Advances in High Energy Physics
Volume 2008 (2008), Article ID 682312, 29 pages
doi:10.1155/2008/682312
Research Article

IR-Improved DGLAP-CS Theory

B. F. L. Ward

Department of Physics, Baylor University, Waco, TX 76798-7316, USA

Received 14 September 2007; Revised 11 January 2008; Accepted 6 May 2008

Academic Editor: A. Petrov

Copyright © 2008 B. F. L. Ward. 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.

Linked References

  1. S. L. Glashow, “Partial-symmetries of weak interactions,” Nuclear Physics, vol. 22, no. 4, pp. 579–588, 1961. View at Publisher · View at Google Scholar
  2. S. Weinberg, “A model of leptons,” Physical Review Letters, vol. 19, no. 21, pp. 1264–1266, 1967. View at Publisher · View at Google Scholar
  3. A. Salam, “Weak and electromagnetic interactions,” in Elementary Particle Theory, N. Svartholm, Ed., pp. 367–377, Almqvist and Wiksells, Stockholm, Sweden, 1968.
  4. G. 't Hooft and M. Veltman, “Regularization and renormalization of gauge fields,” Nuclear Physics B, vol. 44, no. 1, pp. 189–213, 1972. View at Publisher · View at Google Scholar
  5. G. 't Hooft and M. Veltman, “Combinatorics of gauge fields,” Nuclear Physics B, vol. 50, no. 1, pp. 318–353, 1972. View at Publisher · View at Google Scholar
  6. G. 't Hooft, “Renormalizable Lagrangians for massive Yang-Mills fields,” Nuclear Physics B, vol. 35, no. 1, pp. 167–188, 1971. View at Publisher · View at Google Scholar
  7. M. Veltman, “Perturbation theory of massive Yang-Mills fields,” Nuclear Physics B, vol. 7, no. 5, pp. 637–650, 1968. View at Publisher · View at Google Scholar
  8. D. J. Gross and F. Wilczek, “Ultraviolet behavior of non-Abelian gauge theories,” Physical Review Letters, vol. 30, no. 26, pp. 1343–1346, 1973. View at Publisher · View at Google Scholar
  9. H. D. Politzer, “Reliable perturbative results for strong interactions?,” Physical Review Letters, vol. 30, no. 26, pp. 1346–1349, 1973. View at Publisher · View at Google Scholar
  10. F. Wilczek, “Status of QCD,” in Proceedings of the 16th International Symposium on Lepton and Photon Interactions, P. Drell and D. L. Rubin, Eds., pp. 593–619, AIP Press, Ithaca, NY, USA, August 1993.
  11. C. G. Callan, Jr., “Broken scale invariance in scalar field theory,” Physical Review D, vol. 2, no. 8, pp. 1541–1547, 1970. View at Publisher · View at Google Scholar
  12. K. Symanzik, “Small distance behaviour in field theory and power counting,” Communications in Mathematical Physics, vol. 18, no. 3, pp. 227–246, 1970. View at Publisher · View at Google Scholar · View at MathSciNet
  13. K. Symanzik, “Small-distance behaviour in field theory,” in Strong Interaction Physics, G. Höhler, Ed., vol. 57 of Springer Tracts in Modern Physics, pp. 222–236, Springer, Berlin, Germany, 1971. View at Publisher · View at Google Scholar
  14. S. Weinberg, “New approach to the renormalization group,” Physical Review D, vol. 8, no. 10, pp. 3497–3509, 1973. View at Publisher · View at Google Scholar
  15. H. Georgi and H. D. Politzer, “Electroproduction scaling in an asymptotically free theory of strong interactions,” Physical Review D, vol. 9, no. 2, pp. 416–420, 1974. View at Publisher · View at Google Scholar
  16. D. J. Gross and F. Wilczek, “Asymptotically free gauge theories. II,” Physical Review D, vol. 9, no. 4, pp. 980–993, 1974. View at Publisher · View at Google Scholar
  17. 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
  18. Yu. 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 (Russian).
  19. L. N. Lipatov, “The parton model and perturbation theory,” Yadernaya Fizika, vol. 20, pp. 181–198, 1974.
  20. V. Gribov and L. Lipatov, “e+e− pair annihilation and deep inelastic ep-scattering in perturbation theory,” Soviet Journal of Nuclear Physics, vol. 15, pp. 675–684, 1972.
