Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Study of Polarized Structure Functions of 3He and 3H in NNLO Approximation

Document Type : Research Paper

Authors

H Khanpour
S Taheri Monfared
Sh. Atashbar Tehrani
https://doi.org/10.24200/nst.2018.1043
Abstract
Experiments utilizing the deep inelastic scattering of leptons from nucleons have been one of the modern tools to understand the complex structure of nucleons in recent and future lepton and hadron colliders. In addition, scattering of polarized leptons from polarized nucleons and polarized light nuclear targets provides us the possibility to probe the spin structure of the nucleon. In this paper, the polarized structure functions of the nucleon are computed using the Jacobi polynomial approach. The effect of considering non-perturbative target mass corrections (TMCs) as well as higher twist (HT) terms are studied at next-to-next-to leading order (NNLO) accuracy. Finally we calculated the polarized light nuclear structure functions for 3He and 3H at NNLO approximation, using the convolution of the light cone momentum distributions with the polarized structure of the free proton and neutron. The stability and reliability of the results are ensured by a detailed comparison with the available and up-to-date polarized DIS data. Based on our obtained results the predictions are in satisfactory agreement with all data analyzed and other phenomenological models in the literature.

Highlights

[1] K. Ackerstaff, et al. [HERMES Collaboration], Measurement of the neutron spin structure function  with a polarized He-3 internal target, Phys. Lett. B 404 (1997) 383.

 

[2] K. Abe, et al. [E154 Collaboration], Measurement of the neutron spin structure function  and asymmetry , Phys. Lett. B 404 (1997) 377.

 

[3] K. Abe, et al. [E154 Collaboration], Precision determination of the neutron spin structure function , Phys. Rev. Lett.  79 (1997) 26.

 

[4] P.L. Anthony, et al. [E142 Collaboration], Deep inelastic scattering of polarized electrons by polarized He-3 and the study of the neutron spin structure, Phys. Rev. D 54 (1996) 6620.

 

[5] X. Zheng, et al. [Jefferson Lab Hall A Collaboration], Precision measurement of the neutron spin asymmetries and spin-dependent structure functions in the valence quark region, Phys. Rev. C 70 (2004) 065207.

 

[6] X. Zheng, et al. [Jefferson Lab Hall A Collaboration], Precision measurement of the neutron spin asymmetry  and spin flavor decomposition in the valence quark region, Phys. Rev. Lett 92 (2004) 012004.

 

[7] D. Flay, et al. [Jefferson Lab Hall A Collaboration], Measurements of  and : Probing the neutron spin structure, Phys. Rev. D 94 (2016) 052003.

 

[8] K. Abe, et al. [E143 Collaboration], Measurements of the proton and deuteron spin structure functions g(1) and g(2), Phys. Rev. D 58 (1998) 112003.

 

[9] Y.X. Zhao, [Jefferson Lab Hall A Collaboration], Double Spin Asymmetries of Inclusive Hadron Electroproductions from a Transversely Polarized  Target, Phys. Rev. C 92 (2015) 015207.

 

[10] C.A. Aidala, S.D. Bass, D. Hasch, G.K. Mallot, The Spin Structure of the Nucleon, Rev. Mod. Phys. 85 (2013) 655.

[11] B. Lampe, E. Reya, Spin physics and polarized structure functions, Phys. Rept. 332 (2000) 1.

 

[12] E.B. Zijlstra, W.L. Van Neerven, Order-  corrections to the polarized structure function g1, Nucl. Phys. B 417 (1994) 61.

 

[13] S.M. Moosavi Nejad, H. Khanpour, S. Atashbar Tehrani and M. Mahdavi, QCD analysis of nucleon structure functions in deep-inelastic neutrino-nucleon scattering: Laplace transform and Jacobi polynomials approach, Phys. Rev. C 94 (2016) 045201.

 

[14] F. Taghavi-Shahri, H. Khanpour, S. Atashbar Tehrani, Z. Alizadeh Yazdi, Next-to-next-to-leading order QCD analysis of spin-dependent parton distribution functions and their uncertainties: Jacobi polynomials approach, Phys. Rev. D 93 (2016) 114024.

 

[15] H. Khanpour, S. Taheri Monfared, S. Atashbar Tehrani, Nucleon spin structure functions at NNLO in the presence of target mass corrections and higher twist effects, Phys. Rev. D 95 (2017) 074006.

 

[16] H. Khanpour, A. Mirjalili, S. Atashbar Tehrani, Analytic derivation of the next-to-leading order proton structure function  based on the Laplace transformation, Phys. Rev. C 95 (2017) 035201.

