# Nucleon and nuclear structure functions with nonperturbative and higher order perturbative QCD effects

## Abstract

We have studied the nucleon structure functions *F* ^{EM} _{iN}(x,Q ^{2}), i = 1, 2, by including contributions due to the higher order perturbative QCD effect up to next-to-next-to-leading order (NNLO) and the nonperturbative effects due to the kinematical and dynamical higher twist (HT) effects. The numerical results for *F* ^{EM} _{iN}(x,Q ^{2}) are obtained using Martin, Motylinski, Harland-Lang, Thorne 2014 NLO and NNLO nucleon parton distribution functions (PDFs). The dynamical HT correction has been included following the renormalon approach as well as the phenomenological approach, and the kinematical HT effect is incorporated using the works of Schienbein et al. These nucleon structure functions have been used as an input to calculate the nuclear structure functions *F* ^{EM} _{iN}(x,Q ^{2}). In a nucleus, the nuclear corrections arise because of the Fermi motion, binding energy, nucleon correlations, mesonic contribution, and shadowing and antishadowing effects. These nuclear corrections are taken into account in the numerical calculations to obtain the nuclear structure functions *F* ^{EM} _{iN}(x,Q ^{2}), for the various nuclear targets such as ^{12}C, ^{27}Al, ^{56}Fe, ^{64}Cu, ^{118}Sn, ^{197}Au, and ^{208}Pb which are of experimental interest. The effect of isoscalarity correction for nonisoscalar nuclear targets has also been studied. The results for themore »

- Authors:

- Aligarh Muslim Univ., Aligarh (India)
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Univ. de Granada, Granada (Spain)

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1525455

- Report Number(s):
- arXiv:1903.09000; FERMILAB-PUB-19-150-ND

Journal ID: ISSN 2470-0010; PRVDAQ; 1726114

- Grant/Contract Number:
- AC02-07CH11359

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 9; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Zaidi, F., Haider, H., Athar, M. Sajjad, Singh, S. K., and Simo, I. Ruiz. Nucleon and nuclear structure functions with nonperturbative and higher order perturbative QCD effects. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.99.093011.
```

```
Zaidi, F., Haider, H., Athar, M. Sajjad, Singh, S. K., & Simo, I. Ruiz. Nucleon and nuclear structure functions with nonperturbative and higher order perturbative QCD effects. United States. doi:10.1103/PhysRevD.99.093011.
```

```
Zaidi, F., Haider, H., Athar, M. Sajjad, Singh, S. K., and Simo, I. Ruiz. Tue .
"Nucleon and nuclear structure functions with nonperturbative and higher order perturbative QCD effects". United States. doi:10.1103/PhysRevD.99.093011. https://www.osti.gov/servlets/purl/1525455.
```

```
@article{osti_1525455,
```

title = {Nucleon and nuclear structure functions with nonperturbative and higher order perturbative QCD effects},

author = {Zaidi, F. and Haider, H. and Athar, M. Sajjad and Singh, S. K. and Simo, I. Ruiz},

abstractNote = {We have studied the nucleon structure functions FEMiN(x,Q2), i = 1, 2, by including contributions due to the higher order perturbative QCD effect up to next-to-next-to-leading order (NNLO) and the nonperturbative effects due to the kinematical and dynamical higher twist (HT) effects. The numerical results for FEMiN(x,Q2) are obtained using Martin, Motylinski, Harland-Lang, Thorne 2014 NLO and NNLO nucleon parton distribution functions (PDFs). The dynamical HT correction has been included following the renormalon approach as well as the phenomenological approach, and the kinematical HT effect is incorporated using the works of Schienbein et al. These nucleon structure functions have been used as an input to calculate the nuclear structure functions FEMiN(x,Q2). In a nucleus, the nuclear corrections arise because of the Fermi motion, binding energy, nucleon correlations, mesonic contribution, and shadowing and antishadowing effects. These nuclear corrections are taken into account in the numerical calculations to obtain the nuclear structure functions FEMiN(x,Q2), for the various nuclear targets such as 12C, 27Al, 56Fe, 64Cu, 118Sn, 197Au, and 208Pb which are of experimental interest. The effect of isoscalarity correction for nonisoscalar nuclear targets has also been studied. The results for the FEMiN(x,Q2) are compared with nCTEQ nuclear PDFs parametrization as well as with the experimental results from JLab, SLAC, and NMC in the kinematic region of 0.1 ≤ x ≤ 0.8 for several nuclei. We have also calculated the ratio RA(x,Q2) = F2A(x,Q2)/2xF1A(x,Q2) in the moderate Q2 region for various nuclei and compared the results with the available experimental data from JLab to examine the validity of the Callan-Gross relation in the nuclei. We also make predictions for the nuclear structure functions in 12C, 64Cu, and 197Au in the kinematic region of the proposed experiment at JLab.},

doi = {10.1103/PhysRevD.99.093011},

journal = {Physical Review D},

number = 9,

volume = 99,

place = {United States},

year = {2019},

month = {5}

}

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