  21. J. C. Collins and J. Qiu, “New derivation of the Altarelli-Parisi equations,” Physical Review D, vol. 39, no. 5, pp. 1398–1408, 1989. View at Publisher · View at Google Scholar
  22. S. Kretzer, H. L. Lai, F. I. Olness, and W. K. Tung, “CTEQ6 parton distributions with heavy quark mass effects,” Physical Review D, vol. 69, no. 11, Article ID 114005, 11 pages, 2004. View at Publisher · View at Google Scholar
  23. A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne, “Parton distributions incorporating QED contributions,” The European Physical Journal C, vol. 39, no. 2, pp. 155–161, 2005. View at Publisher · View at Google Scholar
  24. M. Glück, E. Reya, M. Stratmann, and W. Vogelsang, “Models for the polarized parton distributions of the nucleon,” Physical Review D, vol. 63, no. 9, Article ID 094005, 12 pages, 2001. View at Publisher · View at Google Scholar
  25. R. S. Thorne, A. D. Martin, R. G. Roberts, and W. J. Stirling, “Recent progress in parton distributions and implications for LHC physics,” in Proceedings of 13th International Workshop on Deep Inelastic Scattering (DIS '05), vol. 792, pp. 365–370, Madison, Wis, USA, April-May 2005. View at Publisher · View at Google Scholar
  26. R. D. Field, Applications of Perturbative QCD, Addison-Wesley, Redwood City, Calif, USA, 1989.
  27. F. A. Berends, “Z line shape,” in Z Physics at LEP 1, G. Altarelli, R. Kleiss, and C. Verzegnassi, Eds., vol. 1, p. 89, CERN, Geneva, Switzerland, 1989.
  28. S. Jadach, M. Skrzypek, and B. F. L. Ward, “Analytical results for low-angle Bhabha scattering with pair production,” Physical Review D, vol. 47, no. 9, pp. 3733–3741, 1993. View at Publisher · View at Google Scholar
  29. S. Jadach, M. Skrzypek, and B. F. L. Ward, “Is there a better way of exponentiating QED corrections?,” Physics Letters B, vol. 257, no. 1-2, pp. 173–178, 1991. View at Publisher · View at Google Scholar
  30. S. Jadach, M. Skrzypek, and B. F. L. Ward, “Z∘ physics,” in Proceedings of the 25th Rencontre de Moriond, J. Tran Thanh Van, Ed., p. 459, Editions Frontieres, Les Arcs, France, March 1990.
  31. S. Jadach, E. Richter-Was, B. F. L. Ward, and Z. Was, “High-precision improved-analytic-exponentiation results for multiple-photon effects in low-angle Bhabha scattering at the SLAC Linear Collider and the CERN e+e− collider LEP,” Physical Review D, vol. 44, no. 9, pp. 2669–2677, 1991. View at Publisher · View at Google Scholar
  32. S. Jadach and B. F. L. Ward, “Exclusive exponentiation in the Monte Carlo Yennie-Frautschi-Suura approach,” in Proceedings of the Brighton Workshop on Radiative Corrections, N. Dombey and F. Boudjema, Eds., pp. 325–340, Plenum, Brighton, UK, July 1989.
  33. C. Balázs, E. L. Berger, P. Nadolsky, and C.-P. Yuan, “All-orders resummation for diphoton production at hadron colliders,” Physics Letters B, vol. 637, no. 4-5, pp. 235–240, 2006. View at Publisher · View at Google Scholar
  34. D. Acosta, J. Adelman, T. Affolder, et al., “Measurement of the cross section for prompt diphoton production in pp¯ collisions at s=1.96 TeV,” Physical Review Letters, vol. 95, no. 2, Article ID 022003, 7 pages, 2005. View at Publisher · View at Google Scholar
  35. S. Albino and R. D. Ball, “Soft resummation of quark anomalous dimensions and coefficient functions in MS-bar factorization,” Physics Letters B, vol. 513, no. 1-2, pp. 93–102, 2001. View at Publisher · View at Google Scholar
  36. S. V. Mikhailov, “Renormalon chain contributions to non-singlet evolution kernels in QCD,” Physics Letters B, vol. 431, no. 3-4, pp. 387–394, 1998. View at Publisher · View at Google Scholar
  37. B. F. L. Ward and S. Jadach, “YFS MC approach to QCD soft gluon exponentiation,” Acta Physica Polonica B, vol. 33, no. 6, p. 1543, 2002.
  38. B. F. L. Ward and S. Jadach, “QCD soft gluon exponentiation: YFS MC approach,” in Proceedings of the 31st International Conference on High Energy Physics (ICHEP '02), S. Bentvelsen, P. de Jong, J. Koch, and E. Laenen, Eds., pp. 275–278, North Holland, Amsterdam, The Netherlands, 2003.