 

[17] A.N. Khorramian, S. Atashbar Tehrani, S. Taheri Monfared, F. Arbabifar, F.I. Olness, Phys. Rev. D 83 054017 (2011).

 

[18] A.N. Khorramian, H. Khanpour, S.A. Tehrani, Nonsinglet parton distribution functions from the precise next-to-next-to-next-to leading order QCD fit, Phys. Rev. D 81 (2010) 014013.

 

[19] Y.B. Dong, Target mass corrections to proton spin structure functions and quark-hadron duality, Phys. Lett. B 641 (2006) 272.

 

[20] Y.B. Dong, Target mass corrections and twist-3 in the nucleon spin structure functions, Phys. Lett. B 653 (2007) 18.

 

[21] Y.B. Dong, D.Y. Chen, Local quark-hadron duality of nucleon spin structure functions with target mass corrections, Nucl. Phys. A 791 (2007) 342.

[22] Y.B. Dong, Target mass corrections to matrix elements in nucleon spin structure functions, Phys. Rev. C 78 (2008) 028201.

 

[23] V.M. Braun, T. Lautenschlager, A.N. Manashov, B. Pirnay, Higher twist parton distributions from light-cone wave functions, Phys. Rev. D 83 (2011) 094023.

 

[24] S. Taheri Monfared, Z. Haddadi, A.N. Khorramian, Target mass corrections and higher twist effects in polarized deep-inelastic scattering, Phys. Rev. D 89  (2014) 074052.

 

[25] F.R.P. Bissey, A.W. Thomas, I.R. Afnan, Structure functions for the three nucleon system, Phys. Rev. C 64 (2001) 024004.

 

[26] F.R.P. Bissey, V.A. Guzey, M. Strikman, A.W. Thomas, Complete analysis of spin structure function g(1) of He-3, Phys. Rev. C 65 (2002) 064317.

 

[27] I.R. Afnan, F.R.P. Bissey, J. Gomez, A.T. Katramatou, S. Liuti, W. Melnitchouk, G.G. Petratos, A.W. Thomas, Deep inelastic scattering from A = 3 nuclei and the neutron structure function, Phys. Rev. C 68 (2003) 035201.

 

[28] S.A. Kulagin, W. Melnitchouk, Deuteron spin structure functions in the resonance and DIS regions, Phys. Rev. C 77 (2008) 015210.

 

[29] X. Yan, et al., [The Jefferson Lab Hall A Collaboration], First measurement of unpolarized SIDIS cross section and cross section ratios from a  target, arXiv: 1610.02350 [nucl-ex].

 

[30] J.L. Friar, B.F. Gibson, G.L. Payne, A.M. Bernstein, T.E. Chupp, Neutron polarization in polarized He-3 targets, Phys. Rev. C 42 (1990) 2310.

 

[31] L. Frankfurt, V. Guzey, M. Strikman, The Nuclear effects in (g1 He-3) and the Bjorken sum rule for A=3, Phys. Lett. B 381 (1996) 379.

 

[32] T.Y. Saito, Y. Wu, S. Ishikawa, T. Sasakawa, Triton beta decay, Phys. Lett. B 242 (1990) 12.

 

[33] J. Carlson, D.O. Riska, R. Schiavilla, R.B. Wiringa, Weak proton capture reactions on 1H and 3He and tritium 2-beta decay, Phys.  Rev. C 44 (1991) 619.

 

[34] C. Boros, V.A. Guzey, M. Strikman, A.W. Thomas, Role of the Delta (1232) in DIS on polarized He-3 and extraction of the neutron spin structure function g1, Phys. Rev. D 64 (2001) 014025.

 

[35] P. Amaudruz, et al. [New Muon Collaboration], A Reevaluation of the nuclear structure function ratios for D, He, Li-6, C and Ca, Nucl. Phys. B 441 (1995) 3.

 

[36] M. Arneodo, et al. [New Muon Collaboration], The Structure Function ratios F2(li)/F2(D) and F2(C)/F2(D) at small x, Nucl. Phys. B 441 (1995) 12.

 

[37] P.L. Anthony, et al. [E142 Collaboration], Deep inelastic scattering of polarized electrons by polarized He-3 and the study of the neutron spin structure, Phys. Rev. D 54 (1996) 6620.

 

[38] X. Zheng, et al. [Jefferson Lab Hall A Collaboration], Precision measurement of the neutron spin asymmetries and spin-dependent structure functions in the valence quark region, Phys. Rev. C 70 (2004) 065207.

 

[39] S. Atashbar Tehrani, A.N. Khorramian, The Jacobi polynomials QCD analysis for the polarized structure function, JHEP 0707 (2007) 048.

