Abstract
Theoretical predictions for t\( \overline{t} \)b\( \overline{b} \) production are of crucial importance for t\( \overline{t} \)H measurements in the H → b\( \overline{b} \) channel at the LHC. To address the large uncertainties associated with the modelling of extra QCD radiation in t\( \overline{t} \)b\( \overline{b} \) events, in this paper we present a calculation of pp → t\( \overline{t} \)b\( \overline{b} \)j at NLO QCD. The behaviour of NLO corrections is analysed in a variety of observables, and to assess theoretical uncertainties we use factor- two rescalings as well as different dynamic scales. In this context, we propose a systematic alignment of dynamic scales that makes it possible to disentangle normalisation and shape uncertainties in a transparent way. Scale uncertainties at NLO are typically at the level of 20–30% in integrated cross sections, and below 10% for the shapes of distributions. The kinematics of QCD radiation is investigated in detail, including the effects of its recoil on the objects of the t\( \overline{t} \)b\( \overline{b} \) system. In particular, we discuss various azimuthal correlations that allow one to characterise the QCD recoil pattern in a precise and transparent way. In general, the calculation at hand provides a variety of precise benchmarks that can be used to validate the modelling of QCD radiation in t\( \overline{t} \)b\( \overline{b} \) generators. Moreover, as we will argue, pp → t\( \overline{t} \)b\( \overline{b} \)j at NLO entails information that can be used to gain insights into the perturbative convergence of the inclusive t\( \overline{t} \)b\( \overline{b} \) cross section beyond NLO. Based on this idea, we address the issue of the large NLO K-factor observed in \( {\sigma}_{t\overline{t}b\overline{b}} \), and we provide evidence that supports the reduction of this K-factor through a mild adjustment of the QCD scales that are conventionally used for this process. The presented 2 → 5 NLO calculations have been carried out using OpenLoops 2 in combination with Sherpa and Munich.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ATLAS collaboration, Search for the standard model Higgs boson produced in association with top quarks and decaying into a b \( \overline{b} \)pair in pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Rev.D 97 (2018) 072016 [arXiv:1712.08895] [INSPIRE].
CMS collaboration, Search for t\( \overline{\mathrm{t}} \)H production in the H → b\( \overline{\mathrm{b}} \)decay channel with leptonic t\( \overline{\mathrm{t}} \)decays in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, JHEP03 (2019) 026 [arXiv:1804.03682] [INSPIRE].
CMS collaboration, Measurement of t\( \overline{\mathrm{t}} \)H production in the H → b\( \overline{\mathrm{b}} \)decay channel in 41.5 fb −1of proton-proton collision data at \( \sqrt{s} \) = 13 TeV, CMS-PAS-HIG-18-030 (2019).
HL/HE WG2 group collaboration, Higgs Physics at the HL-LHC and HE-LHC, arXiv:1902.00134 [INSPIRE].
CMS collaboration, Measurements of t \( \overline{t} \)cross sections in association with b jets and inclusive jets and their ratio using dilepton final states in pp collisions at \( \sqrt{s} \) = 13 TeV, Phys. Lett.B 776 (2018) 355 [arXiv:1705.10141] [INSPIRE].
ATLAS collaboration, Measurements of inclusive and differential fiducial cross-sections of t \( \overline{t} \)production with additional heavy-flavour jets in proton-proton collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, JHEP04 (2019) 046 [arXiv:1811.12113] [INSPIRE].
CMS collaboration, Measurement of the \( \mathrm{t}\overline{\mathrm{t}}\mathrm{b}\overline{\mathrm{b}} \)production cross section in the all-jet final state in pp collisions at \( \sqrt{s} \) = 13 TeV, CMS-PAS-TOP-18-011 (2019).
A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to pp → t \( \overline{t} \)b \( \overline{b} \) + X at the LHC, Phys. Rev. Lett.103 (2009) 012002 [arXiv:0905.0110] [INSPIRE].
G. Bevilacqua, M. Czakon, C.G. Papadopoulos, R. Pittau and M. Worek, Assault on the NLO Wishlist: pp → t \( \overline{t} \)b \( \overline{b} \), JHEP09 (2009) 109 [arXiv:0907.4723] [INSPIRE].
