Abstract
In this paper we investigate the extension of high energy resummation at LLx accuracy to jet observables. In particular, we present the high energy resummed expression of the transverse momentum distribution of the outgoing parton in the general partonic process g(q) + g(q) → g(q) + X. In order to reach this result, several new ideas are introduced and exploited. First we prove that LLx resummation is achieved by dressing with hard radiation an off-shell gluon initiated LO process even if its on-shell limit is vanishing or trivial. Then we present a gauge-invariant framework where these calculations can be performed by using the modern helicity techniques. Finally, we show a possible way to restore gluon indistinguishability in the final state, which is otherwise lost in the resummation procedure, at all orders in α s at LLx. All partonic channels are then resummed and cross-checked against fixed-order calculations up to \( \mathcal{O}\left({\alpha}_s^3\right) \).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L.N. Lipatov, Reggeization of the vector meson and the vacuum singularity in non-Abelian gauge theories, Sov. J. Nucl. Phys. 23 (1976) 338 [Yad. Fiz. 23 (1976) 642] [INSPIRE].
V.S. Fadin, E.A. Kuraev and L.N. Lipatov, On the Pomeranchuk singularity in asymptotically free theories, Phys. Lett. B 60 (1975) 50 [INSPIRE].
S. Catani, M. Ciafaloni and F. Hautmann, Gluon contributions to small x heavy flavor production, Phys. Lett. B 242 (1990) 97 [INSPIRE].
S. Catani and F. Hautmann, High-energy factorization and small x deep inelastic scattering beyond leading order, Nucl. Phys. B 427 (1994) 475 [hep-ph/9405388] [INSPIRE].
S. Catani, M. Ciafaloni and F. Hautmann, High-energy factorization and small x heavy flavor production, Nucl. Phys. B 366 (1991) 135 [INSPIRE].
F. Caola, S. Forte and S. Marzani, Small x resummation of rapidity distributions: the case of Higgs production, Nucl. Phys. B 846 (2011) 167 [arXiv:1010.2743] [INSPIRE].
S. Forte and C. Muselli, High energy resummation of transverse momentum distributions: Higgs in gluon fusion, JHEP 03 (2016) 122 [arXiv:1511.05561] [INSPIRE].
A. van Hameren, Helicity amplitudes for high-energy scattering processes, PoS(RADCOR 2013)036 [INSPIRE].
A. van Hameren, P. Kotko and K. Kutak, Helicity amplitudes for high-energy scattering, JHEP 01 (2013) 078 [arXiv:1211.0961] [INSPIRE].
P. Kotko, Wilson lines and gauge invariant off-shell amplitudes, JHEP 07 (2014) 128 [arXiv:1403.4824] [INSPIRE].
L.N. Lipatov, Gauge invariant effective action for high-energy processes in QCD, Nucl. Phys. B 452 (1995) 369 [hep-ph/9502308] [INSPIRE].
S. Moch, J.A.M. Vermaseren and A. Vogt, The three loop splitting functions in QCD: the nonsinglet case, Nucl. Phys. B 688 (2004) 101 [hep-ph/0403192] [INSPIRE].
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] [INSPIRE].
R.K. Ellis and J.C. Sexton, QCD radiative corrections to parton parton scattering, Nucl. Phys. B 269 (1986) 445 [INSPIRE].
Z. Nagy, Next-to-leading order calculation of three jet observables in hadron hadron collision, Phys. Rev. D 68 (2003) 094002 [hep-ph/0307268] [INSPIRE].
J. Currie, E.W.N. Glover and J. Pires, Next-to-next-to leading order QCD predictions for single jet inclusive production at the LHC, Phys. Rev. Lett. 118 (2017) 072002 [arXiv:1611.01460] [INSPIRE].
J. Currie, E.W.N. Glover, T. Gehrmann, A. Gehrmann-De Ridder, A. Huss and J. Pires, Single jet inclusive production for the individual jet p T scale choice at the LHC, Acta Phys. Polon. B 48 (2017) 955 [arXiv:1704.00923] [INSPIRE].
M. Bonvini, Resummations in PDF fits, PoS(DIS2016)030 [arXiv:1611.01925] [INSPIRE].
R.D. Ball, V. Bertone, M. Bonvini, S. Marzani, J. Rojo and L. Rottoli, Parton distributions with small-x resummation: evidence for BFKL dynamics in HERA data, arXiv:1710.05935 [INSPIRE].
M. Bonvini, S. Marzani and C. Muselli, Towards parton distribution functions with small-x resummation: HELL 2.0, submitted to JHEP (2017) [arXiv:1708.07510] [INSPIRE].
F. Caola, S. Forte, S. Marzani, C. Muselli and G. Vita, The Higgs transverse momentum spectrum with finite quark masses beyond leading order, JHEP 08 (2016) 150 [arXiv:1606.04100] [INSPIRE].
R.K. Ellis, H. Georgi, M. Machacek, H.D. Politzer and G.G. Ross, Perturbation theory and the parton model in QCD, Nucl. Phys. B 152 (1979) 285 [INSPIRE].
G. Curci, W. Furmanski and R. Petronzio, Evolution of parton densities beyond leading order: the nonsinglet case, Nucl. Phys. B 175 (1980) 27 [INSPIRE].
G. Altarelli, R.D. Ball and S. Forte, Small x resummation and HERA structure function data, Nucl. Phys. B 599 (2001) 383 [hep-ph/0011270] [INSPIRE].
G. Altarelli, R.D. Ball and S. Forte, Resummation of singlet parton evolution at small x, Nucl. Phys. B 575 (2000) 313 [hep-ph/9911273] [INSPIRE].
G. Altarelli, R.D. Ball and S. Forte, Factorization and resummation of small x scaling violations with running coupling, Nucl. Phys. B 621 (2002) 359 [hep-ph/0109178] [INSPIRE].
M. Bonvini, S. Marzani and T. Peraro, Small-x resummation from HELL, Eur. Phys. J. C 76 (2016) 597 [arXiv:1607.02153] [INSPIRE].
S. Marzani and R.D. Ball, High energy resummation of Drell-Yan processes, Nucl. Phys. B 814 (2009) 246 [arXiv:0812.3602] [INSPIRE].
M.E. Peskin, Simplifying multi-jet QCD computation, arXiv:1101.2414 [INSPIRE].
L.J. Dixon, Calculating scattering amplitudes efficiently, in QCD and beyond, Boulder U.S.A., (1995), pg. 539 [hep-ph/9601359] [INSPIRE].
C. Muselli, High-energy resummation of Higgs p T distribution, Acta Phys. Polon. B 48 (2017) 1105 [INSPIRE].
T. Jaroszewicz, Gluonic Regge singularities and anomalous dimensions in QCD, Phys. Lett. B 116 (1982) 291 [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: 1710.08416
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
Zoia, S., Muselli, C. High energy resummation of jet observables. J. High Energ. Phys. 2017, 97 (2017). https://doi.org/10.1007/JHEP12(2017)097
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2017)097