 

[40] J. Blumlein, H. Bottcher, QCD analysis of polarized deep inelastic data and parton distributions, Nucl. Phys. B 636 (2002) 225.

 

[41] A.N. Khorramian, S. Atashbar Tehrani, S. Taheri Monfared, F. Arbabifar, F.I. Olness, Polarized Deeply Inelastic Scattering (DIS) Structure Functions for Nucleons and Nuclei, Phys. Rev. D 83 (2011) 054017.

Keywords

Polarized Structure Function
3-Loop Corrections
Feynman Diagrams
Jacobi Polynomial Approach
[1] K. Ackerstaff, et al. [HERMES Collaboration], Measurement of the neutron spin structure function  with a polarized He-3 internal target, Phys. Lett. B 404 (1997) 383.
 
[2] K. Abe, et al. [E154 Collaboration], Measurement of the neutron spin structure function  and asymmetry , Phys. Lett. B 404 (1997) 377.
 
[3] K. Abe, et al. [E154 Collaboration], Precision determination of the neutron spin structure function , Phys. Rev. Lett.  79 (1997) 26.
 
[4] P.L. Anthony, et al. [E142 Collaboration], Deep inelastic scattering of polarized electrons by polarized He-3 and the study of the neutron spin structure, Phys. Rev. D 54 (1996) 6620.
 
[5] X. Zheng, et al. [Jefferson Lab Hall A Collaboration], Precision measurement of the neutron spin asymmetries and spin-dependent structure functions in the valence quark region, Phys. Rev. C 70 (2004) 065207.
 
[6] X. Zheng, et al. [Jefferson Lab Hall A Collaboration], Precision measurement of the neutron spin asymmetry  and spin flavor decomposition in the valence quark region, Phys. Rev. Lett 92 (2004) 012004.
 
[7] D. Flay, et al. [Jefferson Lab Hall A Collaboration], Measurements of  and : Probing the neutron spin structure, Phys. Rev. D 94 (2016) 052003.
 
[8] K. Abe, et al. [E143 Collaboration], Measurements of the proton and deuteron spin structure functions g(1) and g(2), Phys. Rev. D 58 (1998) 112003.
 
[9] Y.X. Zhao, [Jefferson Lab Hall A Collaboration], Double Spin Asymmetries of Inclusive Hadron Electroproductions from a Transversely Polarized  Target, Phys. Rev. C 92 (2015) 015207.
 
[10] C.A. Aidala, S.D. Bass, D. Hasch, G.K. Mallot, The Spin Structure of the Nucleon, Rev. Mod. Phys. 85 (2013) 655.
[11] B. Lampe, E. Reya, Spin physics and polarized structure functions, Phys. Rept. 332 (2000) 1.
 
[12] E.B. Zijlstra, W.L. Van Neerven, Order-  corrections to the polarized structure function g1, Nucl. Phys. B 417 (1994) 61.
 
[13] S.M. Moosavi Nejad, H. Khanpour, S. Atashbar Tehrani and M. Mahdavi, QCD analysis of nucleon structure functions in deep-inelastic neutrino-nucleon scattering: Laplace transform and Jacobi polynomials approach, Phys. Rev. C 94 (2016) 045201.
 
[14] F. Taghavi-Shahri, H. Khanpour, S. Atashbar Tehrani, Z. Alizadeh Yazdi, Next-to-next-to-leading order QCD analysis of spin-dependent parton distribution functions and their uncertainties: Jacobi polynomials approach, Phys. Rev. D 93 (2016) 114024.
 
[15] H. Khanpour, S. Taheri Monfared, S. Atashbar Tehrani, Nucleon spin structure functions at NNLO in the presence of target mass corrections and higher twist effects, Phys. Rev. D 95 (2017) 074006.
 
[16] H. Khanpour, A. Mirjalili, S. Atashbar Tehrani, Analytic derivation of the next-to-leading order proton structure function  based on the Laplace transformation, Phys. Rev. C 95 (2017) 035201.
 
[17] A.N. Khorramian, S. Atashbar Tehrani, S. Taheri Monfared, F. Arbabifar, F.I. Olness, Phys. Rev. D 83 054017 (2011).
 
[18] A.N. Khorramian, H. Khanpour, S.A. Tehrani, Nonsinglet parton distribution functions from the precise next-to-next-to-next-to leading order QCD fit, Phys. Rev. D 81 (2010) 014013.
 
[19] Y.B. Dong, Target mass corrections to proton spin structure functions and quark-hadron duality, Phys. Lett. B 641 (2006) 272.
 
