Nuclear Corrections in Neutrino-Nucleus Deep Inelastic Scattering and their Compatibility with Global Nuclear Parton-Distribution-Function Analyses

We perform a global ${\chi }^2$ analysis of nuclear parton distribution functions using data from charged current neutrino-nucleus ($\nu A$) deep-inelastic scattering (DIS), charged-lepton–nucleus (${\ell }^{\pm }A$) DIS, and the Drell-Yan (DY) process. We show that the nuclear corrections in $\nu A$ DIS are not compatible with the predictions derived from ${\ell }^{\pm }A$ DIS and DY data. We quantify this result using a hypothesis-testing criterion based on the ${\chi }^2$ distribution which we apply to the total ${\chi }^2$ as well as to the ${\chi }^2$ of the individual data sets. We find that it is not possible to accommodate the data from $\nu A$ and ${\ell }^{\pm }A$ DIS by an acceptable combined fit. Our result has strong implications for the extraction of both nuclear and proton parton distribution functions using combined neutrino and charged-lepton data sets.

Figure 1

Predictions from the compromise fits for the nuclear correction factors $R[F_2^{\ell \mathrm{Fe}}]\simeq F_2^{\ell \mathrm{Fe}}/F_2^{\ell N}$ (a) and $R[F_2^{\nu \mathrm{Fe}}]\simeq F_2^{\nu \mathrm{Fe}}/F_2^{\nu N}$ (b) as a function of $x$ for $Q^2=5{\mathrm{GeV}}^2$. The data points displayed in (a) are from BCDMS and SLAC experiments (for references see 4) and those displayed in (b) come from the NuTeV experiment [10].

Figure 2

$\Delta {\chi }^2/\Delta C_{90}$ as defined in Eq. (3) for the 40 individual data sets. Results are shown for the $w=\frac{1}{2}$-fit (a) and the fit “Ucor5” (b) with $w=1$. The solid and dashed lines indicate the 90% and 99% confidence limits. The highlighted data sets correspond to DIS ${\ell }^{\pm }\mathrm{Fe}$ ($\mathrm{ID}=8$), $\nu \mathrm{Fe}$ ($\mathrm{ID}=35$), and $\overline{\nu }\mathrm{Fe}$ ($\mathrm{ID}=36$).