Abstract
We analytically compute non-global logarithms at finite N c fully up to 4 loops and partially at 5 loops, for the hemisphere mass distribution in e + e − → di-jets to leading logarithmic accuracy. Our method of calculation relies solely on integrating the eikonal squared-amplitudes for the emission of soft energy-ordered real-virtual gluons over the appropriate phase space. We show that the series of non-global logarithms in the said distribution exhibits a pattern of exponentiation thus confirming — by means of brute force — previous findings. In the large-N c limit, our results coincide with those recently reported in literature. A comparison of our proposed exponential form with all-orders numerical solutions is performed and the phenomenological impact of the finite-N c corrections is discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Butterworth, A.R. Davison, M. Rubin and G.P. Salam, Jet substructure as a new Higgs search channel at the LHC, Phys. Rev. Lett. 100 (2008) 242001 [arXiv:0802.2470] [INSPIRE].
D.E. Kaplan, K. Rehermann, M.D. Schwartz and B. Tweedie, Top tagging: a method for identifying boosted hadronically decaying top quarks, Phys. Rev. Lett. 101 (2008) 142001 [arXiv:0806.0848] [INSPIRE].
J. Thaler and L.-T. Wang, Strategies to identify boosted tops, JHEP 07 (2008) 092 [arXiv:0806.0023] [INSPIRE].
S.D. Ellis, C.K. Vermilion and J.R. Walsh, Recombination algorithms and jet substructure: pruning as a tool for heavy particle searches, Phys. Rev. D 81 (2010) 094023 [arXiv:0912.0033] [INSPIRE].
J. Gallicchio and M.D. Schwartz, Seeing in color: jet superstructure, Phys. Rev. Lett. 105 (2010) 022001 [arXiv:1001.5027] [INSPIRE].
J. Gallicchio et al., Multivariate discrimination and the Higgs + W/Z search, JHEP 04 (2011) 069 [arXiv:1010.3698] [INSPIRE].
J. Thaler and K. Van Tilburg, Identifying boosted objects with N-subjettiness, JHEP 03 (2011) 015 [arXiv:1011.2268] [INSPIRE].
Y. Cui, Z. Han and M.D. Schwartz, W-jet tagging: optimizing the identification of boosted hadronically-decaying W bosons, Phys. Rev. D 83 (2011) 074023 [arXiv:1012.2077] [INSPIRE].
A. Abdesselam et al., Boosted objects: a probe of beyond the Standard Model physics, Eur. Phys. J. C 71 (2011) 1661 [arXiv:1012.5412] [INSPIRE].
J. Gallicchio and M.D. Schwartz, Quark and gluon tagging at the LHC, Phys. Rev. Lett. 107 (2011) 172001 [arXiv:1106.3076] [INSPIRE].
A. Altheimer et al., Jet substructure at the Tevatron and LHC: new results, new tools, new benchmarks, J. Phys. G 39 (2012) 063001 [arXiv:1201.0008] [INSPIRE].
S.D. Ellis, A. Hornig, T.S. Roy, D. Krohn and M.D. Schwartz, Qjets: a non-deterministic approach to tree-based jet substructure, Phys. Rev. Lett. 108 (2012) 182003 [arXiv:1201.1914] [INSPIRE].
A. Altheimer, A. Arce, L. Asquith, J. Backus Mayes, E. Bergeaas Kuutmann et al., Boosted objects and jet substructure at the LHC. Report of BOOST2012, held at IFIC Valencia, 23rd –27th of July 2012, Eur. Phys. J. C 74 (2014) 2792 [arXiv:1311.2708] [INSPIRE].
D. Krohn, J. Thaler and L.-T. Wang, Jet trimming, JHEP 02 (2010) 084 [arXiv:0912.1342] [INSPIRE].
M. Dasgupta, A. Fregoso, S. Marzani and G.P. Salam, Towards an understanding of jet substructure, JHEP 09 (2013) 029 [arXiv:1307.0007] [INSPIRE].
M. Bahr et al., HERWIG++ physics and manual, Eur. Phys. J. C 58 (2008) 639 [arXiv:0803.0883] [INSPIRE].
S. Gieseke et al., HERWIG++ 2.5 release note, arXiv:1102.1672 [INSPIRE].
T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].
T. Sjöstrand, S. Mrenna and P.Z. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].
T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [INSPIRE].
A.H. Hoang, D.W. Kolodrubetz, V. Mateu and I.W. Stewart, C-parameter distribution at N 3 LL ′ including power corrections, arXiv:1411.6633 [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Principles of general final-state resummation and automated implementation, JHEP 03 (2005) 073 [hep-ph/0407286] [INSPIRE].
A. Banfi, H. McAslan, P.F. Monni and G. Zanderighi, A general method for the resummation of event-shape distributions in e + e − annihilation, arXiv:1412.2126 [INSPIRE].
M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].
M. Dasgupta and G.P. Salam, Accounting for coherence in interjet E t flow: a case study, JHEP 03 (2002) 017 [hep-ph/0203009] [INSPIRE].
A. Banfi, G. Marchesini and G. Smye, Away from jet energy flow, JHEP 08 (2002) 006 [hep-ph/0206076] [INSPIRE].
Y. Hatta and T. Ueda, Resummation of non-global logarithms at finite N c , Nucl. Phys. B 874 (2013) 808 [arXiv:1304.6930] [INSPIRE].
