Proton and deuteron $F_2$ structure function at low $Q^2$

Measurements of the proton and deuteron $F_2$ structure functions are presented. The data, taken at Jefferson Lab Hall C, span the four-momentum transfer range $0.06<Q^2<2.8$ GeV${}^2$ and Bjorken $x$ values from 0.009 to 0.45, thus extending the knowledge of $F_2$ to low values of $Q^2$ at low $x$. Next-to-next-to-leading-order calculations using recent parton distribution functions start to deviate from the data for $Q^2<2$ GeV${}^2$ at the low and high $x$ values. Down to the lowest value of $Q^2$, the structure function is in good agreement with a parametrization of $F_2$ based on data that have been taken at much higher values of $Q^2$ or much lower values of $x$, and which are constrained by data at the photon point. The ratio of the deuteron and proton structure functions at low $x$ remains well described by a logarithmic dependence on $Q^2$ at low $Q^2$.

Figure 1

Comparison of the results for $F_2^p(x,Q^2)$ from the present experiment (E99-118) to the results of other experiments. Both the Rosenbluth-separated data (open red squares) and the model-dependent extracted data (red circles) are shown. The thick dashed curve represents the result of a NNLO calculation based upon the MRST [29] parton distributions including target-mass effects. The solid and dot-dashed curves are the results of the phenomenological paramterization from Refs. [31] and [32], respectively.

Figure 2

Comparison of the results for $F_2^d(x,Q^2)$ from the present experiment (E99-118) to the results of other experiments. Both the Rosenbluth-separated data (open red squares) and the model-dependent extracted data (red circles) are shown. The solid and dot-dashed curves result from multiplying the phenomenological parametrizations shown in Fig. 1 with ($1+F_2^n/F_2^p)/2$ using the NMC parametrization [27] for the ratio $F_2^n/F_2^p$.

Figure 3

$Q^2$ dependence of the ratio $F_2^d/F_2^p$ for some selected $x$ bins. Both the present data and data from previous experiments are shown. The lines are the results of a linear (in $\ln Q^2$) fit of all data described in the text.