Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2014, Article ID 379823, 9 pages
http://dx.doi.org/10.1155/2014/379823
Research Article

An Analytical Study of the Nonsinglet Spin Structure Function Up to NLO in the DGLAP Approach at Small

1Department of Physics, Gauhati University, Guwahati 781014, India
2Physics Academy of North East, Assam, Guwahati 781014, India
3Centre for Theoretical Physics, Pandu College, Guwahati 781012, India

Received 16 July 2014; Accepted 28 October 2014; Published 23 November 2014

Academic Editor: George Siopsis

Copyright © 2014 Neelakshi N. K. Borah and D. K. Choudhury. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. V. N. Gribov and L. N. Lipatov, “Deep inelastic ep scattering in perturbation theory,” Soviet Journal of Nuclear Physics, vol. 15, p. 438, 1972. View at Google Scholar
  2. L. N. Lipatov, “The parton model and perturbation theory,” Soviet Journal of Nuclear Physics, vol. 20, pp. 94–102, 1975. View at Google Scholar
  3. Y. L. Dokshitzer, “Calculation of the structure functions for deep inelastic scattering and e+ e− annihilation by perturbation theory in quantum chromodynamics,” Soviet Physics—JETP, vol. 46, pp. 641–653, 1977. View at Google Scholar
  4. G. Altarelli and G. Parisi, “Asymptotic freedom in parton language,” Nuclear Physics B, vol. 126, no. 2, pp. 298–318, 1977. View at Publisher · View at Google Scholar
  5. R. Toldra, “A C++ code to solve the DGLAP equations applied to Ultra High Energy Cosmic Rays,” Computer Physics Communications, vol. 143, no. 3, pp. 287–304, 2002. View at Publisher · View at Google Scholar
  6. C. Pascaud and F. Zomer, “A fast and precise method to solve the Altarelli-Parisi equations in x space,” http://arxiv.org/abs/hep-ph/0104013.
  7. N. Cabibbo and R. Petronzio, “Two-stage model of hadron structure: parton distributions and their Q2 dependence,” Nuclear Physics B, vol. 137, no. 4, pp. 395–412, 1978. View at Publisher · View at Google Scholar
  8. M. Stratmann and W. Vogelsang, “Towards a global analysis of polarized parton distributions,” Physical Review D, vol. 64, no. 11, Article ID 114007, 10 pages, 2001. View at Publisher · View at Google Scholar
  9. A. Vogt, “Efficient evolution of unpolarized and polarized parton distributions with QCD-Pegasus,” Computer Physics Communications, vol. 170, pp. 65–92, 2005. View at Publisher · View at Google Scholar
  10. M. Botje, QCDNUM, http://www.nikhef.nl/~h24/qcdnum.
  11. L. Schoeffel, “An elegant and fast method to solve QCD evolution equations. Application to the determination of the gluon content of the Pomeron,” Nuclear Instruments and Methods in Physics Research Section A, vol. 423, no. 2-3, pp. 439–445, 1999. View at Publisher · View at Google Scholar
  12. A. Cafarella and C. Corianò, “Direct solution of renormalization group equations of QCD in x-space: NLO implementations at leading twist,” Computer Physics Communications, vol. 160, no. 3, pp. 213–242, 2004. View at Publisher · View at Google Scholar
  13. A. Cafarella, C. Corianò, and M. Guzzi, “NNLO logarithmic expansions and exact solutions of the DGLAP equations from x-space: new algorithms for precision studies at the LHC,” Nuclear Physics B, vol. 748, no. 1-2, pp. 253–308, 2006. View at Publisher · View at Google Scholar
  14. A. Cafarella, C. Coriano, and M. Guzzi, “Precision studies of the NNLO DGLAP evolution at the LHC with Candia,” Computer Physics Communications, vol. 179, no. 9, pp. 665–684, 2008. View at Publisher · View at Google Scholar
  15. S. Weinzierl, “Fast evolution of parton distributions,” Computer Physics Communications, vol. 148, no. 3, pp. 314–326, 2002. View at Publisher · View at Google Scholar
