力将是针对最终状态的达里兹分布的现象学模型。除了更正式的方面，如在微扰展开的高阶分解定理的有效性，我们还将进行专门的现象学分析，以更新和改进非轻子B和d衰变为轻最终态的理论预测-在B介子的情况下也进入重最终态。在此过程中，我们将使用更新和改进的输入参数以及来自非微扰方法（如QCD和规则和光锥和规则）的通用强子矩阵元素的可靠估计。与非轻子的b -衰变相比，d -衰变提供了SM内CP违背的重要补充检验。由于粲夸克的质量小于底夸克的质量，因此离重质量极限更远，对d介子衰变的理论描述预计将由增强的功率修正来塑造，这必须仔细研究和量化。

Nonleptonic exclusive decays of heavy mesons play a decisive role in quantifying the amount of CP violation, the most subtle phenomenon of flavour physics. In order to be competitive with precise measurements from current and future collider facilities, precision predictions from the theory side are indispensable for our understanding of the quark sector of the Standard Model (SM) and potentially even for finding hints for new physics. The aim of this project is to combine effective theory methods with the analysis of decay topologies and flavor symmetry relations and to increase the precision of the predicted amplitudes of two and three-body nonleptonic decays of bottomed (B) and charmed (D) mesons. For the two-body decays the emphasis is on achieving a quantitatively new level of accuracy. To this end we follow two approaches. On the one hand corrections to factorization theorems will be calculated in the effective theory framework, notably QCD factorization elaborated within Soft-Collinear Effective Theory. Besides higher-order perturbative (multi-loop) corrections, we will focus on contributions that are power-suppressed with respect to the inverse of the heavy quark mass. On the other hand we will make use of flavour symmetries and their breaking. By means of group-theoretical parameterizations of flavor symmetries we will derive amplitude relations which will be used for a model-independent description of the observables in these decays. One of the major goals is to quantify the final-state rescattering phases in two-body nonleptonic B-decays. Three-body decays offer ideal opportunities to search for CP violation in differential distributions. Therefore, the main effort will be aimed at phenomenological models for the Dalitz-distributions of the final states. Besides the more formal aspects such as the validity of factorization theorems at higher orders of the perturbative expansion, we will also perform dedicated phenomenological analyses which update and improve the theory predictions for nonleptonic B- and D-decays into light – in the case of B-mesons also into heavy – final states. In doing so, we will use updated and improved input parameters as well as reliable estimates for the universal hadronic matrix elements, derived from nonperturbative methods such as QCD sum rules and light-cone sum rules. Compared to nonleptonic B-decays, D-decays provide an important complementary test of CP violation within the SM. Since the mass of the charm quark is smaller than the mass of the bottom quark, and hence is further away from the heavy-mass limit, the theoretical description of D-meson decays is expected to be shaped by enhanced power corrections, which have to be carefully investigated and quantified.