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arXiv 0811.1434hep-ph
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介子核韧致辐射的辐射修正

Radiative corrections to pion-nucleus bremsstrahlung

N. Kaiser, J. M. Friedrich

备注：
15 pages, 16 figures, accepted for publication in European Physical Journal A
发表信息：
Eur.Phys.J.A39:71-80,2009
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摘要：

我们计算了虚π介子康普顿散射$π^- γ^* \to π^- γ$的单光子环辐射修正，在单光子交换近似下，该子过程决定了π介子-核韧致辐射反应$π^- Z\to π^- Z γ$。对环积分的紫外发散和红外发散都进行了量纲正则化处理。从9类贡献单圈图中导出了完全依赖于（小）光子虚性$Q$的${\cal O}(α)$对虚康普顿散射振幅修正的解析表达式$A(s,u,Q)$和$B(s,u,Q)$.这些虚拟辐射校正的红外有限性通过包括低于能量截止$λ$的软光子辐射来实现（以标准方式）。在$π^- γ$质心能量较低的区域，利用π介子-核韧致辐射过程提取π介子的电、磁极化率，发现对$λ=5 $ MeV的辐射修正可达-3%.此外，我们将辐射修正的计算扩展到虚π康普顿散射$π^-γ^* \to π^- γ$，引入了以极化率差$α_π- β_π$形式表示的主导π结构效应。我们的分析结果是特别相关的分析数据的COMPASS实验在欧洲核子研究中心，其目的是在测量的π介子的电和磁的极化率与高统计使用Primakoff效应。

英文摘要：

We calculate the one-photon loop radiative corrections to virtual pion Compton scattering $π^- γ^* \to π^- γ$, that subprocess which determines in the one-photon exchange approximation the pion-nucleus bremsstrahlung reaction $π^- Z\to π^- Z γ$. Ultraviolet and infrared divergencies of the loop integrals are both treated by dimensional regularization. Analytical expressions for the ${\cal O}(α)$ corrections to the virtual Compton scattering amplitudes, $A(s,u,Q)$ and $B(s,u,Q)$, are derived with their full dependence on the (small) photon virtuality $Q$ from 9 classes of contributing one-loop diagrams. Infrared finiteness of these virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $λ$. In the region of low $π^- γ$ center-of-mass energies, where the pion-nucleus bremsstrahlung process is used to extract the pion electric and magnetic polarizabilities, we find radiative corrections up to about -3% for $λ=5 $MeV. Furthermore, we extend our calculation of the radiative corrections to virtual pion Compton scattering $π^-γ^* \to π^- γ$ by including the leading pion structure effect in form of the polarizability difference $α_π- β_π$. Our analytical results are particularly relevant for analyzing the data of the COMPASS experiment at CERN which aims at measuring the pion electric and magnetic polarizabilities with high statistics using the Primakoff effect.

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