Abstract The anti-kaon nucleon scattering lengths resulting from a Hamiltonian effective field theory analysis of experimental data and lattice QCD studies are presented. The same Hamiltonian is then used to compute the scattering length for the K − d system, taking careful account of the effects of recoil on the energy at which the K ¯ N T-matrices are evaluated. These results are then used to estimate the shift and width of the 1S levels of anti-kaonic hydrogen and deuterium. The K − p result is in excellent agreement with the SIDDHARTA measurement. In the K − d case the imaginary part of the scattering length and consequently the width of the 1S state are considerably larger than found in earlier work. This is a consequence of the effect of recoil on the energy of the K ¯ N energy, which enhances the role of the Λ ( 1405 ) resonance.

中文翻译：

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哈密​​顿有效场论中的 Kaonic 氢和氘

摘要 提出了由哈密顿有效场论分析实验数据和晶格 QCD 研究得出的反 kaon 核子散射长度。然后使用相同的哈密顿量来计算 K - d 系统的散射长度，仔细考虑反冲对评估 K ¯ N T 矩阵的能量的影响。然后将这些结果用于估计反 kaonic 氢和氘的 1S 能级的偏移和宽度。K - p 结果与 SIDDHARTA 测量非常一致。在 K - d 情况下，散射长度的虚部以及因此 1S 状态的宽度比早期工作中发现的要大得多。这是反冲对K¯N能量的影响的结果，它增强了Λ(1405)共振的作用。