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arXiv 2402.14715hep-lathep-phnucl-th
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从格点QCD研究$T_{cc}^+$的夸克质量依赖性

Towards the quark mass dependence of $T_{cc}^+$ from lattice QCD

Sara Collins, Alexey Nefediev, M. Padmanath, Sasa Prelovsek

备注：
18 pages, 17 figures, 3 tables, version to appear in Phys.Rev.D
发表信息：
Phys.Rev.D 109 (2024) 9, 094509
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AI总结：

本文通过格点QCD计算不同粲夸克质量下$T_{cc}^+$道中$DD^*$散射相移，结合有效力程展开和有效场论分析极点轨迹，揭示了$T_{cc}^+$从阈下共振到虚态再到束缚态的演化机制。

摘要：

在$T_{cc}^+=cc\bar{u}\bar{d}$道中，从格点QCD提取了五种不同粲夸克质量下的$DD^*$散射相移，轻夸克质量固定为$m_π\simeq 280$ MeV。采用两种方法分析相移：有效力程展开和有效场论中导出的Lippmann-Schwinger方程。后一种方法的结果表明，短程存在由接触项参数化的吸引，长程存在由单π交换介导的轻微排斥，其中$m_π>m_{D^*}-m_D$。提取了复能量平面上振幅的极点，并讨论了其轨迹随粲夸克质量的变化。在$m_c$接近物理值时，发现了两个复共轭极点，对应于阈下共振。在所研究的最大$m_c$处，它们变成一对虚态。随着$m_c$进一步增大，代表$T_{cc}^+$的一个虚极点预期会向两体阈值移动并转变为束缚态。利用其他格点合作组关于$DD^*$散射的数据，简要讨论了$T_{cc}^+$极点的轻夸克质量依赖性。

英文摘要：

The $DD^*$ scattering phase shifts in the $T_{cc}^+=cc\bar{u}\bar{d}$ channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to $m_π\simeq 280$~MeV. The phase shifts are analysed employing two approaches: effective range expansion and Lippmann--Schwinger equation derived in the effective field theory. In the latter case, the results imply an attraction at short range parametrised by contact terms and a slight repulsion at long range mediated by one-pion exchange with $m_π>m_{D^*}-m_D$. The poles in the amplitude across the complex energy plane are extracted and their trajectories are discussed as the charm quark mass is varied. Two complex conjugate poles corresponding to a resonance below threshold are found for $m_c$ close to the physical value. They turn into a pair of virtual states at the largest $m_c$ studied. With further increasing $m_c$, one virtual pole representing $T_{cc}^+$ is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the $T_{cc}^+$ pole is briefly discussed using the data on $DD^*$ scattering from other lattice collaborations.

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