Nuclear Dependence in Weak Structure Functions and the Determination of Weak Mixing Angle
We have studied nuclear medium effects in the weak structure functions and and in the extraction of weak mixing angle using Paschos Wolfenstein(PW) relation. We have modified the PW relation for nonisoscalar nuclear target. We have incorporated the medium effects like Pauli blocking, Fermi motion, nuclear binding energy, nucleon correlations, pion rho cloud contributions, and shadowing and antishadowing effects.
In this paper, we have studied the impact of nuclear effects and nonisoscalarity corrections on the weak structure functions and using the expression discussed in the other paper presented in this conference. Using the results for and , we obtain the results for charged and neutral current differential scattering cross sections [1, 2]. The expression for the (anti)neutrino induced charged current differential scattering cross section is written as:
where the plus(minus) sign stands for the cross section. Similarly, one can write the differential scattering cross section for the neutral current induced reactions by changing the couplings and the nucleon structure functions . Using these expressions, the result for the ratio
is obtained. Paschos and Wolfenstein(PW)  demonstrated that for an isoscalar nuclear target the ratio of neutral current to charged current cross sections is related to the Weinberg angle as:
The above relation is also valid for the ratio obtained using differential scattering cross sections under more general assumptions. NuTeV Collaboration  has extracted the weak mixing angle using beam on iron target and the above relation, and obtained , which is 3 above the global fit of and is known as NuTeV anomaly. Since iron is a nonisoscalar nuclear target, therefore, we have studied the effect of nuclear medium as well as nonisoscalarity correction on the extraction of weak mixing angle using PW relation. The details are given in Ref. . given by Eq. 2, for a nonisoscalar nuclear target, may be written as
where is the nonisoscalarity effect the expression for which is given in Ref. .
2 Results and Discussions
Here we present the numerical results for and structure functions in Fig.1 for iron nucleus along with the experimental data of CDHSW  and NuTeV  collaborations for a wide range of x and . The results are obtained using target mass correction and for nucleon parton distribution functions we have used CTEQ PDFs. When the effect of Pauli blocking, Fermi motion, nuclear binding energy and nucleon correlations are taken, we call the results as the base results. Then we include pion, rho cloud contributions and shadowing and antishadowing effects and the results obtained using the full calculation, we call it as the results with the full calculation. We find that the effect of shadowing is about 3-5 at x=0.1 for Q=1-5GeV and 1-2 at x=0.2 for Q=1-5GeV which dies out with the increase in x and Q. Furthermore, in the evaluation of nuclear structure function there is contribution from pion and rho clouds. Pion contribution is significant in the region of which is 14-16 at x=0.1 which reduces to 4-6 at mid values of x. It is the meson cloud contribution which is dominant at low and intermediate x for . In Fig.2, we have shown the numerical results for and structure functions in lead along with the experimental data of CHORUS collaboration for a wide range of x and . Similar to the case of iron, shadowing is negligible as compared to the other nuclear effects and meson cloud contribution plays a significant role at low and mid x. We observe that the results at NLO are in better agreement with experimental data. In Fig.3, we have shown the results for in Fe at =65 GeV. Similarly in Fig.4, we have shown the results for Pb at =25 GeV. We find that the results of the full calculation at NLO are in general in good agreement with the experimental observations of CDHSW, NuTeV and CHORUS collaborations. In Fig. 5, we have presented the results for vs y and vs y for different values of x at energy E= 80 GeV in the left(right) panel respectively. We find that is almost independent of x and y for an isoscalar target, while for the nonisoscalar target there is x as well as y dependence. In the right panel of Fig.5, we find that the effect of non-isoscalarity is large at low y and high x which decreases with the increase in the value of y. In Fig.6, we have depicted the results of vs y for different values of x at energy E= 80 GeV. We find that due to medium effects, is different from the global fit, and this difference is when evaluated for low value of y at x=0.2 and this decreases to at high values of y, while this change is when calculated for low y at x=0.6 and this reduces to at high values of y. Thus, we observe that nonisoscalarity as well as nuclear medium effects are important while extracting .
One of the authors(MSA) is thankful to PURSE program of D.S.T., Govt. of India and the Aligarh Muslim University for the financial support. This research was supported by the Spanish Ministerio de EconomÃa y Competitividad and European FEDER funds under Contracts FIS2011-28853-C02-01, by Generalitat Valenciana under Contract No. PROMETEO/20090090 and by the EU HadronPhysics3 project, Grant Agreement No. 283286.
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