arXiv 2103.019662021-03hep-phhep-exnucl-th

关于弹性区域以外的标量$πK$形状因子

On the scalar $πK$ form factor beyond the elastic region

Leon von Detten, Frederic Noël, Christoph Hanhart, Martin Hoferichter, Bastian Kubis

备注：: 18 pages, 12 figures; journal version
发表信息：: Eur. Phys. J. C 81 (2021) 420
DOI：: 10.1140/epjc/s10052-021-09169-7

摘要：

介子-K介子（PDMATHAMM）对经常出现在重粒子衰变的末态。因此，在广泛的能量范围内对$πK$散射和产生振幅进行一致的处理对于多种应用是强制性的：在标准模型测试中;描述在寻求奇异强子态时的交叉通道;以及改进激发的K介子共振的光谱。在弹性区域中，在给定的分波中的$πK$散射的相移通过沃森定理与相应的$πK$形状因子的相位相关。除此之外，我们在这里构建了一个表示的标量$πK$形状因子，包括通过共振交换的非弹性效应，同时满足所有的约束$πK$散射和保持正确的分析结构。作为第一个应用程序，我们考虑衰减${τ\to K_Sπν_τ}$，特别是，我们研究在何种程度上的$S$波$K_0^*(1430)$和$P$波$K^*(1410)$共振可以区分，并提供一个改进的估计的$CP$不对称产生的张量操作。最后，我们通过Padé近似，$\sqrt{s_{K_0^*(1430)}}=[1408(48)-i\, 180(48)]$ MeV和$\sqrt{s_{K_0^*(1950)}}=[1863(12)-i\,136(20)]$ MeV，以及极残基，提取了$K_0^*(1430)$和$K_0^*(1950)$共振的极参数。该方法的推广也使我们能够正式定义一个分支分数${τ\to K_0^*(1430) ν_τ}$在相应的残基，导致上限${\text{BR}(τ\to K_0^*(1430) ν_τ)<1.6 \times 10^{-4}}$。

英文摘要：

Pion-kaon ($πK$) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of $πK$ scattering and production amplitudes over a wide energy range is therefore mandatory for multiple applications: in Standard Model tests; to describe crossed channels in the quest for exotic hadronic states; and for an improved spectroscopy of excited kaon resonances. In the elastic region, the phase shifts of $πK$ scattering in a given partial wave are related to the phases of the respective $πK$ form factors by Watson's theorem. Going beyond that, we here construct a representation of the scalar $πK$ form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from $πK$ scattering and maintaining the correct analytic structure. As a first application, we consider the decay ${τ\to K_Sπν_τ}$, in particular, we study to which extent the $S$-wave $K_0^*(1430)$ and the $P$-wave $K^*(1410)$ resonances can be differentiated and provide an improved estimate of the $CP$ asymmetry produced by a tensor operator. Finally, we extract the pole parameters of the $K_0^*(1430)$ and $K_0^*(1950)$ resonances via Padé approximants, $\sqrt{s_{K_0^*(1430)}}=[1408(48)-i\, 180(48)]$ MeV and $\sqrt{s_{K_0^*(1950)}}=[1863(12)-i\,136(20)]$ MeV, as well as the pole residues. A generalization of the method also allows us to formally define a branching fraction for ${τ\to K_0^*(1430) ν_τ}$ in terms of the corresponding residue, leading to the upper limit ${\text{BR}(τ\to K_0^*(1430) ν_τ)<1.6 \times 10^{-4}}$.

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