Abstract
Results for the two real parton differential distributions needed for implementing a next-to-leading order (NLO) parton shower Monte Carlo are presented. They are also integratedoverthephasespaceinordertoprovidesolidnumericalcontroloftheMCcodes and for the discussion of the differences between the standard \( \overline {MS} \) factorization and Monte Carlo implementation at the level of inclusive NLO evolution kernels. Presented results cover the class of non-singlet diagrams entering into NLO kernels. The classic work of Curci-Furmanski-Pertonzio was used as a guide in the calculations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.J. Gross and F. Wilczek, Asymptotically Free Gauge Theories.1, Phys. Rev. D 8 (1973) 3633 [SPIRES].
D. J. Gross and F. Wilczek, Asymptotically Free Gauge Theories. 2, Phys. Rev. D 9 (1974) 980 [SPIRES].
H. Georgi and H.D. Politzer, Electroproduction scaling in an asymptotically free theory of strong interactions, Phys. Rev. D 9 (1974) 416 [SPIRES].
R.K. Ellis, H. Georgi, M. Machacek, H.D. Politzer and G.G. Ross, Perturbation Theory and the Parton Modelin QCD, Nucl. Phys. B 152 (1979) 285 [SPIRES].
J.C. Collins, D.E. Soper and G.F. Sterman, Transverse Momentum Distributionin Drell-Yan Pairand W and Z Boson Production, Nucl. Phys. B 250 (1985) 199 [SPIRES].
G.T. Bodwin, Factorization of the Drell-Yan Cross-Section in Perturbation Theory, Phys. Rev. D 31 (1985) 2616 [SPIRES].
L.N. Lipatov, The parton model and perturbation theory, Sov. J. Nucl. Phys. 20 (1975) 95 [Yad. Fiz. 20 (1974) 181] [SPIRES].
V.N. Gribov and L.N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [SPIRES].
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. 126 (1977) 298 [SPIRES].
Yu.L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e + e − Annihilation by Perturbation Theory in Quantum Chromodynamics, Sov. Phys. JETP 46 (1977) 641 [Zh. Eksp. Teor. Fiz. 73 (1977) 1216] [SPIRES].
E.G. Floratos, D.A. Ross and C.T. Sachrajda, Higher Order Effects in Asymptotically Free Gauge Theories. 2. Flavor Singlet Wilson Operators and Coeffcient Functions, Nucl. Phys. B 152 (1979) 493 [SPIRES].
G. Curci, W. Furmanski and R. Petronzio, Evolution of Parton Densities Beyond Leading Order: The Nonsinglet Case, Nucl. Phys. B 175 (1980) 27 [SPIRES].
A. Vogt, S. Moch and J.A.M. Vermaseren, The three-loop splitting functions in QCD: The singlet case, Nucl. Phys. B 691 (2004) 129 [hep-ph/0404111] [SPIRES].
S. Moch, J.A.M. Vermaseren and A. Vogt, The three-loop splitting functions in QCD: The non-singlet case, Nucl. Phys. B 688 (2004) 101 [hep-ph/0403192] [SPIRES].
T. Sjöstrand, A Model for Initial State Parton Showers, Phys. Lett. B 157 (1985) 321 [SPIRES].
B.R. Webber, A QCD Model for Jet Fragmentation Including Soft Gluon Interference, Nucl. Phys. B 238 (1984) 492 [SPIRES].
A .Kulesza and W.J. Stirling, On there summation of subleading logarithms in the transverse momentum distribution of vector bosons produced at hadron colliders, JHEP 01 (2000) 016 [hep-ph/9909271] [SPIRES].
A. Kulesza, G.F. Sterman and W. Vogelsang, Joint resummation in electroweak boson production, Phys. Rev. D 66 (2002) 014011 [hep-ph/0202251] [SPIRES].
G. Marchesini and B.R. Webber, Monte Carlo Simulation of General Hard Processes with Coherent QCD Radiation, Nucl. Phys. B 310 (1988) 461 [SPIRES].
G. Altarelli, R.K. Ellis and G. Martinelli, Large Perturbative Corrections to the Drell-Yan Processin QCD, Nucl. Phys. B 157 (1979) 461 [SPIRES].
C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, High precision QCD at hadron colliders: Electroweak gauge boson rapidity distributions at NNLO, Phys. Rev. D 69 (2004) [hep-ph/0312266] [SPIRES].
S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [SPIRES].
S. Jadach, A. Kusina, W. Placzek, M. Skrzypek and M. Slawinska, On the inclusion of the QCD NLO corrections in the quark-gluon Monte Carlo shower, arXiv:1103.5015 [SPIRES].
B.F.L. Ward, IR-Improved DGLAP Theory: Kernels, Parton Distributions, Reduced Cross Sections, Annals Phys. 323 (2008) 2147 [arXiv:0707.3424] [SPIRES].
S. Joseph, S. Majhi, B.F.L. Ward and S.A. Yost, HERWIRI1.0: MC Realization of IR-Improved DGLAP-CS Parton Showers, Phys. Lett. B 685 (2010) 283 [arXiv:0906.0788] [SPIRES].
