arXiv 1105.60082011-05hep-phhep-th

全息QCD的光子-π介子跃迁形状因子和π介子分布振幅

Photon-to-pion transition form factor and pion distribution amplitude from holographic QCD

Fen Zuo, Tao Huang

备注：: a few typos corrected, references added, version published in EPJC
发表信息：: Eur. Phys. J. C (2011) 72:1813
DOI：: 10.1140/epjc/s10052-011-1813-0

摘要：

我们试图理解最近在全息QCD方法中观察到的光子-π介子跃迁形状因子的反常行为。首先回顾了反常γ^*γ^*π^0形状因子的全息描述，并将其应用于各种模型。结果表明，在描述反常形状因子时，全息方法与微扰QCD（pQCD）框架是渐近对偶的，π（z）\sim z对应于渐近π分布振幅.这表明在光前全息中存在一些不一致性，因为π（z）\sim z在那里与φ（x）\sim \sqrt{x(1-x)}是对偶的。在澄清这些微妙之处后，我们采用全息和微扰表达式之间的关系来研究可能的过渡形状因子的渐近破坏。结果表明，如果要求渐近形状因子具有类似pQCD的表达式，则π模只能被对数因子紫外增强。最小变形的π介子模的形式为π（z）\sim z \ln（zΛ）^{-1}。我们假设这种形变可能是由于π介子与非平凡的开弦快子场的耦合引起的，那么参数$Λ$将与夸克凝聚有关。有趣的是，这种π介子模式直接导致了拉久什金的对数模型，该模型在大Q ^2区域非常符合实验数据。另一方面，Radyushkin和Polyakov提出的具有类平坦π介子分布振幅的pQCD解释不具有全息表达式。

英文摘要：

We try to understand the recently observed anomalous behavior of the photon-to-pion transition form factor in the holographic QCD approach. First the holographic description of the anomalous γ^*γ^*π^0 form factor is reviewed and applied to various models. It is illustrated that in describing the anomalous form factor, the holographic approach is asymptotically dual to the perturbative QCD (pQCD) framework, with the pion mode π(z)\sim z corresponding to the asymptotic pion distribution amplitude. This indicates some inconsistency in light-front holography, since π(z)\sim z would be dual to φ(x)\sim \sqrt{x(1-x)} there. After clarifying these subtleties, we employ the relation between the holographic and the perturbative expressions to study possible asymptotic violation of the transition form factor. It is found that if one require that the asymptotic form factor possess a pQCD-like expression, the pion mode can only be ultraviolet-enhanced by logarithmic factors. The minimally deformed pion mode will then be of the form π(z)\sim z\ln (zΛ)^{-1}. We suppose that this deformation may be due to the coupling of the pion with a nontrivial open string tachyon field, and then the parameter $Λ$ will be related to the quark condensate. Interestingly, this pion mode leads immediately to Radyushkin's logarithmic model, which fitted very well the experimental data in the large-Q^2 region. On the other side, the pQCD interpretation with a flat-like pion distribution amplitude, proposed by Radyushkin and Polyakov, fails to possess a holographic expression.

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