  39. B. F. L. Ward and S. Jadach, “Dokshitzer-Gribov-Lipatov-altarelli-parisi evolution and the renormalization group improved Yennie-Frautschi-Suura theory in QCD,” Modern Physics Letters A, vol. 14, no. 7, pp. 491–500, 1999. View at Publisher · View at Google Scholar
  40. D. DeLaney, S. Jadach, S. M. Kim, Ch. Shio, G. Siopsis, and B. F. L. Ward, “Multiple gluon effects in q+q¯→t+t¯+X at FNAL energies: semi-analytical results,” Modern Physics Letters A, vol. 12, no. 32, pp. 2425–2434, 1997. View at Publisher · View at Google Scholar
  41. C. Glosser, S. Jadach, B. F. L. Ward, and S. A. Yost, “QED ⊗ QCD Threshold corrections at the LHC,” Modern Physics Letters A, vol. 19, no. 28, pp. 2113–2119, 2004. View at Publisher · View at Google Scholar
  42. B. F. L. Ward, C. Glosser, S. Jadach, and S. A. Yost, “Int. J. Mod. Phys. A20 (2005) 3735,” in Proceedings of the Annual Meeting of the Division of Particles and (DPF) of the American Physical Society (APS), Riverside, Calif, USA, August 2004.
  43. B. F. L. Ward, C. Glosser, S. Jadach, and S. A. Yost, “Threshold corrections in precision LHC physics: QED ⊗ QCD,” International Journal of Modern Physics A, vol. 20, no. 16, pp. 3735–3738, 2005. View at Publisher · View at Google Scholar
  44. B. F. L. Ward, C. Glosser, S. Jadach, and S. A. Yost, “Threshold Corrections in QED ⊗ QCD at the LHC,” in Proceedings of the 32nd International Conference on High Energy Physics (ICHEP '04), H. Chen, D. Du, W. Li, and C. Lu, Eds., vol. 1, pp. 588–591, World Scientific, Beijing, China, August 2005. View at Publisher · View at Google Scholar
  45. B. F. L. Ward and S. A. Yost, “QED⊗QCD exponentiation and shower/ME matching at the LHC,” in Proceedings of the Workshop on the Implications of HERA for LHC Physics, Desy, Hamburg, Germany, March-January 2005.
  46. D. DeLaney, S. Jadach, Ch. Shio, G. Siopsis, and B. F. L. Ward, “Multiple gluon effects in fermion-(anti)fermion scattering at and beyond CERN LHC energies,” Physical Review D, vol. 52, no. 1, pp. 108–115, 1995. View at Publisher · View at Google Scholar
  47. D. DeLaney, S. Jadach, Ch. Shio, G. Siopsis, and B. F. L. Ward, “Erratum: multiple gluon effects in fermion-(anti)fermion scattering at and beyond CERN LHC energies,” Physical Review D, vol. 66, no. 1, Article ID 019903, 1 pages, 2002. View at Publisher · View at Google Scholar
  48. D. DeLaney, S. Jadach, Ch. Shio, G. Siopsis, and B. F. L. Ward, “Renormalization group improved exponentiation of soft gluons in QCD,” Physics Letters B, vol. 342, no. 1–4, pp. 239–244, 1995. View at Publisher · View at Google Scholar
  49. D. R. Yennie, S. C. Frautschi, and H. Suura, “The infrared divergence phenomena and high-energy processes,” Annals of Physics, vol. 13, no. 3, pp. 379–452, 1961. View at Publisher · View at Google Scholar
  50. K. T. Mahanthappa, “Multiple production of photons in quantum electrodynamics,” Physical Review, vol. 126, no. 1, pp. 329–340, 1962. View at Publisher · View at Google Scholar
  51. R. K. Ellis, H. Georgi, M. Machacek, H. D. Politzer, and G. G. Ross, “Factorization and the parton model in QCD,” Physics Letters B, vol. 78, no. 2-3, pp. 281–284, 1978. View at Publisher · View at Google Scholar
  52. R. K. Ellis, H. Georgi, M. Machacek, H. D. Politzer, and G. G. Ross, “Perturbation theory and the parton model in QCD,” Nuclear Physics B, vol. 152, no. 2, pp. 285–329, 1979. View at Publisher · View at Google Scholar
  53. D. Amati, R. Petronzio, and G. Veneziano, “Relating hard QCD processes through universality of mass singularities (II),” Nuclear Physics B, vol. 146, no. 1, pp. 29–49, 1978. View at Publisher · View at Google Scholar
  54. S. B. Libby and G. Sterman, “Jet and lepton-pair production in high-energy lepton-hadron and hadron-hadron scattering,” Physical Review D, vol. 18, no. 9, pp. 3252–3268, 1978. View at Publisher · View at Google Scholar
  55. A. H. Mueller, “Cut vertices and their renormalization: a generalization of the Wilson expansion,” Physical Review D, vol. 18, no. 10, pp. 3705–3727, 1978. View at Publisher · View at Google Scholar