S. Joseph, S. Majhi, B.F.L. Ward and S.A. Yost, New Approach to Parton Shower MC’s for Precision QCD Theory: HERWIRI 1.0 (31), Phys. Rev. D 81 (2010) 076008 [arXiv:1001.1434] [SPIRES].
J.C. Collins, Hard-scattering factorization with heavy quarks: A general treatment, Phys. Rev. D 58 (1998) 094002 [hep-ph/9806259] [SPIRES].
G. Altarelli, R.K. Ellis, M. Greco and G. Martinelli, Vector Boson Production at Colliders: A Theoretical Reappraisal, Nucl. Phys. B 246 (1984) 12 [SPIRES].
P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [SPIRES].
J.C. Collins, T.C. Rogers and A.M. Stasto, Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering, Phys. Rev. D 77 (2008) 085009 [arXiv:0708.2833] [SPIRES].
S. Jadach, M. Skrzypek, A. Kusina and M. Slawinska, Exclusive Monte Carlo modelling of NLO DGLAP evolution, PoS(RADCOR2009)069 [arXiv:1002.0010] [SPIRES].
S. Jadach, A. Kusina, M. Skrzypek and M. Slawinska, Monte Carlo modelling of NLO DGLAP QCD evolution in the fully unintegrated form, Nucl. Phys. Proc. Suppl. 205 – 206 (2010) 295 [arXiv:1007.2437] [SPIRES].
D.R. Yennie, S.C. Frautschi and H. Suura, The infrared divergence phenomena and high-energy processes, Ann. Phys. 13 (1961) 379 [SPIRES].
Y. Dokshitzer, V. Khoze, A. Mueller and S. Troyan, Basics of Perturbative QCD, Editions Frontieres, Singapore (1991).
M. Slawinska and A. Kusina, Non-abelian infra-red cancellations in the unintegrated NLO kernel, Acta Phys. Polon. B 40 (2009) 2097 [arXiv:0905.1403] [SPIRES].
A. Kusina, S. Jadach, M. Skrzypek and M. Slawinska, Properties of inclusive versus exclusive QCD evolution kernels, Acta Phys. Polon. B 41 (2010) 1683 [arXiv:1004.4131] [SPIRES].
C. Everett and E. Cashwell, Monte carlo sampler, Los Alamos Report: LA-5061-MS, 1972 [SPIRES].
S. Jadach and M. Skrzypek, Solving constrained Markovian evolution in QCD with the help of the non-Markovian Monte Carlo, Comput. Phys. Commun. 175 (2006) 511 [hep-ph/0504263] [SPIRES].
S. Jadach and M. Skrzypek, Non-Markovian Monte Carlo algorithm for the constrained Markovian evolution in QCD, Acta Phys. Polon. B 36 (2005) 2979 [hep-ph/0504205] [SPIRES].
A. Kusina, S. Jadach, M. Skrzypek and M. Slawinska, NLO evolution kernels: Monte Carlo versus MSbar, arXiv:1106.1787 [SPIRES].
R.K. Ellis, H. Georgi, M. Machacek, H.D. Politzer and G.G. Ross, Factorization and the Parton Modelin QCD, Phys. Lett. B 78 (1978) 281 [SPIRES].
K.J. Golec-Biernat, S. Jadach, W. Placzek and M. Skrzypek, Markovian Monte Carlo solutions of the NLO QCD evolution equations, Acta Phys. Polon. B 37 (2006) 1785 [hep-ph/0603031] [SPIRES].
S. Jadach, W. Placzek, M. Skrzypek, P. Stephens and Z. Was, Constrained MC for QCD evolution with rapidity ordering and minimum k(T), Comput. Phys. Commun. 180 (2009) 675 [hep-ph/0703281] [SPIRES].
S. Catani and M.H. Seymour, A general algorithm for calculating jet cross sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [hep-ph/9605323] [SPIRES].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna Subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [SPIRES].
G. Heinrich and Z. Kunszt, Two-loop anomalous dimension in light-cone gauge with Mandelstam-Leibbrandt prescription, Nucl. Phys. B 519 (1998) 405 [hep-ph/9708334] [SPIRES].
A. Bassetto, G. Heinrich, Z. Kunszt and W. Vogelsang, The light-cone gauge and the calculation of the two-loop splitting functions, Phys. Rev. D 58 (1998) 094020 [hep-ph/9805283] [SPIRES].
S. Jadach, Foam: A general purpose cellular Monte Carlo event generator, Comput. Phys. 152 (2003) 55 [physics/0203033].
M. Slawinska and S. Jadach, MC develop—the universal framework for Stochastic Simulations, Comput. Phys. Commun. 182 (2011) 748 [arXiv:1006.5633] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1102.5083
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Jadach, S., Kusina, A., Skrzypek, M. et al. Two real parton contributions to non-singlet kernels for exclusive QCD DGLAP evolution. J. High Energ. Phys. 2011, 12 (2011). https://doi.org/10.1007/JHEP08(2011)012
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2011)012