arXiv 2203.048642022-03hep-phnucl-th

次领先阶Weinberg关系下S波弱束缚态的复合性

Compositeness of S-wave weakly-bound states from next-to-leading order Weinberg's relations

M. Albaladejo, J. Nieves

备注：: Reviewed version matching the published one
发表信息：: Eur. Phys. J. C82, 724 (2022)
DOI：: 10.1140/epjc/s10052-022-10695-1

摘要：

我们讨论了一个模型独立的估计的可能性的复合浅S波束缚或虚拟状态。该方法是基于Weinberg在Phys.Rev.137，B672（1965）中的关系的扩展，它只依赖于态能量与它显著耦合的两个强子阈值的接近程度。该方案只利用了实验散射长度和有效射程低能参数，并且对主要是分子强子的情况是完全一致的。作为显式应用，我们分析的情况下，氘核，$^1{\rm S}_0$核子核子虚态和异国情调的$D^{\ast}_{s0}(2317)^\pm$，并找到强有力的支持，在所有情况下的分子解释。对于$D^{\ast}_{s0}(2317)^\pm$，结果不太确定，因为这种状态的结合能明显高于氘核的结合能，并且这里采用的方法处于其适用性的极限。我们还定性地解决了最近发现的$T_{cc}^+$状态的情况下，在同位旋极限，以避免非常接近的阈值$D^0D^{\ast +}$和$D^+D^{\ast 0}$，这可能会掩盖在这项工作中提出的方法的成分的复杂性。

英文摘要：

We discuss a model-independent estimator of the likelihood of the compositeness of a shallow S-wave bound or virtual state. The approach is based on an extension of Weinberg's relations in Phys. Rev. 137, B672 (1965) and it relies only on the proximity of the energy of the state to the two-hadron threshold to which it significantly couples. The scheme only makes use of the experimental scattering length and the effective range low energy parameters, and it is shown to be fully consistent for predominantly molecular hadrons. As explicit applications, we analyse the case of the deuteron, the $^1{\rm S}_0$ nucleon-nucleon virtual state and the exotic $D^{\ast}_{s0}(2317)^\pm$, and find strong support to the molecular interpretation in all cases. Results are less conclusive for the $D^{\ast}_{s0}(2317)^\pm$, since the binding energy of this state is significantly higher than that of the deuteron, and the approach employed here is at the limit of its applicability. We also qualitatively address the case of the recently discovered $T_{cc}^+$ state, within the isospin limit to avoid the complexity of the very close thresholds $D^0D^{\ast +}$ and $D^+D^{\ast 0}$, which could mask the ingredients of the approach proposed in this work.

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