  16. M. Roth and S. Weinzierl, “QED corrections to the evolution of parton distributions,” Physics Letters B, vol. 590, no. 3-4, pp. 190–198, 2004. View at Publisher · View at Google Scholar
  17. L. del Debbio, S. Forte, J. I. Latorre, A. Piccione, and J. Rojo, “Neural network determination of parton distributions: the Nonsinglet case,” Journal of High Energy Physics, vol. 2007, article 039, 2007. View at Publisher · View at Google Scholar
  18. D. K. Choudhury and J. K. Sarma, “Perturbative and nonperturbative evolutions of structure functions at low x,” Pramana-Journal of Physics, vol. 38, p. 481, 1992. View at Google Scholar
  19. D. K. Choudhury, J. K. Sarma, and G. K. Medhi, “x-distribution of deuteron structure function at low-x,” Physics Letters B, vol. 403, no. 1-2, pp. 139–144, 1997. View at Publisher · View at Google Scholar
  20. D. K. Choudhury and A. Deshamukhya, “Non-singlet structure function at high x and neutrino scattering,” Indian Journal of Physics A, vol. 75, no. 2, p. 175, 2001. View at Google Scholar
  21. D. K. Choudhury and P. K. Sahariah, “A solution of the DGLAP equation for gluon at low x,” Pramana, vol. 58, no. 4, pp. 599–610, 2002. View at Publisher · View at Google Scholar · View at Scopus
  22. D. K. Choudhury and P. K. Sahariah, “Analytic and semi-analytic solution of the coupled DGLAP equations at small x by the method of characteristics,” http://arxiv.org/abs/hep-ph/0606085.
  23. D. K. Choudhury and P. K. Sahariah, “Solution of polarised singlet DGLAP evolution equations by the method of characteristics,” http://arxiv.org/abs/hep-ph/0601059.
  24. NNPDF Collaboration, “Unbiased determination of polarized parton distributions and their uncertainties,” Nuclear Physics B, vol. 874, no. 1, pp. 36–84, 2013. View at Publisher · View at Google Scholar
  25. M. Hirai, S. Kumano, N. Saito, and Asymmetry Analysis Collaboration, “Determination of polarized parton distribution functions and their uncertainties,” Physical Review D, vol. 69, no. 5, Article ID 054021, 10 pages, 2004. View at Publisher · View at Google Scholar
  26. M. Glück, E. Reya, M. Stratmann, and W. Vogelsang, “Models for the polarized parton distributions of the nucleon,” Physical Review D, vol. 63, Article ID 094005, 2001. View at Publisher · View at Google Scholar
  27. E. Leader, A. V. Sidorov, and D. B. Stamenov, “Determination of polarized parton densities from a QCD analysis of inclusive and semi-inclusive deep inelastic scattering data,” Physical Review D, vol. 82, no. 11, Article ID 114018, 12 pages, 2010. View at Publisher · View at Google Scholar
  28. J. Blimlein and H. Böttcher, “QCD analysis of polarized deep inelastic scattering data,” Nuclear Physics B, vol. 841, no. 1-2, pp. 205–230, 2010. View at Publisher · View at Google Scholar
  29. E. R. Nocera, R. D. Balla, S. Forteb, G. Ridolfic, and J. Rojod, “A first unbiased global determination of polarized PDFs and their uncertainties,” Nuclear Physics B, vol. 887, pp. 276–308, 2014. View at Publisher · View at Google Scholar
  30. G. P. Salam and J. Rojo, “A Higher Order Perturbative Parton Evolution Toolkit (HOPPET),” Computer Physics Communications, vol. 180, no. 1, pp. 120–156, 2009. View at Publisher · View at Google Scholar · View at Scopus
  31. D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, “Global analysis of helicity parton densities and their uncertainties,” Physical Review Letters, vol. 101, no. 7, Article ID 072001, 4 pages, 2001. View at Publisher · View at Google Scholar
  32. D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, “Extraction of spin-dependent parton densities and their uncertainties,” Physical Review D, vol. 80, no. 3, Article ID 034030, 26 pages, 2009. View at Publisher · View at Google Scholar