A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD Corrections to Top Anti-Top Bottom Anti-Bottom Production at the LHC: 2. full hadronic results, JHEP03 (2010) 021 [arXiv:1001.4006] [INSPIRE].
F. Cascioli, P. Maierhöfer, N. Moretti, S. Pozzorini and F. Siegert, NLO matching for t \( \overline{t} \)b \( \overline{b} \)production with massive b-quarks, Phys. Lett.B 734 (2014) 210 [arXiv:1309.5912] [INSPIRE].
T. Ježo, J.M. Lindert, N. Moretti and S. Pozzorini, New NLOPS predictions for t \( \overline{t} \)+b-jet production at the LHC, Eur. Phys. J.C 78 (2018) 502 [arXiv:1802.00426] [INSPIRE].
M.V. Garzelli, A. Kardos and Z. Trócsányi, Hadroproduction of t \( \overline{t} \)b \( \overline{b} \)final states at LHC: predictions at NLO accuracy matched with Parton Shower, JHEP03 (2015) 083 [arXiv:1408.0266] [INSPIRE].
G. Bevilacqua, M.V. Garzelli and A. Kardos, t \( \overline{t} \)b \( \overline{b} \)hadroproduction with massive bottom quarks with PowHel, arXiv:1709.06915 [INSPIRE].
J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations, JHEP07 (2014) 079 [arXiv:1405.0301] [INSPIRE].
J. Bellm et al., HERWIG 7.0/HERWIG++ 3.0 release note, Eur. Phys. J.C 76 (2016) 196 [arXiv:1512.01178] [INSPIRE].
LHC Higgs Cross Section Working Group collaboration, Handbook of LHC Higgs Cross Sections: 4. Deciphering the Nature of the Higgs Sector, arXiv:1610.07922 [INSPIRE].
F. Buccioni, NLO predictions for t \( \overline{t} \)b \( \overline{b} \)production in association with a light-jet at the LHC, talk given at QCD@LHC 2018, 27–31 August 2018, Dresden, Germany [https://indico.cern.ch/event/662485/contributions/3074074/].
F. Buccioni, NLO predictions for t \( \overline{t} \)b \( \overline{b} \)production in association with a light-jet at the LHC, talk given at The 7th International Workshop on High Precision for Hard Processes (HP2 2018), 1–3 October 2018, Freiburg, Germany [https://indico.cern.ch/event/694599/contributions/3142622/].
F. Buccioni et al., OpenLoops 2, Eur. Phys. J.C 79 (2019) 866 [arXiv:1907.13071] [INSPIRE].
F. Buccioni, S. Pozzorini and M. Zoller, On-the-fly reduction of open loops, Eur. Phys. J.C 78 (2018) 70 [arXiv:1710.11452] [INSPIRE].
F. Krauss, R. Kuhn and G. Soff, AMEGIC++ 1.0: A Matrix element generator in C++,JHEP02 (2002) 044 [hep-ph/0109036] [INSPIRE].
T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP02 (2009) 007 [arXiv:0811.4622] [INSPIRE].
T. Gleisberg and S. Hoeche, Comix, a new matrix element generator, JHEP12 (2008) 039 [arXiv:0808.3674] [INSPIRE].
T. Gleisberg and F. Krauss, Automating dipole subtraction for QCD NLO calculations, Eur. Phys. J.C 53 (2008) 501 [arXiv:0709.2881] [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, S. Dittmaier, M.H. Seymour and Z. Trócsányi, The Dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys.B 627 (2002) 189 [hep-ph/0201036] [INSPIRE].
F. Cascioli, P. Maierhofer and S. Pozzorini, Scattering Amplitudes with Open Loops, Phys. Rev. Lett.108 (2012) 111601 [arXiv:1111.5206] [INSPIRE].
A. Denner and S. Dittmaier, Scalar one-loop 4-point integrals, Nucl. Phys.B 844 (2011) 199 [arXiv:1005.2076] [INSPIRE].
A. Denner, S. Dittmaier and L. Hofer, COLLIER — A fortran-library for one-loop integrals, PoS(LL2014)071 (2014) [arXiv:1407.0087] [INSPIRE].
A. Denner, S. Dittmaier and L. Hofer, Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations, Comput. Phys. Commun.212 (2017) 220 [arXiv:1604.06792] [INSPIRE].
