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arXiv 1202.2145hep-lathep-ph
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格点量子色动力学中两个总动量不为零的不同质量粒子的散射相移

Scattering phase shifts for two particles of different mass and non-zero total momentum in lattice QCD

Luka Leskovec, Sasa Prelovsek

备注：
26 pages, 3 figures, version to appear in PRD; a list of meson-meson interpolators added; Figure 1 presenting an example of spectrum added
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摘要：

导出了有限盒中散射相移与两粒子能量的关系，这对格点量子色动力学中强相移的提取是有意义的。在格点坐标系中考虑两个总动量不为零的不同质量粒子的弹性散射。这是一个推广的Luscher公式，它考虑零总动量，和推广的Rummukainen-Gottlieb公式，它考虑退化粒子与非零总动量。我们着重讨论了实际中最相关的总动量，即P=（2π/L）ez和P=（2π/L）（ex + ey），包括它们的倍数和排列。我们发现，当l>=2时的相移可以忽略不计时，P波相移可以可靠地从两粒子能量中提取出来，并给出了相应的关系式。S波相移的可靠提取更具挑战性，因为delta（l=0）总是伴随着delta（l=1）的相移关系，我们提出了估计delta（l=0）的策略。我们还提出了夸克-反夸克和介子-介子插值变换根据考虑的不可约表示。

英文摘要：

We derive the relation between the scattering phase shift and the two-particle energy in the finite box, which is relevant for extracting the strong phase shifts in lattice QCD. We consider elastic scattering of two particles with different mass and with non-zero total momentum in the lattice frame. This is a generalization of the Luscher formula, which considers zero total momentum, and the generalization of Rummukainen-Gottlieb's formula, which considers degenerate particles with non-zero total momentum. We focus on the most relevant total momenta in practice, i.e. P=(2π/L) e_z and P=(2π/L) (e_x+e_y) including their multiples and permutations. We find that the P-wave phase shift can be reliably extracted from the two-particle energy if the phase shifts for l>=2 can be neglected, and we present the corresponding relations. The reliable extraction of S-wave phase shift is much more challenging since delta(l=0) is always accompanied by delta(l=1) in the phase shift relations, and we propose strategies for estimating delta(l=0). We also propose the quark-antiquark and meson-meson interpolators that transform according the considered irreducible representations.

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