Nuclear modifications on longitudinal-transverse structure-function ratio $R$ in the deuteron

Abstract

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.