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arXiv 1503.06329hep-lathep-phnucl-th
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核子两点和三点关联函数的手征修正

Chiral Corrections to Nucleon Two- and Three-Point Correlation Functions

Brian C. Tiburzi

备注：
18 pages, 3 figures, v.2 comparison with arXiv:1503.03649 added, v.3 phase-space argument corrected
发表信息：
Phys. Rev. D 91, 094510 (2015)
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摘要：

我们从手征动力学的角度考虑多粒子对核子二点和三点函数的贡献。格点核子插值算子具有明确的手征变换性质，可以映射到手征微扰论中。使用最常见的这样的运营商，我们确定π介子核子和π介子三角洲耦合核子两点和三点关联函数在领导为了在低能量的扩展。根据莱曼谱表示，两点函数中π介子与核子和δ的耦合与简单的相空间考虑是一致的。基于环面上的可用相空间的参数被用来导出多π介子耦合的标度。虽然多π介子态确实被抑制，但与无限体积相比，这种抑制与粒子数的比例不同。对于核子三点关联函数，我们研究了动量转移消失时的轴矢量流。研究了π-核子和π-δ态对核子轴向电荷提取的影响。我们表明，耦合到有限体积多粒子状态可能会导致高估的轴向电荷。因此，π介子-核子激发态不能解释在格点量子色动力学计算核子轴向电荷时所看到的趋势。

英文摘要：

We consider multi-particle contributions to nucleon two- and three-point functions from the perspective of chiral dynamics. Lattice nucleon interpolating operators, which have definite chiral transformation properties, can be mapped into chiral perturbation theory. Using the most common of such operators, we determine pion-nucleon and pion-delta couplings to nucleon two- and three-point correlation functions at leading order in the low-energy expansion. The couplings of pions to nucleons and deltas in two-point functions are consistent with simple phase-space considerations, in accordance with the Lehmann spectral representation. An argument based on available phase space on a torus is utilized to derive the scaling of multiple-pion couplings. While multi-pion states are indeed suppressed, this suppression scales differently with particle number compared to that in infinite volume. For nucleon three-point correlation functions, we investigate the axial-vector current at vanishing momentum transfer. The effect of pion-nucleon and pion-delta states on the extraction of the nucleon axial charge is assessed. We show that couplings to finite volume multi-particle states could potentially lead to overestimation of the axial charge. Hence pion-nucleon excited states cannot explain the trend seen in lattice QCD calculations of the nucleon axial charge.

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