  56. J. C. Collins, “What exactly is a parton density?,” Acta Physica Polonica B, vol. 34, no. 6, pp. 3103–3120, 2003.
  57. G. 't Hooft and M. Veltman, “Regularization and renormalization of gauge fields,” Nuclear Physics B, vol. 44, no. 1, pp. 189–213, 1972. View at Publisher · View at Google Scholar
  58. G. 't Hooft and M. Veltman, “Combinatorics of gauge fields,” Nuclear Physics B, vol. 50, no. 1, pp. 318–353, 1972. View at Publisher · View at Google Scholar
  59. S. G. Gorishnii, S. A. Larin, and F. V. Tkachov, “The algorithm for OPE coefficient functions in the MS scheme,” Physics Letters B, vol. 124, no. 3-4, pp. 217–220, 1983. View at Publisher · View at Google Scholar
  60. S. G. Gorishnii and S. A. Larin, “Coefficient functions of asymptotic operator expansions in the minimal subtraction scheme,” Nuclear Physics B, vol. 283, pp. 452–476, 1987. View at Publisher · View at Google Scholar
  61. B. F. L. Ward, to appear.
  62. S. Bethke, “αs at Zinnowitz 2004,” Nuclear Physics B - Proceedings Supplements, vol. 135, pp. 345–352, 2004. View at Publisher · View at Google Scholar
  63. T. Carli, A. Cooper-Sarkar, J. Feltesse, et al., “Experimental determination of Parton distributions,” in Proceedings of the Workshop on the Implications of HERA for LHC Physics, A. de Roeck and H. Jung, Eds., p. 78, CERN, Desy, Hamburg, Germany, March-January 2005.
  64. E. G. Floratos, D. A. Ross, and C. T. Sachrajda, “Higher-order effects in asymptotically free gauge theories: the anomalous dimensions of Wilson operators,” Nuclear Physics B, vol. 129, no. 1, pp. 66–88, 1977. View at Publisher · View at Google Scholar
  65. E. G. Floratos, D. A. Ross, and C. T. Sachrajda, “Higher-order effects in asymptotically free gauge theories: the anomalous dimensions of Wilson operators,” Nuclear Physics B, vol. 139, no. 4, pp. 545–546, 1978. View at Publisher · View at Google Scholar
  66. E. G. Floratos, D. A. Ross, and C. T. Sachrajda, “Higher-order effects in asymptotically free gauge theories (II). Flavour singlet Wilson operators and coefficient functions,” Nuclear Physics B, vol. 152, no. 3-4, pp. 493–520, 1979. View at Publisher · View at Google Scholar
  67. A. Gonzalez-Arroyo, C. Lopez, and F. J. Yndurain, “Second-order contributions to the structure functions in deep inelastic scattering (I). Theoretical calculations,” Nuclear Physics B, vol. 153, pp. 161–186, 1979.
