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arXiv 1306.4038hep-phhep-lat
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共形标度与$m$ -强子的尺寸

Conformal scaling and the size of $m$-hadrons

Luigi Del Debbio, Roman Zwicky

备注：
26pp, 3 figures, version nearly identical to PRD version (added appendix B finite size effects)
发表信息：
Phys. Rev. D 89, 014503 (2014)
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摘要：

红外共形（IR）理论中的标度律由相关算子的临界指数决定。我们已经调查了这些标度律在领导秩序在以前的两篇论文。在这项工作中，我们调查的尺度律的进一步后果，试图确定潜在的签名，可以通过晶格模拟研究。从形状因子的一阶导数出发，我们导出了强子态平均电荷半径在理论中的行为。我们得到了与$\langle r_H^2 \rangle \sim 1/M_H^{2}$一致的$\langle r_H^2 \rangle \sim m^{-2/(1+γ^*_m)}$。在数值模拟中，平均电荷半径可以用作评估物理状态大小的替代观测值，从而评估有限尺寸效应。此外，我们讨论的情况下，共形的，标度不变的，并限制理论利用选择规则在标度尺寸和自旋的特定领域的recruitators在坐标空间中的行为。我们通过线性化重整化群方程来计算相关函数的标度修正。我们发现，这些修正是潜在的大接近的边缘的共形窗口。作为一个应用，我们直接通过其相关器以及通过迹异常计算公式$M_H \sim m^{1/(1+γ_m^*)}$的标度校正。这两个计算被证明是等价的，通过推广的费曼-赫尔曼定理的费米子质量，和规范耦合。

英文摘要：

The scaling laws in an infrared conformal (IR) theory are dictated by the critical exponents of relevant operators. We have investigated these scaling laws at leading order in two previous papers. In this work we investigate further consequences of the scaling laws, trying to identify potential signatures that could be studied by lattice simulations. From the first derivative of the form factor we derive the behaviour of the mean charge radius of the hadronic states in the theory. We obtain $\langle r_H^2 \rangle \sim m^{-2/(1+γ^*_m)}$ which is consistent with $\langle r_H^2 \rangle \sim 1/M_H^{2}$. The mean charge radius can be used as an alternative observable to assess the size of the physical states, and hence finite size effects, in numerical simulations. Furthermore, we discuss the behaviour of specific field correlators in coordinate space for the case of conformal, scale-invariant, and confining theories making use of selection rules in scaling dimensions and spin. We compute the scaling corrections to correlations functions by linearizing the renormalization group equations. We find that these correction are potentially large close to the edge of the conformal window. As an application we compute the scaling correction to the formula $M_H \sim m^{1/(1+γ_m^*)}$ directly through its associated correlator as well as through the trace anomaly. The two computations are shown to be equivalent through a generalisation of the Feynman-Hellmann theorem for the fermion mass, and the gauge coupling.

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