arXiv 2303.112852023-03hep-phhep-lat

由幺正性和解析性约束的形状因子拟合的贝叶斯推断

Bayesian inference for form-factor fits regulated by unitarity and analyticity

J. M. Flynn, A. Jüttner, J. T. Tsang

备注：: 46 pages, 8 figures, version as published in JHEP with updated references, extended discussion of the truncation dependence (Sec. 3.4) and the asymptotic behaviour of the BGL expansion (App. C)

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AI总结：

提出一种基于幺正性和解析性的贝叶斯框架，用于模型无关地拟合强子形状因子数据，并应用于$B_s\to K \nu$衰变，预测$|V_{ub}|$等物理量。

摘要：

我们提出一个模型无关的框架，用于拟合强子形状因子数据，这些数据通常仅在离散的运动学点上可用，该框架基于由幺正性和解析性约束的参数化。在这种新方法中，量子场论的这两个性质规范了不适定的拟合问题，并允许在整个物理范围内进行模型无关的预测。运动学约束，例如半轻子介子衰变中的矢量和标量形状因子，可以精确施加。核心公式易于使用标准数学库实现。我们考虑了原始Boyd-Grinstein-Lebed（BGL）幺正性约束的推广，并演示了我们的方法在独占半轻子衰变$B_s\to K \nu$中的应用，为此我们做出了若干与现象学相关的预测，包括CKM矩阵元$|V_{ub}|$。

英文摘要：

We propose a model-independent framework for fitting hadronic form-factor data, which is often only available at discrete kinematical points, using parameterisations based on to unitarity and analyticity. In this novel approach the latter two properties of quantum-field theory regulate the ill-posed fitting problem and allow model-independent predictions over the entire physical range. Kinematical constraints, for example for the vector and scalar form factors in semileptonic meson decays, can be imposed exactly. The core formulae are straight-forward to implement with standard math libraries. We take account of a generalisation of the original Boyd Grinstein Lebed (BGL) unitarity constraint for form factors and demonstrate our method for the exclusive semileptonic decay $B_s\to K \ell ν$, for which we make a number of phenomenologically relevant predictions, including the CKM matrix element $|V_{ub}|$.

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