A. van Hameren, OneLOop: For the evaluation of one-loop scalar functions, Comput. Phys. Commun.182 (2011) 2427 [arXiv:1007.4716] [INSPIRE].
A. Denner and S. Dittmaier, Reduction of one loop tensor five point integrals, Nucl. Phys.B 658 (2003) 175 [hep-ph/0212259] [INSPIRE].
A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys.B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].
G. Ossola, C.G. Papadopoulos and R. Pittau, CutTools: A Program implementing the OPP reduction method to compute one-loop amplitudes, JHEP03 (2008) 042 [arXiv:0711.3596] [INSPIRE].
G. Ossola, C.G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys.B 763 (2007) 147 [hep-ph/0609007] [INSPIRE].
S. Actis, A. Denner, L. Hofer, J.-N. Lang, A. Scharf and S. Uccirati, RECOLA: REcursive Computation of One-Loop Amplitudes, Comput. Phys. Commun.214 (2017) 140 [arXiv:1605.01090] [INSPIRE].
A. Denner, J.-N. Lang and S. Uccirati, Recola2: REcursive Computation of One-Loop Amplitudes 2, Comput. Phys. Commun.224 (2018) 346 [arXiv:1711.07388] [INSPIRE].
C. Duhr, S. Hoeche and F. Maltoni, Color-dressed recursive relations for multi-parton amplitudes, JHEP08 (2006) 062 [hep-ph/0607057] [INSPIRE].
A. Buckley et al., Rivet user manual, Comput. Phys. Commun.184 (2013) 2803 [arXiv:1003.0694] [INSPIRE].
M. Cacciari and G.P. Salam, Dispelling the N 3myth for the k tjet-finder, Phys. Lett.B 641 (2006) 57 [hep-ph/0512210] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J.C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].
M. Grazzini, S. Kallweit and M. Wiesemann, Fully differential NNLO computations with MATRIX, Eur. Phys. J.C 78 (2018) 537 [arXiv:1711.06631] [INSPIRE].
F. Cascioli, S. Kallweit, P. Maierhöfer and S. Pozzorini, A unified NLO description of top-pair and associated Wt production, Eur. Phys. J.C 74 (2014) 2783 [arXiv:1312.0546] [INSPIRE].
S. Catani, S. Devoto, M. Grazzini, S. Kallweit, J. Mazzitelli and H. Sargsyan, Top-quark pair hadroproduction at next-to-next-to-leading order in QCD, Phys. Rev.D 99 (2019) 051501 [arXiv:1901.04005] [INSPIRE].
S. Catani, S. Devoto, M. Grazzini, S. Kallweit and J. Mazzitelli, Top-quark pair production at the LHC: Fully differential QCD predictions at NNLO, JHEP07 (2019) 100 [arXiv:1906.06535] [INSPIRE].
NNPDF collaboration, Parton distributions for the LHC Run II, JHEP04 (2015) 040 [arXiv:1410.8849] [INSPIRE].
A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J.C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, The anti-k tjet clustering algorithm, JHEP04 (2008) 063 [arXiv:0802.1189] [INSPIRE].
S. Pozzorini, ttH recent theory developments, talk given at The 15th Workshop of the LHC Higgs Cross Section Working Group, 10–12 December 2018, CERN [https://indico.cern.ch/event/740110/contributions/3192779/].
S. Pozzorini, Heavy flavour backgrounds in ttH(bb), talk given at The HXSWG meeting on “Parton Shower Uncertainties in Higgs Measurements”, 27 June 2019, CERN [https://indico.cern.ch/event/827858/contributions/3481144/].
S. Pozzorini, Theory progress on t \( \overline{t} \)H(b \( \overline{b} \)) background, talk given at The 11th International Workshop on Top Quark Physics (TOP2018), 16–21 September 2018, Bad Neuenahr, Germany [https://indico.cern.ch/event/690229/contributions/2979729/].
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: 1907.13624
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Buccioni, F., Kallweit, S., Pozzorini, S. et al. NLO QCD predictions for t\( \overline{t} \)b\( \overline{b} \) production in association with a light jet at the LHC. J. High Energ. Phys. 2019, 15 (2019). https://doi.org/10.1007/JHEP12(2019)015
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2019)015