氘核中纵向-横向结构函数比 $R$ 的核修正
Nuclear modifications on longitudinal-transverse structure-function ratio $R$ in the deuteron
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中文总结 AI 辅助
本文通过卷积模型研究氘核中纵向-横向结构函数比 $R$ 的核修正，指出核子费米运动导致纵向与横向结构函数混合，并给出数值结果，供实验验证。
中文摘要 AI 辅助
在轻子与原子核的散射中，人们一直理所当然地认为纵向-横向结构函数比 $R$ 不存在核修正，尽管 $F_2$ 中的核效应已被研究了很长时间。事实上，轻子-原子核散射的实验数据一直是在这一假设下进行分析的。这显然是不合适的，因为如本工作所示，理论上函数 $R$ 中存在核修正。在本工作中，我们利用卷积描述来解释核子费米运动的影响，特别是对氘核的影响。纵向和横向结构函数是通过将虚光子动量方向取为 $z$ 轴来定义的。然而，原子核中的核子可以向任意方向运动，因此核子的纵向和横向结构函数在核介质中可能相互混合。这种混合效应可能达到 $\vec p_\perp^{\\,2}/Q^2$ 的量级，其中 $\vec p_\perp$ 是核子的横向动量，$Q^2$ 由 $Q^2=-q^2$ 给出，$q$ 为虚光子动量，因为横向费米运动是这种混合的来源。此外，在卷积模型中，纵向和横向结构函数的核效应不同，因为它们的 $x$ 依赖函数形式不同。对于原子核，纵向和横向结构函数的卷积积分结果不同。由于托马斯·杰斐逊国家加速器实验室正在进行测量氘核函数 $R$ 的实验，我们给出了氘核中 $R$ 的核效应的数值结果。希望未来的实验（包括重核靶）能在实验上发现这些核效应。
英文摘要
In lepton scattering from nuclei, it has been taken for granted that nuclear modifications do not exist for the longitudinal-transverse structure-function ratio $R$, although nuclear effects in $F_2$ have been investigated for a long time. In fact, experimental data of lepton-nucleus scattering have been analyzed with this assumption. It is obviously not appropriate because nuclear modifications exist in the function $R$ theoretically as shown in this work. In this work, we explain nucleon's Fermi motion's effects by using a convolution description for nuclear structure functions, especially on the deuteron. The longitudinal and transverse structure functions are defined by taking the virtual photon momentum direction along the $z$ axis. However, nucleons in a nucleus could move in any direction, so that nucleon's longitudinal and transverse structure functions could mix with each other in the nuclear medium. Such mixing effects could be of the order of $\vec p_\perp^{\,2}/Q^2$, where $\vec p_\perp$ is the nucleon's transverse momentum and $Q^2$ is given by $Q^2=-q^2$ with the virtual-photon momentum $q$, because the transverse Fermi-motion is the source of such a mixture. In addition, nuclear effects are different between the longitudinal and transverse structure functions in the convolution model because their $x$-dependent functional forms are different. Convolution integrals have different results between the longitudinal and transverse structure functions for nuclei. Because the experiment is in progress at the Thomas Jefferson National Accelerator Facility to measure the function $R$ for the deuteron, the numerical results are shown on the nuclear effects of $R$ in the deuteron. Hopefully, such nuclear effects are found experimentally by future experiments including heavy nuclear targets.
