协变规范旋量幅对于部分波分析
Covariant canonical-spinor amplitudes for partial wave analysis
AI总结：
本文提出一种协变旋量幅方法，用于部分波分析，通过质量旋量螺旋形式实现自旋-轨道分解，验证其在复杂衰变链分析中的实用性。
摘要：
我们提出了一种协变轨道-自旋（LS）分解幅，用于部分波分析，采用质量旋量螺旋形式。首先我们回顾了传统-LS方法在小群空间中的方法，以及在SO(3)空间的双覆盖中的Zemach张量方法。为了恢复SO(3,1)洛伦兹协变性，已经构建了几种洛伦兹协变LS张量，通过几种不同的方法：协变张量、纯旋和一般旋方案中的协变投影张量，但进行内在分离LS耦合同时保持协变性并不明显。我们利用质量规范旋量变量来确定一般的三点幅，其中自旋-轨道分解在单个小群空间中通过将每个粒子的小群索引投影到一个中实现，而洛伦兹协变性则通过旋量形式自然保证。这种协变旋量方法允许在任何框架中直接评估，并在单一框架内流线型处理级联衰变，而无需在非协变处理中进行额外的对齐旋转。作为基准，我们在TF-PWA中实现该方法，并分析Λ_c^+→Λπ^+π^0，发现在 helicity、传统-LS 和 canonical-spinor 幅度之间的一致拟合结果。这验证了 canonical-spinor 幅度作为现代复杂衰变链部分波分析实用工具的可行性。
英文摘要：
We propose a covariant orbital-spin ($LS$) decomposed amplitude for the partial wave analysis using the massive spinor-helicity formalism. First we review the traditional-$LS$ method in the little group space and the Zemach tensor method in the double cover of the $\mathrm{SO}(3)$ space. To recover the $\mathrm{SO}(3,1)$ Lorentz covariance, several Lorentz covariant $LS$ tensors have been constructed in several different methods: covariant tensor, covariant projection tensor in pure-spin and general-spin schemes, but performing a intrinsic separation between $LS$ coupling while maintaining covariance is not obvious. We utilize the massive canonical-spinor variables to determine general three-point amplitudes, in which the spin-orbital decomposition is realized in single little group space by projecting little group indices of each particles into one, while the Lorentz covariance is ensured by the spinor form naturally. This covariant spinor method allows direct evaluation in any frame and a streamlined treatment of cascade decays within a single frame without additional alignment rotations in non-covariant treatment. As a benchmark, we implement the method in TF-PWA and analyze $Λ_c^+\toΛπ^+π^0$, finding consistent fit results across the helicity, traditional-$LS$, and canonical-spinor amplitudes. This validates the canonical-spinor amplitude as a practical tool for modern partial wave analyses of complex decay chains.
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