Charged-current deep-inelastic scattering of muon neutrinos (${\nu }_{\mu }$) off ${}^{56}\mathrm{Fe}$

In this paper, we study charged-current deep-inelastic scattering of muon neutrinos off ${}^{56}\mathrm{Fe}$ nuclei by using the Hirai, Kumano, and Saito model. The LHA parton distribution functions (PDFs) - CT10 are used to describe the partonic content of hadrons. Modification of PDFs inside the nuclei is done by using EPPS16 parametrization at next-to-leading order. Target mass correction has also been incorporated in the calculations. We calculate the structure functions $[F_2(x,Q^2)$ and $x{F}_3(x,Q^2)]$, the ratios $[R_2(x,Q^2)=F_2^{{}^{56}\mathrm{Fe}}/F_2^{\text{Nucleon}}$ and $R_3(x,Q^2)=F_3^{{}^{56}\mathrm{Fe}}/F_3^{\text{Nucleon}}]$, and the differential cross sections of ${\nu }_{\mu }$ deep-inelastic scattering off nucleons and ${}^{56}\mathrm{Fe}$ nuclei. We compare the results obtained with measured experimental data. The present theoretical approach gives a good description of data.

Figure 1

Charged current $\nu \text{−}N$ deep-inelastic scattering.

Figure 2

$F_2(x,Q^2)$ with EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30] for ${}^{56}\mathrm{Fe}$ as a function of $Q^2$ for different values of Bjorken variable $x$. The results are compared with measured data of CDHSW [39] and CCFR [40] experiments.

Figure 3

$F_2(x,Q^2)$ with EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30] for ${}^{56}\mathrm{Fe}$ as a function of $Q^2$ for different values of Bjorken variable $x$. The results are compared with measured data of CDHSW [39] and CCFR [40] experiments.

Figure 4

$x{F}_3(x,Q^2)$ with EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30] for ${}^{56}\mathrm{Fe}$ as a function of $Q^2$ for different values of the Bjorken variable $x$. The results are compared with measured data of the CDHSW [39] and CCFR [40] experiments.

Figure 5

$x{F}_3(x,Q^2)$ with EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30] for ${}^{56}\mathrm{Fe}$ as a function of $Q^2$ for different values of the Bjorken variable $x$. The results are compared with measured data of the CDHSW [39] and CCFR [40] experiments.

Figure 6

Ratios (a) $R_2(x,Q^2)=F_2^{{}^{56}\mathrm{Fe}}/F_2^{\text{Nucleon}}$ and (b) $R_3(x,Q^2)=F_3^{{}^{56}\mathrm{Fe}}/F_3^{\text{Nucleon}}$ as a function of Bjorken variable $x$ with EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30] for $Q^2=5.0{\mathrm{GeV}}^2$ and $Q^2=50.0{\mathrm{GeV}}^2$.

Figure 7

$\frac{1}{E}\frac{d^2\sigma }{dxdy}$ for ${}^{56}\mathrm{Fe}$ as a function of inelasticity $y$, for different values of the Bjorken variable $x$ and $E_{{\nu }_{\mu }}=65$ GeV using EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30]. Results are compared with measured data of the CCFR [41] and CDHSW [41] experiments.

Figure 8

$\frac{1}{E}\frac{d^2\sigma }{dxdy}$ for ${}^{56}\mathrm{Fe}$ as a function of inelasticity $y$, for different values of the Bjorken variable $x$ and $E_{{\nu }_{\mu }}=65$ GeV using EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30]. Results are compared with measured data of the CCFR [41] and CDHSW [41] experiments.

Figure 9

$\frac{1}{E}\frac{d^2\sigma }{dxdy}$ for ${}^{56}\mathrm{Fe}$ as a function of inelasticity $y$, for different values of the Bjorken variable $x$ and $E_{{\nu }_{\mu }}=110$ GeV using EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30]. Results are compared with measured data of the CCFR [41] and CDHSW [41] experiments.

Figure 10

$\frac{1}{E}\frac{d^2\sigma }{dxdy}$ for ${}^{56}\mathrm{Fe}$ as a function of inelasticity $y$, for different values of Bjorken variable $x$ and $E_{{\nu }_{\mu }}=110$ GeV using EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30]. Results are compared with measured data of the CCFR [41] and CDHSW [41] experiments.

Figure 11

$\frac{1}{E}\frac{d^2\sigma }{dxdy}$ for ${}^{56}\mathrm{Fe}$ as a function of inelasticity $y$, for different values of Bjorken variable $x$ and $E_{{\nu }_{\mu }}=190$ GeV using EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30]. Results are compared with measured data of the CCFR [41] and CDHSW [41] experiments.

Figure 12

$\frac{1}{E}\frac{d^2\sigma }{dxdy}$ for ${}^{56}\mathrm{Fe}$ as a function of inelasticity $y$, for different values of Bjorken variable $x$ and $E_{{\nu }_{\mu }}=190$ GeV using EPPS16 nuclear corrections [37] at NLO and LHAPDF (CT10) parton distribution functions [30]. Results are compared with measured data of the CCFR [41] and CDHSW [41] experiments.