Ms
Huma Haider
(Aligarh Muslim University)Prof.
M.Sajjad Athar
(Aligarh Muslim University)

We shall present the results for the ratio of weak nuclear structure functions $\frac{F_{2}^{A}}{F_{2}^{proton}}$ and $\frac{F_{3}^{A}}{F_{3}^{proton}}$,
where A is the different nuclear targets like $_1^2D$, CH, $H_{2}O$, $^{56}Fe$ and $^{208}Pb$ which are being used in the ongoing Miner$\nu$A experiment at Fermilab.
We have studied these nuclear structure functions
using relativistic nuclear spectral function which incorporate Fermi motion,
nuclear binding, and nucleon correlations. We have also included the pion and rho meson cloud contributions calculated
from a microscopic model for meson-nucleus self-energies. Shadowing and anti-shadowing effects have also been taken into account.
The deuteron structure functions have been calculated using
the same formulas as used for the weak nuclear structure functions, but performing the
convolution with the deuteron wave function squared instead
of the spectral function. For the numerical calculations,
parton distribution functions for the nucleons have been taken from the parametrization of
CTEQ Collaboration (CTEQ6.6) and we have performed the calculations at LO as well as at NLO.
The details of the model are given in Refs.
1. $\nu(\bar\nu)$-208Pb deep inelastic scattering.
H. Haider, I. Ruiz Simo and M. Sajjad Athar
Phys. Rev. C 85 (2012) 055201.
2. Nuclear medium effects in $\nu(\bar\nu)$-nucleus deep inelastic scattering.
H. Haider, I. Ruiz Simo, M. Sajjad Athar and M. J. Vicente Vacas
Phys. Rev. C 84 (2011) 054610

### Summary

We find that the nuclear medium effects like Fermi motion and binding energy corrections are the same in $F_2$ and $F_3$ nuclear structure functions which have been incorporated by using the spectral function obtained for nuclear matter and implemented in nuclei using the

local-density approximation. The differences in our results for $F_2$ and $F_3$ are due to the meson cloud contributions in the $F_2$

structure function whereas in the $F_3$ structure function they are absent. We have observed that the effect of meson clouds are large at low and intermediate x.

Furthermore, the shadowing effects in $F_2$ and $F_3$ structure functions are different.

Thus it is not appropriate to take the same correction factor for the $F_2$ and the $F_3$ nuclear structure functions.

The ratios of structure functions for different nuclei are not the same. This study may be useful in understanding the medium effects in the nuclear structure functions when the results from

$Miner\nu A$ would come up. Also this study is important in the incorporation of medium correction for the deep inelastic scattering presently considered in the Neutrino Monte Carlo event generators.

Dr
I. Ruiz Simo
(Departamento de F\'isica At\'omica Molecular y Nuclear, Universidad de Granada, E-18071 Granada, Spain)
Prof.
M.Sajjad Athar
(Aligarh Muslim University)