赝标介子的希尔伯特级数：算符与求和规则
Hilbert Series of Pseudoscalar Mesons: Operators and Sum Rules
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中文总结 AI 辅助
该研究基于希尔伯特级数方法，构造赝标介子的非冗余算符基，纳入标准模型弱相互作用后为重介子弱衰变振幅提供模型无关参数化，推导振幅求和规则并预测额外味恒等式。
中文摘要 AI 辅助
我们采用希尔伯特级数方法，在全局味对称性 $SU(3)_L \ imes SU(3)_R \ imes SU(2)_{L_H} \ imes SU(2)_{R_H}$ 以及 underlying 移位对称的约束下，构造了由赝标介子构成的完整非冗余算符基。我们通过将CKM矩阵元提升为在全局对称下变换的 spurion 场，系统地纳入了标准模型弱相互作用。所得算符基为重介子的两体和三体弱衰变振幅提供了模型无关的参数化，对应的威尔逊系数作为约化强子振幅。我们证明所有振幅求和规则可直接从算符基的结构导出，并提出了一种展开程序，将有效算符与其可能的紫外起源相联系。我们的框架重现了已知的味关系，同时预测了由对称约束算符基产生的额外恒等式。
英文摘要
We construct the complete non-redundant basis of operators built from pseudoscalar mesons using the Hilbert series method, subject to the global flavor symmetry $SU(3)_L \times SU(3)_R \times SU(2)_{L_H} \times SU(2)_{R_H}$, together with the underlying shift symmetry. The SM weak interactions are incorporated systematically by promoting the CKM matrix elements to spurion fields transforming under the global symmetry. The resulting operator basis provides a model-independent parametrization of two- and three-body weak decay amplitudes of heavy mesons, with the corresponding Wilson coefficients serving as reduced hadronic amplitudes. We demonstrate that all amplitude sum rules follow directly from the structure of the operator basis and propose an unfolding procedure that connects the effective operators to their possible ultraviolet origins. Our framework reproduces the known flavor relations while predicting additional identities arising from the symmetry-constrained operator basis.
发表机构
- Indian Institute of Technology Kanpur（坎普尔印度理工学院）
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