[20] Y.B. Dong, Target mass corrections and twist-3 in the nucleon spin structure functions, Phys. Lett. B 653 (2007) 18.
 
[21] Y.B. Dong, D.Y. Chen, Local quark-hadron duality of nucleon spin structure functions with target mass corrections, Nucl. Phys. A 791 (2007) 342.
[22] Y.B. Dong, Target mass corrections to matrix elements in nucleon spin structure functions, Phys. Rev. C 78 (2008) 028201.
 
[23] V.M. Braun, T. Lautenschlager, A.N. Manashov, B. Pirnay, Higher twist parton distributions from light-cone wave functions, Phys. Rev. D 83 (2011) 094023.
 
[24] S. Taheri Monfared, Z. Haddadi, A.N. Khorramian, Target mass corrections and higher twist effects in polarized deep-inelastic scattering, Phys. Rev. D 89  (2014) 074052.
 
[25] F.R.P. Bissey, A.W. Thomas, I.R. Afnan, Structure functions for the three nucleon system, Phys. Rev. C 64 (2001) 024004.
 
[26] F.R.P. Bissey, V.A. Guzey, M. Strikman, A.W. Thomas, Complete analysis of spin structure function g(1) of He-3, Phys. Rev. C 65 (2002) 064317.
 
[27] I.R. Afnan, F.R.P. Bissey, J. Gomez, A.T. Katramatou, S. Liuti, W. Melnitchouk, G.G. Petratos, A.W. Thomas, Deep inelastic scattering from A = 3 nuclei and the neutron structure function, Phys. Rev. C 68 (2003) 035201.
 
[28] S.A. Kulagin, W. Melnitchouk, Deuteron spin structure functions in the resonance and DIS regions, Phys. Rev. C 77 (2008) 015210.
 
[29] X. Yan, et al., [The Jefferson Lab Hall A Collaboration], First measurement of unpolarized SIDIS cross section and cross section ratios from a  target, arXiv: 1610.02350 [nucl-ex].
 
[30] J.L. Friar, B.F. Gibson, G.L. Payne, A.M. Bernstein, T.E. Chupp, Neutron polarization in polarized He-3 targets, Phys. Rev. C 42 (1990) 2310.
 
[31] L. Frankfurt, V. Guzey, M. Strikman, The Nuclear effects in (g1 He-3) and the Bjorken sum rule for A=3, Phys. Lett. B 381 (1996) 379.
 
[32] T.Y. Saito, Y. Wu, S. Ishikawa, T. Sasakawa, Triton beta decay, Phys. Lett. B 242 (1990) 12.
 
[33] J. Carlson, D.O. Riska, R. Schiavilla, R.B. Wiringa, Weak proton capture reactions on 1H and 3He and tritium 2-beta decay, Phys.  Rev. C 44 (1991) 619.
 
[34] C. Boros, V.A. Guzey, M. Strikman, A.W. Thomas, Role of the Delta (1232) in DIS on polarized He-3 and extraction of the neutron spin structure function g1, Phys. Rev. D 64 (2001) 014025.
 
[35] P. Amaudruz, et al. [New Muon Collaboration], A Reevaluation of the nuclear structure function ratios for D, He, Li-6, C and Ca, Nucl. Phys. B 441 (1995) 3.
 
[36] M. Arneodo, et al. [New Muon Collaboration], The Structure Function ratios F2(li)/F2(D) and F2(C)/F2(D) at small x, Nucl. Phys. B 441 (1995) 12.
 
[37] P.L. Anthony, et al. [E142 Collaboration], Deep inelastic scattering of polarized electrons by polarized He-3 and the study of the neutron spin structure, Phys. Rev. D 54 (1996) 6620.
 
[38] X. Zheng, et al. [Jefferson Lab Hall A Collaboration], Precision measurement of the neutron spin asymmetries and spin-dependent structure functions in the valence quark region, Phys. Rev. C 70 (2004) 065207.
 
[39] S. Atashbar Tehrani, A.N. Khorramian, The Jacobi polynomials QCD analysis for the polarized structure function, JHEP 0707 (2007) 048.
 
[40] J. Blumlein, H. Bottcher, QCD analysis of polarized deep inelastic data and parton distributions, Nucl. Phys. B 636 (2002) 225.
 
[41] A.N. Khorramian, S. Atashbar Tehrani, S. Taheri Monfared, F. Arbabifar, F.I. Olness, Polarized Deeply Inelastic Scattering (DIS) Structure Functions for Nucleons and Nuclei, Phys. Rev. D 83 (2011) 054017.

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