A posteriori inclusion of parton density functions in NLO QCD final-state calculations at hadron colliders: the APPLGRID project


A method to facilitate the consistent inclusion of cross-section measurements based on complex final-states from HERA, TEVATRON and the LHC in proton parton density function (PDF) fits has been developed. This can be used to increase the sensitivity of LHC data to deviations from Standard Model predictions. The method stores perturbative coefficients of NLO QCD calculations of final-state observables measured in hadron colliders in look-up tables. This allows the a posteriori inclusion of parton density functions (PDFs), and of the strong coupling, as well as the a posteriori variation of the renormalisation and factorisation scales in cross-section calculations. The main novelties in comparison to original work on the subject are the use of higher-order interpolation of Lagrangian form, which substantially improves the trade-off between accuracy and memory use, and a CPU and computer memory optimised way to construct and store the look-up table using modern software tools. It is demonstrated that a sufficient accuracy on the cross-section calculation can be achieved with reasonably small look-up table size by using the examples of jet production and electro-weak boson (ZW) production in proton-proton collisions at a center-of-mass energy of 14 TeV at the LHC. The use of this technique in PDF fitting is demonstrated in a PDF-fit to HERA data and simulated LHC jet cross-sections as well as in a study of the jet cross-section uncertainties at various centre-of-mass energies.


  1. 1.

    D. Graudenz, M. Hampel, A. Vogt, C. Berger, Z. Phys. C 70, 77 (1996)

    Article  Google Scholar 

  2. 2.

    D.A. Kosower, Nucl. Phys. B 520, 263 (1998)

    Article  ADS  Google Scholar 

  3. 3.

    M. Stratmann, W. Vogelsang, Phys. Rev. D 64, 114007 (2001)

    Article  ADS  Google Scholar 

  4. 4.

    M. Wobisch, Internal Report PITHA 00/12 and DESY-THESIS-2000-049, PhD-thesis RWTH Aachen, 2000

  5. 5.

    S. Chekanov et al. (ZEUS Collaboration), Eur. Phys. J. C 42, 1 (2005)

    Article  ADS  Google Scholar 

  6. 6.

    P.G. Ratcliffe, Phys. Rev. D 63, 116004 (2001)

    Article  ADS  Google Scholar 

  7. 7.

    M. Dasgupta, G.P. Salam, Eur. Phys. J. C 24, 213 (2002)

    Article  ADS  Google Scholar 

  8. 8.

    G.P. Salam, J. Rojo, Comput. Phys. Commun. 180, 120 (2009)

    Article  ADS  Google Scholar 

  9. 9.

    T. Carli, G.P. Salam, F. Siegert, Contributed to HERA and the LHC: a Workshop on the Implications of HERA for LHC Physics, Geneva, Switzerland. hep-ph/0510324 (2005)

  10. 10.

    T. Kluge, K. Rabbertz, M. Wobisch, in Proceedings of the DIS 2006 Conference, Tsukuba, Japan, hep-ph/0609285 (2006)

  11. 11.

    A. Banfi, G.P. Salam, G. Zanderighi, J. High Energy Phys. 07, 026 (2007)

    Article  ADS  Google Scholar 

  12. 12.

    S. Eidelman et al., Phys. Lett. B 592, 1 (2004)

    Article  ADS  Google Scholar 

  13. 13.

    Z. Nagy, Phys. Rev. D 68, 094002 (2003)

    Article  ADS  Google Scholar 

  14. 14.

    Z. Nagy, Phys. Rev. Lett. 88, 122003 (2002)

    Article  ADS  Google Scholar 

  15. 15.

    Z. Nagy, Z. Trocsanyi, Phys. Rev. Lett. 87, 082001 (2001)

    Article  ADS  Google Scholar 

  16. 16.

    J.M. Campbell, R.K. Ellis, Phys. Rev. D 60, 113006 (1999)

    Article  ADS  Google Scholar 

  17. 17.

    J.M. Campbell, R.K. Ellis, Phys. Rev. D 62, 114012 (2000)

    Article  ADS  Google Scholar 

  18. 18.

    J. Pumplin et al. (CTEQ Collaboration), J. High Energy Phys. 07, 012 (2002)

    Article  ADS  Google Scholar 

  19. 19.

    G.C. Blazey et al., hep-ex/0005012 (2000)

  20. 20.

    G.P. Salam, G. Soyez, J. High Energy Phys. 0705, 086 (2007)

    Article  ADS  Google Scholar 

  21. 21.

    M. Cacciari, G.P. Salam, G. Soyez, J. High Energy Phys. 0804, 005 (2008)

    Article  ADS  Google Scholar 

  22. 22.

    P.M. Nadolsky et al. (CTEQ Collaboration), Phys. Rev. D 78, 013004 (2008)

    Article  ADS  Google Scholar 

  23. 23.

    A.D. Martin, W. J Stirling, R.S. Thorne, G. Watt, Eur. Phys. J. C 63, 189–285 (2009)

    Article  ADS  Google Scholar 

  24. 24.

    H1 and ZEUS Collaborations, H1prelim-08-045; ZEUS-prel-08-003 (2008)

  25. 25.

    R. Ball et al. Nucl. Phys. B 809, 1–63 (2009)

    Article  ADS  Google Scholar 

  26. 26.

    J.M. Campbell, J.W. Huston, W.J. Stirling, Rep. Prog. Phys. 70, 89 (2007)

    Article  ADS  Google Scholar 

  27. 27.

    W.T. Giele, E.W.N. Glover, D.A. Kosower, Nucl. Phys. B 403, 633 (1993)

    Article  ADS  Google Scholar 

  28. 28.

    D. Stump et al. (CTEQ Collaboration), J. High Energy Phys. 0310, 046 (2003)

    Article  ADS  Google Scholar 

  29. 29.

    M. Botje, J. Phys. G 28, 779 (2002)

    Article  ADS  Google Scholar 

  30. 30.

    S.I. Alekhin, IHEP-2000-17 and hep-ex/0005042 (2000)

  31. 31.

    A.M. Cooper-Sarkar, J. Phys. G 28, 2609 (2002)

    Article  Google Scholar 

  32. 32.

    R.S. Thorne et al., J. Phys. G 28, 2717 (2002)

    Article  ADS  Google Scholar 

  33. 33.

    A.M. Cooper-Sarkar, in Proceedings of the DIS 2007 Conference, Munich, Germany, 0707.1593 [hep-ph] (2007)

  34. 34.

    M. Kobayashi, T. Maskawa, Prog. Theor. Phys. 49, 652 (1973)

    Article  ADS  Google Scholar 

  35. 35.

    N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963)

    Article  ADS  Google Scholar 

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Correspondence to Tancredi Carli.

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Carli, T., Clements, D., Cooper-Sarkar, A. et al. A posteriori inclusion of parton density functions in NLO QCD final-state calculations at hadron colliders: the APPLGRID project. Eur. Phys. J. C 66, 503–524 (2010). https://doi.org/10.1140/epjc/s10052-010-1255-0

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  • Large Hadron Collider
  • Large Hadron Collider Data
  • Parton Density Function
  • Posteriori Variation
  • Weight Grid