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arXiv 2106.13616hep-phhep-ex
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根据NLO的光锥求和规则计算带电和中性$\bar B_{u,d,s} \to γ$形状因子

Charged and Neutral $\bar B_{u,d,s} \to γ$ Form Factors from Light Cone Sum Rules at NLO

Tadeusz Janowski, Ben Pullin, Roman Zwicky

摘要:

我们提出了第一个分析${\cal O}(α_s)$ -计算在扭转$1$,$2$的$\bar B_{u,d,s} \to γ$形状因子的框架内的总和规则的光锥。这些形状因子描述了带电衰减$\bar B_u \to γ\ell^- \barν$,有助于味道改变中性电流$\bar B_{d,s} \to γ\ell^+ \ell^-$,并用作更复杂过程的输入。我们提供了一个适合的$z$ -扩展相关矩阵和外推的形状因子的运动学端点通过使用$g_{BB^*γ}$耦合作为约束。分析结果以多个多边形作为辅助文件。我们给出了分组预测的$\bar B_u \to γ\ell^- \barν$分支比以及相关的相关矩阵。通过与三种SCET计算结果的比较,我们提取了逆矩$B$介子分布振幅参数$λ_B = 360 (110) \text{MeV}$。其不确定性可以通过更专门的分析来改善。顺便说一下,我们扩展了光子分布振幅,包括夸克质量修正与磁真空磁化率,$χ_q$,与扭曲膨胀兼容的处方。获得值$χ_q = 3.21 (15) \text{GeV}^{-2}$和$χ_s = 3.79 (17) \text{GeV}^{-2}$。

英文摘要:

We present the first analytic ${\cal O}(α_s)$-computation at twist-$1$,$2$ of the $\bar B_{u,d,s} \to γ$ form factors within the framework of sum rules on the light-cone. These form factors describe the charged decay $\bar B_u \to γ\ell^- \barν$, contribute to the flavour changing neutral currents $\bar B_{d,s} \to γ\ell^+ \ell^-$ and serve as inputs to more complicated processes. We provide a fit in terms of a $z$-expansion with correlation matrix and extrapolate the form factors to the kinematic endpoint by using the $g_{BB^*γ}$ couplings as a constraint. Analytic results are available in terms of multiple polylogarithms as ancillary files. We give binned predictions for the $\bar B_u \to γ\ell^- \barν$ branching ratio along with the associated correlation matrix. By comparing with three SCET-computations we extract the inverse moment $B$-meson distribution amplitude parameter $λ_B = 360 (110) \text{MeV}$. The uncertainty thereof could be improved by a more dedicated analysis. In passing, we extend the photon distribution amplitude to include quark mass corrections with a prescription for the magnetic vacuum susceptibility, $χ_q$, compatible with the twist-expansion. The values $χ_q = 3.21 (15) \text{GeV}^{-2}$ and $χ_s = 3.79 (17) \text{GeV}^{-2}$ are obtained.

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