QCD analysis of structure functions in deep inelastic neutrino-nucleon scattering without using the orthogonal polynomials approach

A nonsinglet QCD analysis of neutrino-nucleon structure function is performed based on all the data for charged current neutrino-nucleon deep inelastic scattering (DIS) corresponds to NLO and NNLO approximations, with taking into account the nuclear and higher twist corrections. In this analysis, we extract $x{u}_v(x,Q^2)$ and $x{d}_v(x,Q^2)$ valence parton distribution functions (PDFs) in a wide range of $x$ and $Q^2$, and determine their parametrization with the correlated errors using the xFitter framework. Our results regarding valence-quark densities with their uncertainties are compared to the prediction extracted using other PDF sets from different groups. We determine ${\alpha }_s\left(M_Z^2\right)=0.1199\pm 0.0031$ and $0.1185\pm 0.0023$ with considering the nuclear and higher twist corrections at the NLO and NNLO, respectively, and perform a comparison with other reported results. The extracted results regarding valence-quark distributions and the value of ${\alpha }_s\left(M_Z^2\right)$ are in good agreement with available theoretical models.

Figure 1

Different experiments of DIS neutrino-nucleon data in the $x$ and $Q^2$ plane. The dashed line represents the kinematic $W^2$ and $Q^2$ cuts on the data ($Q^2\ge 4{\mathrm{GeV}}^2$ and $W^2\ge 12.5{\mathrm{GeV}}^2$) in this analysis. The data points lying below these lines are only excluded in the present QCD fits.

Figure 2

The comparison of structure function $x{F}_3$ obtained from the fit at NLO and NNLO as a function of $Q^2$ in various $x$ with considering nuclear corrections, by using CCFR [20], NuTeV [21], CHORUS [22], and CDHSW [23] data sets.

Figure 3

The comparison of the structure function $x{F}_3$ obtained from the fit with and without higher twist corrections as a function of $Q^2$ in the various $x$, at NNLO approximation.

Figure 4

The comparison of the proton valence $x{u}_v$ and $x{d}_v$ PDFs as a function of $x$ at $Q^2=1$ ${\mathrm{GeV}}^2$ taking into account nuclear corrections (left) and nuclear and higher twist corrections (right), at NLO and NNLO with their uncertainty bands.

Figure 5

The comparison of the iron valence $x{u}_v^{p/Fe}$ and $x{d}_v^{p/Fe}$ PDFs as a function of $x$ at $Q^2=1$ ${\mathrm{GeV}}^2$ taking into account nuclear corrections (left) and nuclear and higher twist corrections (right), at NLO and NNLO with their uncertainty bands.

Figure 6

$x{u}_v$ valence PDF results at different values of $Q^2=4$, 100, $M_W^2$, and $M_Z^2{\mathrm{GeV}}^2$ obtained with our QCD fits to the DIS neutrino-nucleon data, which have been compared with the results obtained by CT14 [90] and MMHT [91] as a function of $x$ at the NNLO (left panel) and the ratio of $x{u}_v/{\left(x{u}_v\right)}_{\mathrm{ref}}$ (right panel) with respect to NNLO (proton). We show our results only in the range of $x\in [{10}^{-2},0.8]$, where the data existed and were applied in the present analysis.

Figure 7

$x{d}_v$ valence PDF results at different values of $Q^2=4$, 100, $M_W^2$, and $M_Z^2{\mathrm{GeV}}^2$ obtained with our QCD fits to the DIS neutrino-nucleon data, which have been compared with the results obtained by CT14 [90] and MMHT [91] as a function of $x$ at the NNLO (left panel) and the ratio of $x{d}_v/{\left(x{d}_v\right)}_{\mathrm{ref}}$ (right panel) with respect to NNLO (proton). We show our results only in the range of $x\in [{10}^{-2},0.8]$, where the data existed and were applied in the present analysis.

Figure 8

The ${x{u}_v}^{p/Fe}$ and ${x{d}_v}^{p/Fe}$ parton density distribution at the NLO and NNLO with their uncertainty bands as a function of $x$ at different values of $Q^2=4$, 100, $M_W^2$, and $M_Z^2{\mathrm{GeV}}^2$.

Figure 9

The value of ${\alpha }_s\left(M_Z^2\right)$ in comparison with different QCD analyses at NLO A02 [92], MMHT [91], BBG [82], MRST03 [94], H1 [95], ZEUS [96], NMC [97], KKT [51], VK17 [62], ABM11 [2], MSTW [5], NNPDF2.1 [98], ABKM09 [99], CT14 [90], ABMP16 [100], HERAPDF [101], and NNLO A02 [92], A06 [93], MRST03 [94], ABMP16 [100], BBG [82], MMMHT [91], NNPDF [102], JR [103], ABKM09 [99], ABM11 [2], H1 and ZEUS [104], MSTW [5], NMC [97], KKT [51], CT14 [90] approximations. The dotted line with yellow band indicates the preaverage results of the strong coupling constant ${\alpha }_s\left(M_Z^2\right)$ in the DIS subfield [83]. Also, the grey band and dashed line present the world average value of the strong coupling constant ${\alpha }_s\left(M_Z^2\right)$.