Resummation for rapidity distributions in top-quark pair production

  • Benjamin D. Pecjak
  • Darren J. ScottEmail author
  • Xing Wang
  • Li Lin Yang
Open Access
Regular Article - Theoretical Physics


We extend our framework for the simultaneous resummation of soft and small-mass logarithms to rapidity distributions in top quark pair production. We give numerical results for the rapidity distribution of the top quark or the anti-top quark, as well as the rapidity distribution of the \( t\overline{t} \) pair, finding that resummation effects stabilize the dependence of the differential cross sections on the choice of factorization scale. We compare our results with recent measurements at the Large Hadron Collider and find good agreement. Our results may be useful in the extraction of the gluon parton distribution function from \( t\overline{t} \) production.


QCD Phenomenology 


Open Access

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  1. [1]
    M. Czakon, M.L. Mangano, A. Mitov and J. Rojo, Constraints on the gluon PDF from top quark pair production at hadron colliders, JHEP 07 (2013) 167 [arXiv:1303.7215] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    R. Gauld, Feasibility of top quark measurements at LHCb and constraints on the large-x gluon PDF, JHEP 02 (2014) 126 [arXiv:1311.1810] [INSPIRE].
  3. [3]
    M. Czakon, N.P. Hartland, A. Mitov, E.R. Nocera and J. Rojo, Pinning down the large-x gluon with NNLO top-quark pair differential distributions, JHEP 04 (2017) 044 [arXiv:1611.08609] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    M. Czakon, D. Heymes and A. Mitov, Dynamical scales for multi-TeV top-pair production at the LHC, JHEP 04 (2017) 071 [arXiv:1606.03350] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    V. Ahrens, A. Ferroglia, M. Neubert, B.D. Pecjak and L.L. Yang, Renormalization-Group Improved Predictions for Top-Quark Pair Production at Hadron Colliders, JHEP 09 (2010) 097 [arXiv:1003.5827] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  6. [6]
    A. Ferroglia, B.D. Pecjak and L.L. Yang, Soft-gluon resummation for boosted top-quark production at hadron colliders, Phys. Rev. D 86 (2012) 034010 [arXiv:1205.3662] [INSPIRE].
  7. [7]
    B.D. Pecjak, D.J. Scott, X. Wang and L.L. Yang, Resummed differential cross sections for top-quark pairs at the LHC, Phys. Rev. Lett. 116 (2016) 202001 [arXiv:1601.07020] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    M. Czakon et al., Resummation for (boosted) top-quark pair production at NNLO + NNLL in QCD, JHEP 05 (2018) 149 [arXiv:1803.07623] [INSPIRE].
  9. [9]
    N. Kidonakis and G.F. Sterman, Resummation for QCD hard scattering, Nucl. Phys. B 505 (1997) 321 [hep-ph/9705234] [INSPIRE].
  10. [10]
    G. Wang, X. Xu, L.L. Yang and H.X. Zhu, The next-to-next-to-leading order soft function for top quark pair production, JHEP 06 (2018) 013 [arXiv:1804.05218] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  11. [11]
    A. Broggio, A. Ferroglia, B.D. Pecjak and Z. Zhang, NNLO hard functions in massless QCD, JHEP 12 (2014) 005 [arXiv:1409.5294] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    A. Ferroglia, B.D. Pecjak, L.L. Yang, B.D. Pecjak and L.L. Yang, The NNLO soft function for the pair invariant mass distribution of boosted top quarks, JHEP 10 (2012) 180 [arXiv:1207.4798] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
  14. [14]
    S. Catani, M.L. Mangano, P. Nason and L. Trentadue, The Resummation of soft gluons in hadronic collisions, Nucl. Phys. B 478 (1996) 273 [hep-ph/9604351] [INSPIRE].
  15. [15]
    A. Kulesza, G.F. Sterman and W. Vogelsang, Joint resummation in electroweak boson production, Phys. Rev. D 66 (2002) 014011 [hep-ph/0202251] [INSPIRE].
  16. [16]
    M. Bonvini, Resummation of soft and hard gluon radiation in perturbative QCD, Ph.D. Thesis, Università degli Studi di Genova, Genova Italy (2012) [arXiv:1212.0480] [INSPIRE].
  17. [17]
    M. Bonvini, S. Forte and G. Ridolfi, Soft gluon resummation of Drell-Yan rapidity distributions: Theory and phenomenology, Nucl. Phys. B 847 (2011) 93 [arXiv:1009.5691] [INSPIRE].
  18. [18]
    CMS collaboration, Measurement of differential cross sections for the production of top quark pairs and of additional jets in lepton + jets events from pp collisions at \( \sqrt{s}=13 \) TeV, Phys. Rev. D 97 (2018) 112003 [arXiv:1803.08856] [INSPIRE].
  19. [19]
    S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D 93 (2016) 033006 [arXiv:1506.07443] [INSPIRE].
  20. [20]
    NNPDF collaboration, Parton distributions from high-precision collider data, Eur. Phys. J. C 77 (2017) 663 [arXiv:1706.00428] [INSPIRE].
  21. [21]
    P. Nason, S. Dawson and R.K. Ellis, The One Particle Inclusive Differential Cross-Section for Heavy Quark Production in Hadronic Collisions, Nucl. Phys. B 327 (1989) 49 [Erratum ibid. B 335 (1990) 260] [INSPIRE].
  22. [22]
    M.L. Mangano, P. Nason and G. Ridolfi, Heavy quark correlations in hadron collisions at next-to-leading order, Nucl. Phys. B 373 (1992) 295 [INSPIRE].
  23. [23]
    S. Frixione, M.L. Mangano, P. Nason and G. Ridolfi, Top quark distributions in hadronic collisions, Phys. Lett. B 351 (1995) 555 [hep-ph/9503213] [INSPIRE].
  24. [24]
    J.M. Campbell and R.K. Ellis, MCFM for the Tevatron and the LHC, Nucl. Phys. Proc. Suppl. 205-206 (2010) 10 [arXiv:1007.3492] [INSPIRE].
  25. [25]
    T. Kluge, K. Rabbertz and M. Wobisch, FastNLO: Fast pQCD calculations for PDF fits, in proceedings of the 14th International Workshop on Deep Inelastic Scattering (DIS 2006), Tsukuba, Japan, 20-24 April 2006, World Scientific (2007), pp. 483-486 [hep-ph/0609285] [INSPIRE].
  26. [26]
    fastNLO collaboration, Theory-Data Comparisons for Jet Measurements in Hadron-Induced Processes, arXiv:1109.1310 [INSPIRE].
  27. [27]
    M. Czakon, D. Heymes and A. Mitov, fastNLO tables for NNLO top-quark pair differential distributions, arXiv:1704.08551 [INSPIRE].
  28. [28]
    Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
  29. [29]
    NNPDF collaboration, Parton distributions for the LHC Run II, JHEP 04 (2015) 040 [arXiv:1410.8849] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Institute for Particle Physics PhenomenologyUniversity of DurhamDurhamU.K.
  2. 2.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands
  3. 3.Nikhef, Theory GroupAmsterdamThe Netherlands
  4. 4.School of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijingChina
  5. 5.Collaborative Innovation Center of Quantum MatterBeijingChina
  6. 6.Center for High Energy PhysicsPeking UniversityBeijingChina

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