arXiv 1109.03962011-09hep-lathep-ph

有限体积中$KD$、$ηD_s$相互作用及$D_{s^* 0}(2317)$共振的性质

The $KD$, $ηD_s$ interaction in finite volume and the nature of the $D_{s^* 0}(2317)$ resonance

A. Martínez Torres, L. R. Dai, C. Koren, D. Jido, E. Oset

备注：: Published version
DOI：: 10.1103/PhysRevD.85.014027

摘要：

本文将耦合通道中手征幺正理论的SU（4）外推法推广到有限体积中，得到了手征幺正理论在粲扇形标量介子中的结果。无限体积中的理论通过耦合通道$KD$、$ηD_s$动态地产生$D_{s^*0}(2317)$共振。在有限的盒子中的能级进行评估，并假设它们将对应于晶格的结果，从晶格数据中的无限体积中确定的束缚态和相移的逆问题被解决。我们观察到，它是可能的，以获得准确的$KD$相移和位置的$D_{s^*0}(2317)$状态，但它需要明确考虑的两个耦合通道的分析，如果一个去接近的$ηD_s$阈值。当$D_{s^*0}(2317)$是两个介子的复合态时，或当它对应于一个与两个介子系统有小重叠的非分子态时，有限体积谱看起来有很大的不同.然后，我们表明，仔细分析的有限体积数据可以揭示一些光的性质的$D_{s^*0}(2317)$共振作为一个$KD$分子或其他。

英文摘要：

An SU(4) extrapolation of the chiral unitary theory in coupled channels done to study the scalar mesons in the charm sector is extended to produce results in finite volume. The theory in the infinite volume produces dynamically the $D_{s^*0}(2317)$ resonance by means of the coupled channels $KD$, $ηD_s$. Energy levels in the finite box are evaluated and, assuming that they would correspond to lattice results, the inverse problem of determining the bound states and phase shifts in the infinite volume from the lattice data is addressed. We observe that it is possible to obtain accurate $KD$ phase shifts and the position of the $D_{s^*0}(2317)$ state, but it requires the explicit consideration of the two coupled channels in the analysis if one goes close to the $ηD_s$ threshold. We also show that the finite volume spectra look rather different in case the $D_{s^*0}(2317)$ is a composite state of the two mesons, or if it corresponds to a non molecular state with a small overlap with the two meson system. We then show that a careful analysis of the finite volume data can shed some light on the nature of the $D_{s^*0}(2317)$ resonance as a $KD$ molecule or otherwise.

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