Nuclear effects on longitudinal-transverse structure function ratio in the deuteron

TL;DR

This paper investigates the theoretical nuclear modifications of the longitudinal-transverse structure function ratio in the deuteron, revealing small but significant effects due to transverse Fermi motion that are important for precise high-energy nuclear data analysis.

Contribution

It demonstrates the existence of nuclear modifications to the ratio R_N due to transverse Fermi motion using a convolution model, which had been assumed negligible before.

Findings

Nuclear modifications to R_N are of the order of a few percent in the deuteron.

Such modifications are expected to be larger in heavier nuclei.

The effects are relevant for high-precision nuclear physics experiments.

Abstract

Nuclear modifications of the nucleon's structure function $F_2^N$ have been investigated mainly since the discovery of the EMC nuclear effect in 1983, and there were many experimental measurements from the deuteron to a heavy nucleus. Now, the details of the modifications of $F_2^N$ are known from small $x$ to large $x$. On the other hand, it is taken as granted that a nuclear modification does not exist for the longitudinal-transverse structure function ratio $R_N=F_L^N/(2xF_1^N)$. However, such a nuclear modification does exist theoretically. A nucleon in a nucleus moves in any space direction, which is not necessary the longitudinal direction along the virtual-photon momentum in charged-lepton scattering. Because of this transverse Fermi motion, the longitudinal and transverse structure functions mix with the mixture probability proportional to the nucleon's transverse-momentum squared $\vec p_T^{\,\, 2}/Q^2$. In this paper, the nuclear modifications are shown numerically for the deuteron by using a standard convolution description. The magnitude of the modifications is of the order of a few percent in the deuteron; however, they should be large in large nuclei. In handling high-energy nuclear data, such nuclear modifications need to be taken into account for a precise determination of physical quantities. Now, the longitudinal-transverse structure-function ratio and tensor-polarized experiments are under preparation for the deuteron at JLab. We hope that such effects will be confirmed experimentally for not only for the deuteron but also for larger nuclei.