H. Weigert, Nonglobal jet evolution at finite N c , Nucl. Phys. B 685 (2004) 321 [hep-ph/0312050] [INSPIRE].
M. Rubin, Non-global logarithms in filtered jet algorithms, JHEP 05 (2010) 005 [arXiv:1002.4557] [INSPIRE].
M.D. Schwartz and H.X. Zhu, Nonglobal logarithms at three loops, four loops, five loops and beyond, Phys. Rev. D 90 (2014) 065004 [arXiv:1403.4949] [INSPIRE].
M. Levy and J. Sucher, Eikonal approximation in quantum field theory, Phys. Rev. 186 (1969) 1656 [INSPIRE].
Y.L. Dokshitzer, V.A. Khoze, A.H. Mueller and S. Troian, Basics of perturbative QCD, Editions Frontieres, Gif-sur-Yvette, France (1991).
A. Bassetto, M. Ciafaloni and G. Marchesini, Jet structure and infrared sensitive quantities in perturbative QCD, Phys. Rept. 100 (1983) 201 [INSPIRE].
S. Catani and M. Grazzini, Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond, Nucl. Phys. B 570 (2000) 287 [hep-ph/9908523] [INSPIRE].
S. Catani and M.H. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [Erratum ibid. B 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
S. Catani and M.H. Seymour, The dipole formalism for the calculation of QCD jet cross-sections at next-to-leading order, Phys. Lett. B 378 (1996) 287 [hep-ph/9602277] [INSPIRE].
M. Sjödahl, ColorMath — a package for color summed calculations in SU(NC), Eur. Phys. J. C 73 (2013) 2310 [arXiv:1211.2099] [INSPIRE].
M. Sjödahl and S. Keppeler, Tools for calculations in color space, PoS(DIS 2013)166 [arXiv:1307.1319] [INSPIRE].
Y. Delenda and K. Khelifa-Kerfa, Eikonal gluon bremsstrahlung at finite N c to any loop order, in preparation.
R. Kelley, M.D. Schwartz, R.M. Schabinger and H.X. Zhu, The two-loop hemisphere soft function, Phys. Rev. D 84 (2011) 045022 [arXiv:1105.3676] [INSPIRE].
A. Hornig, C. Lee, I.W. Stewart, J.R. Walsh and S. Zuberi, Non-global structure of the \( \mathcal{O}\left({\alpha}_s^2\right) \) dijet soft function, JHEP 08 (2011) 054 [arXiv:1105.4628] [INSPIRE].
A.H. Hoang and S. Kluth, Hemisphere soft function at \( \mathcal{O}\left({\alpha}_s^2\right) \) for dijet production in e + e − annihilation, arXiv:0806.3852 [INSPIRE].
K. Khelifa-Kerfa, Non-global logs and clustering impact on jet mass with a jet veto distribution, JHEP 02 (2012) 072 [arXiv:1111.2016] [INSPIRE].
G. Marchesini and B.R. Webber, Simulation of QCD jets including soft gluon interference, Nucl. Phys. B 238 (1984) 1 [INSPIRE].
T. Hahn, CUBA: a library for multidimensional numerical integration, Comput. Phys. Commun. 168 (2005) 78 [hep-ph/0404043] [INSPIRE].
Y. Hatta and T. Ueda, private communication.
Y. Delenda and K. Khelifa-Kerfa, On the resummation of clustering logarithms for non-global observables, JHEP 09 (2012) 109 [arXiv:1207.4528] [INSPIRE].
Y.L. Dokshitzer, G.D. Leder, S. Moretti and B.R. Webber, Better jet clustering algorithms, JHEP 08 (1997) 001 [hep-ph/9707323] [INSPIRE].
M. Wobisch and T. Wengler, Hadronization corrections to jet cross-sections in deep inelastic scattering, hep-ph/9907280 [INSPIRE].
R.B. Appleby and M.H. Seymour, Nonglobal logarithms in interjet energy flow with kt clustering requirement, JHEP 12 (2002) 063 [hep-ph/0211426] [INSPIRE].
A. Banfi and M. Dasgupta, Problems in resumming interjet energy flows with k t clustering, Phys. Lett. B 628 (2005) 49 [hep-ph/0508159] [INSPIRE].
Y. Delenda, R. Appleby, M. Dasgupta and A. Banfi, On QCD resummation with k(t) clustering, JHEP 12 (2006) 044 [hep-ph/0610242] [INSPIRE].
A. Banfi, M. Dasgupta, K. Khelifa-Kerfa and S. Marzani, Non-global logarithms and jet algorithms in high-pT jet shapes, JHEP 08 (2010) 064 [arXiv:1004.3483] [INSPIRE].
C. Tagaris, Mellin transform and applications, http://www.math.clemson.edu/~kevja/COURSES/Math952/MTHSC952-2013-SPRING/.
S. Catani, L. Trentadue, G. Turnock and B.R. Webber, Resummation of large logarithms in e + e − event shape distributions, Nucl. Phys. B 407 (1993) 3 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1501.00475
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Khelifa-Kerfa, K., Delenda, Y. Non-global logarithms at finite N c beyond leading order. J. High Energ. Phys. 2015, 94 (2015). https://doi.org/10.1007/JHEP03(2015)094
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2015)094