  33. N. N. K. Borah, D. K. Choudhury, and P. K. Sahariah, “Non-singlet spin structure function g1NS(x,t) in the DGLAP approach,” Pramana—Journal of Physics, vol. 79, no. 4, pp. 833–837, 2012. View at Google Scholar
  34. R. D. Ball, S. Forte, and G. Ridolfi, “Scale dependence and small-x behaviour of polarized parton distributions,” Nuclear Physics B, vol. 444, no. 1-2, pp. 287–309, 1995. View at Publisher · View at Google Scholar · View at Scopus
  35. B. Lampe and E. Reya, “Spin physics and polarized structure functions,” Physics Reports, vol. 332, no. 1–3, pp. 1–163, 1998. View at Publisher · View at Google Scholar
  36. T. Gehrmann and W. J. Stirling, “Analytic approaches to the evolution of polarised parton distributions at small x,” Physics Letters B, vol. 365, no. 1–4, pp. 347–358, 1996. View at Publisher · View at Google Scholar
  37. N. N. K. Borah, D. K. Choudhury, and P. K. Sahariah, “Comparison of analytical solution of DGLAP equations for F2NS(x,t) at small x by two methods,” Advances in High Energy Physics, vol. 2013, Article ID 829803, 10 pages, 2013. View at Publisher · View at Google Scholar
  38. R. Choudhury, “Spin-dependent coupled Altarelli-Parisi equations in the NLO and the method of successive approximations,” ISRN High Energy Physics, vol. 2012, Article ID 943871, 22 pages, 2012. View at Publisher · View at Google Scholar
  39. D. K. Atri Deshamukhya, in Proceedings of the 2nd Regional Conference on Physics Research in North East, 2001.
  40. R. Baishya and J. K. Sarma, “Solution of non-singlet DGLAP evolution equation in leading order and next to leading order at small-x,” Indian Journal of Physics, vol. 83, no. 9, pp. 1333–1341, 2009. View at Publisher · View at Google Scholar · View at Scopus
  41. I. N. Sneddon, Elements of Partial Differential Equations, McGraw-Hill, New York, NY, USA, 1957. View at MathSciNet
  42. W. E. Williams, Partial Differential Equations, Oxford University Press, Oxford, UK, 1980. View at MathSciNet
  43. S. J. Farlow, Partial Differential Equations for Scientists and Engineers, John Wiley & Sons, New York, NY, USA, 1982. View at MathSciNet
  44. H. B. Dwight, Table of Integrals and Other Mathematical Data, Macmillan Publishers, New York, NY, USA, 1961. View at MathSciNet
  45. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, NY, USA, 1965. View at MathSciNet
  46. R. Rajkhowa, “Comparison of analytical solutions of DGLAP evolution equations,” http://arxiv.org/abs/1004.3731.
  47. A. Airapetian, W. Deconinck, W. Lorenzon et al., “Precise determination of the spin structure function g1 of the proton, deuteron, and neutron,” Physical Review D, vol. 75, Article ID 012007, 2007. View at Publisher · View at Google Scholar
  48. A. N. Khorramian, S. A. Tehrani, S. T. Monfared, F. Arbabifar, and F. I. Olnes, “Polarized deeply inelastic scattering (DIS) structure functions for nucleons and nuclei,” Physical Review D, vol. 83, Article ID 054017, 2011. View at Publisher · View at Google Scholar
  49. B. I. Ermolaev, M. Greco, and S. I. Troyan, “Non-singlet structure functions: combining the leading logarithms resummation at small-x with DGLAP,” Physics Letters B, vol. 622, no. 1-2, pp. 93–101, 2005. View at Publisher · View at Google Scholar
  50. A. Vogt, S. Moch, and J. A. M. Vermaseren, “A calculation of the three-loop helicity-dependent splitting functions in QCD,” http://arxiv.org/abs/1405.3407.
  51. S. Moch, J. A. M. Vermaseren, and A. Vogt, “The three-loop splitting functions in QCD: the helicity-dependent case,” http://arxiv.org/abs/1409.5131.