高能轻子与原子电子散射的末态相互作用
Final state interactions for high energy scattering off atomic electrons
AI总结：
本文研究高能轻子与原子电子散射中的末态库仑交换效应，证明其经算符重求和后在截面中至少到 O(α^3) 阶均抵消，对精密实验无影响。
摘要：
我们考虑高能轻子与束缚原子电子的散射，主要关注末态相互作用，即出射高能电子与末态中重的带电“碎片”之间交换虚光子的过程。这些效应在对静止自由电子的计算中天然不存在。库仑交换因原子碎片中大量电子的存在而增强，并且不会被碎片中的非相对论速度所压低。我们发现这些交换可以利用算符方法进行重求和，并且在截面层面上至少在 O(α^3) 阶之前相互抵消。此外，我们论证无论是末态还是初态的库仑交换（均因原子中的电子数而增强）在至少 O(α^3) 阶之前都不会影响截面。横波光子与非相对论电子的耦合正比于其很小的速度，而旋转不变性将其贡献压低到 O(α^3) 阶。我们的结果对涉及中微子、电子、正电子和 μ 子与固定靶中原子电子散射的精密实验具有重要意义。
英文摘要：
We consider the scattering of high energy leptons off bound atomic electrons focusing primarily on final state interactions i.e., the exchange of virtual photons between the outgoing energetic electron, and the heavy residual charged "debris" in the final state. These effects are inherently absent from calculations for a free electron at rest. Coulomb exchanges are enhanced by the large number of electrons in the atomic debris, and are unsuppressed by non-relativistic velocities in the debris. We find that these exchanges can be resummed using operator methods, and cancel at the level of the cross section until at least $O(α^3)$. Furthermore, we argue that both final {\it and} initial state Coulomb exchanges (enhanced by the number of electrons in the atom) do not affect the cross section until at least $O(α^3)$. Transverse photon couplings to non relativistic electrons are proportional to their small velocities, and rotational invariance suppresses their contribution to $O(α^3)$. Our results are relevant for precision experiments involving neutrinos, electrons, positrons, and muons scattering off of atomic electrons in a fixed target.
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