Padé近似下带电π介子磁极化率的手征外推
Chiral extrapolation of the charged-pion magnetic polarizability with Padé approximant
摘要：
格点量子色动力学的背景磁场形式最近被用来计算带电π介子的磁极化率。这些$n_f = 2 + 1$数值模拟是电淬灭的，这样QCD真空中的虚海夸克就不会与背景场相互作用。为了理解这种影响，我们利用部分猝灭的手征微扰理论。在这种情况下，与$1/M_π$成比例的前导项在树级从$\mathcal{L}_4$产生。为了描述格点量子色动力学的结果，在保持手征微扰理论的精确前导项的同时，我们引入了一个Padé近似，用来再现在格点量子色动力学结果中观察到的慢变化.双回路的贡献，以评估与高阶项的扩展的系统的不确定性。外推后，在物理质量下的带电π介子的磁极化率被发现是$β_{π^\pm}=-1.70\,(14)_{\rm stat}(25)_{\rm syst}\times 10^{-4}$ fm $^3$，与最近的实验测量结果吻合得很好。
英文摘要：
The background magnetic-field formalism of Lattice QCD has been used recently to calculate the magnetic polarizability of the charged pion. These $n_f = 2 + 1$ numerical simulations are electro-quenched, such that the virtual sea-quarks of the QCD vacuum do not interact with the background field. To understand the impact of this, we draw on partially quenched chiral perturbation theory. In this case, the leading term proportional to $1/M_π$ arises at tree level from $\mathcal{L}_4$. To describe the results from lattice QCD, while maintaining the exact leading terms of chiral perturbation theory, we introduce a Padé approximant designed to reproduce the slow variation observed in the lattice QCD results. Two-loop contributions are introduced to assess the systematic uncertainty associated with higher-order terms of the expansion. Upon extrapolation, the magnetic polarizability of the charged pion at the physical pion mass is found to be $β_{π^\pm}=-1.70\,(14)_{\rm stat}(25)_{\rm syst}\times 10^{-4}$ fm$^3$, in good agreement with the recent experimental measurement.
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