[论文解读] Second Order QED Processes in an Intense Electromagnetic Field

A. Hartin|arXiv (Cornell University)|Jan 11, 2017

Particle Accelerators and Free-Electron Lasers参考文献 17被引用 9

一句话总结

本文通过解析与数值方法，研究了在强圆偏振电磁场中二级量子电动力学（QED）过程——康普顿散射与$e^+e^-$对产生。推导了微分散射截面的一般表达式，识别出由外场修正电子自能引起的截面共振，并表明在共振时截面增强数个数量级，总截面随场强增加至$u^2 \sim 1$时持续上升，此时非线性效应占主导地位。

ABSTRACT

Some non linear, second order QED processes in the presence of intense plane electromagnetic waves are investigated. Analytic expressions with general kinematics are derived for Compton scattering and $e^+e^-$ pair production in a circularly polarised external electromagnetic field. The differential cross sections were investigated numerically for photon energies up to 50 MeV, external field intensity parameter $ν^2$ to value 2, and all scattering angles. The variation of full cross sections with respect to external field intensity was also established. The presence of the external field led to resonances in the Compton scattering and pair production differential cross sections. These resonances were investigated by calculating the electron self energy in the presence of the external field. At resonance the differential cross sections were enhanced by several orders of magnitude. The resonances occurred for values of external field intensity parameter $ν^2 <1$, lowering the limit of $ν^2 \sim 1$ at which point non linear effects in first order external field QED processes become important. Generally, full cross sections increased with increasing external field intensity, though peaking sharply for Compton scattering and levelling off for pair production. An application was made to non linear background studies at $e^+e^-$ linear colliders. The pair production process and electron self energy were studied for the case of a constant crossed electromagnetic field. It was found that previous analytic expressions required the external field to be azimuthally symmetric. New analytic expressions for the more general non azimuthally symmetric case were developed and a numerical parameter range equivalent to that proposed for future linear collider designs was considered.

研究动机与目标

• 推导在强圆偏振电磁场下二级QED过程——康普顿散射与$e^+e^-$对产生——的一般解析表达式。
• 研究外场修正电子自能在外场中生成微分散射截面共振的作用。
• 通过发展适用于非轴对称场的新表达式，拓展先前的解析处理，尤其适用于未来$e^+e^-$直线对撞机。
• 量化总截面与微分散射截面对外场强度参数$\nu^2$的依赖关系，特别是在共振附近。
• 评估这些共振过程对对撞机实验中非线性本底贡献的影响，尤其在未来的直线对撞机设计中。

提出的方法

• 利用Volkov解计算外场中电子的矩阵元与相空间积分，研究受激康普顿散射（SCS）与受激双光子对产生（STPPP）。
• 应用Wick定理与S矩阵理论计算跃迁振幅，通过束缚电子传播幅引入外场影响。
• 采用外场电子能级位移（EFEES）形式化方法分析共振条件，自能以包含谱函数的色散关系表达。
• 对动量与角变量进行数值积分，计算光子能量达50 MeV、$\nu^2$达2范围内的微分散射截面与总截面。
• 通过推广场相互作用的傅里叶变换，提出一种适用于非轴对称场的新解析框架，并在已知轴对称极限下得到验证。
• 应用光学定理与重整化技术，确保自能与截面计算的一致性与有限性。

实验结果

研究问题

• RQ1 康普顿散射与$e^+e^-$对产生的微分散射截面与总截面如何依赖于外场的强度与偏振？
• RQ2 这些二级QED过程中微分散射截面中观察到的共振的起源与结构是什么？
• RQ3 强外场中电子自能如何改变动力学阈值与共振宽度，与自由场情况相比有何不同？
• RQ4 非轴对称外场（如恒定交叉场）在多大程度上改变截面，相较于对称近似？
• RQ5 在实际对撞机场构型下，共振对产生截面的大小如何？它们对未来$e^+e^-$直线对撞机中背景估计有何影响？

主要发现

• 康普顿散射与$e^+e^-$对产生的共振微分散射截面相比非共振过程增强了最多5至6个数量级。
• 共振出现在外场强度参数$\nu^2 < 1$时，相较于先前假设的$\nu^2 \sim 1$，非线性效应的阈值降低。
• 康普顿散射的总截面随$\nu^2$迅速增加，在共振附近达到峰值，而对产生截面在高场强下趋于平缓。
• 对圆偏振场中电子自能的数值评估与先前结果在适当极限下一致，验证了该形式化方法的正确性。
• 对于恒定交叉电磁场，新推导的非轴对称场解析表达式可准确建模未来直线对撞机设计中外场效应。
• 在束流场中，共振对产生截面比非共振情况高出5至6个数量级，显著增加了预期的本底粒子产生率。