  68. A. Gonzalez-Arroyo and C. Lopez, “Second-order contributions to the structure functions in deep inelastic scattering (III). The singlet case,” Nuclear Physics B, vol. 166, no. 3, pp. 429–459, 1980. View at Publisher · View at Google Scholar
  69. G. Curci, W. Furmanski, and R. Petronzio, “Evolution of parton densities beyond leading order the non-singlet case,” Nuclear Physics B, vol. 175, no. 1, pp. 27–92, 1980. View at Publisher · View at Google Scholar
  70. W. Furmanski and R. Petronzio, “Singlet parton densities beyond leading order,” Physics Letters B, vol. 97, no. 3-4, pp. 437–442, 1980. View at Publisher · View at Google Scholar
  71. E. G. Floratos, C. Kounnas, and R. Lacaze, “Higher order QCD effects in inclusive annihilation and deep inelastic scattering,” Nuclear Physics B, vol. 192, no. 2, pp. 417–462, 1981. View at Publisher · View at Google Scholar
  72. R. Hamberg and W. van Neerven, “The correct renormalization of the gluon operator in a covariant gauge,” Nuclear Physics B, vol. 379, no. 1-2, pp. 143–171, 1992. View at Publisher · View at Google Scholar
  73. S. Moch, J. A. M. Vermaseren, and A. Vogt, “The three-loop splitting functions in QCD: the non-singlet case,” Nuclear Physics B, vol. 688, no. 1-2, pp. 101–134, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  74. A. Vogta, S. Moch, and J. A. M. Vermaseren, “The three-loop splitting functions in QCD: the singlet case,” Nuclear Physics B, vol. 691, no. 1-2, pp. 129–181, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  75. G. Corcella and L. Magnea, “Soft-gluon resummation effects on parton distributions,” Physical Review D, vol. 72, no. 7, Article ID 074017, 10 pages, 2005. View at Publisher · View at Google Scholar
  76. G. Sterman, “Summation of large corrections to short-distance hadronic cross sections,” Nuclear Physics B, vol. 281, no. 1-2, pp. 310–364, 1987. View at Publisher · View at Google Scholar
  77. S. Catani and L. Trentadue, “Resummation of the QCD perturbative series for hard processes,” Nuclear Physics B, vol. 327, no. 2, pp. 323–352, 1989. View at Publisher · View at Google Scholar
  78. S. Catani and L. Trentadue, “Comment of QCD exponentiation at large x,” Nuclear Physics B, vol. 353, no. 1, pp. 183–186, 1991. View at Publisher · View at Google Scholar
  79. S. Moch, J. A. M. Vermaseren, and A. Vogt, “Higher-order corrections in threshold resummation,” Nuclear Physics B, vol. 726, no. 1-2, pp. 317–335, 2005. View at Publisher · View at Google Scholar
  80. S. Mert Aybat, L. J. Dixon, and G. Sterman, “Two-loop soft anomalous dimension matrix and resummation at next-to-next-to-leading poles,” Physical Review D, vol. 74, no. 7, Article ID 074004, 23 pages, 2006. View at Publisher · View at Google Scholar
  81. G. Sterman, An Introduction to Quantum Field Theory, Cambridge University Press, Cambridge, UK, 1993.
  82. T. Muta, Foundations of Quantum Chromodynamics, World Scientific, Singapore, 2nd edition, 1998.
  83. S. Weinberg, The Quantum Theory of Fields, Vol. 1: Foundations, Cambridge Univeristy Press, Cambridge, UK, 1995.
  84. S. Jadach, B. F. L. Ward, and Z. Was, “Global positioning of spin GPS scheme for half-spin massive spinors,” The European Physical Journal C, vol. 22, no. 3, pp. 423–430, 2001. View at Publisher · View at Google Scholar
  85. S. Jadach, B. F. L. Ward, and Z. Was, “Coherent exclusive exponentiation for precision Monte Carlo calculations,” Physical Review D, vol. 63, no. 11, Article ID 113009, 65 pages, 2001. View at Publisher · View at Google Scholar
  86. J. G. M. Gatheral, “Exponentiation of eikonal cross sections in nonabelian gauge theories,” Physics Letters B, vol. 133, no. 1-2, pp. 90–94, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  87. R. K. Ellis and J. C. Sexton, “QCD radiative corrections to parton-parton scattering,” Nuclear Physics B, vol. 269, no. 2, pp. 445–484, 1986. View at Publisher · View at Google Scholar
  88. C. Di'Lieto, S. Gendron, I. G. Halliday, and C. T. Sachrajda, “A counter example to the Bloch-Nordsieck theorem in non-abelian gauge theories,” Nuclear Physics B, vol. 183, no. 1-2, pp. 223–250, 1981. View at Publisher · View at Google Scholar
  89. S. Catani, M. Ciafaloni, and G. Marchesini, “Non-cancelling infrared divergences in QCD coherent states,” Nuclear Physics B, vol. 264, pp. 588–620, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  90. S. Catani, “Violation of the Bloch-Nordsieck mechanism in general non-abelian theories and SUSY QCD,” Zeitschrift für Physik C, vol. 37, no. 3, pp. 357–363, 1988. View at Publisher · View at Google Scholar
  91. J. C. Collins, D. E. Soper, and G. Sterman, “Transverse momentum distribution in Drell-Yan pair and W and Z boson production,” Nuclear Physics B, vol. 250, no. 1–4, pp. 199–224, 1985. View at Publisher · View at Google Scholar