# Infrared sensitivity of single jet inclusive production at hadron colliders

## Abstract

Jet production at hadron colliders is a benchmark process to probe the dynamics of the strong interaction and the structure of the colliding hadrons. One of the most basic jet production observables is the single jet inclusive cross section, which is obtained by summing all jets that are observed in an event. Our recent computation of next-to-next-to-leading order (NNLO) QCD contributions to single jet inclusive observables uncovered large corrections in certain kinematical regions, which also resulted in a sizeable ambiguity on the appropriate choice of renormalization and factorization scales. We now perform a detailed investigation of the infrared sensitivity of the different ingredients to the single jet inclusive cross section. We show that the contribution from the second jet, ordered in transverse momentum *p*_{T}, in the event is particularly sensitive to higher order effects due to implicit restrictions on its kinematics. By investigating the second-jet transverse momentum distribution, we identify large-scale cancellations between different kinematical event configurations, which are aggravated by certain types of scale choice. Taking perturbative convergence and stability as selection criteria enables us to single out the total partonic transverse energy *Ĥ*_{T} and twice the individual jet transverse momentum 2 *p*_{T} (with which *Ĥ*_{T} coincides in Born kinematics) as the most appropriate scales in the perturbative description of single jet inclusive production.

## Keywords

Jets QCD Phenomenology## Notes

### **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.

## References

- [1]UA1 collaboration, G. Arnison et al.,
*Measurement of the Inclusive Jet Cross-Section at the CERN*\( p\overline{p} \)*Collider*,*Phys. Lett.***B 172**(1986) 461 [INSPIRE]. - [2]UA2 collaboration, M. Banner et al.,
*Observation of Very Large Transverse Momentum Jets at the CERN*\( \overline{p}p \)*Collider*,*Phys. Lett.***B 118**(1982) 203 [INSPIRE]. - [3]CDF collaboration, T. Aaltonen et al.,
*Measurement of the Inclusive Jet Cross Section at the Fermilab Tevatron*\( p\overline{p} \)*Collider Using a Cone-Based Jet Algorithm*,*Phys. Rev.***D 78**(2008) 052006 [*Erratum ibid.***D 79**(2009) 119902] [arXiv:0807.2204] [INSPIRE]. - [4]D0 collaboration, V.M. Abazov et al.,
*Measurement of the inclusive jet cross section in*\( p\overline{p} \)*collisions at*\( \sqrt{s}=1.96 \)*TeV*,*Phys. Rev.***D 85**(2012) 052006 [arXiv:1110.3771] [INSPIRE]. - [5]ALICE collaboration,
*Measurement of the inclusive differential jet cross section in pp collisions at*\( \sqrt{s}=2 \)*.*76*TeV*,*Phys. Lett.***B 722**(2013) 262 [arXiv:1301.3475] [INSPIRE]. - [6]ATLAS collaboration,
*Measurement of the inclusive jet cross section in pp collisions at*\( \sqrt{s}=2.76 \)*TeV and comparison to the inclusive jet cross section at*\( \sqrt{s}=7 \)*TeV using the ATLAS detector*,*Eur. Phys. J.***C 73**(2013) 2509 [arXiv:1304.4739] [INSPIRE]. - [7]CMS collaboration,
*Measurement of the inclusive jet cross section in pp collisions at*\( \sqrt{s}=2.76 \)*TeV*,*Eur. Phys. J.***C 76**(2016) 265 [arXiv:1512.06212] [INSPIRE]. - [8]ATLAS collaboration,
*Measurement of inclusive jet and dijet cross sections in proton-proton collisions at*7*TeV centre-of-mass energy with the ATLAS detector*,*Eur. Phys. J.***C 71**(2011) 1512 [arXiv:1009.5908] [INSPIRE]. - [9]CMS collaboration,
*Measurements of differential jet cross sections in proton-proton collisions at*\( \sqrt{s}=7 \)*TeV with the CMS detector*,*Phys. Rev.***D 87**(2013) 112002 [*Erratum ibid.***D 87**(2013) 119902] [arXiv:1212.6660] [INSPIRE]. - [10]ATLAS collaboration,
*Measurement of the inclusive jet cross-sections in proton-proton collisions at*\( \sqrt{s}=8 \)*TeV with the ATLAS detector*,*JHEP***09**(2017) 020 [arXiv:1706.03192] [INSPIRE]. - [11]CMS collaboration,
*Measurement and QCD analysis of double-differential inclusive jet cross sections in pp collisions at*\( \sqrt{s}=8 \)*TeV and cross section ratios to*2*.*76*and*7*TeV*,*JHEP***03**(2017) 156 [arXiv:1609.05331] [INSPIRE]. - [12]CMS collaboration,
*Measurement of the double-differential inclusive jet cross section in proton-proton collisions at*\( \sqrt{s}=13 \)*TeV*,*Eur. Phys. J.***C 76**(2016) 451 [arXiv:1605.04436] [INSPIRE]. - [13]ATLAS collaboration,
*Measurement of inclusive jet and dijet cross-sections in proton-proton collisions at*\( \sqrt{s}=13 \)*TeV with the ATLAS detector*,*JHEP***05**(2018) 195 [arXiv:1711.02692] [INSPIRE]. - [14]A.J. Larkoski, I. Moult and B. Nachman,
*Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning*, arXiv:1709.04464 [INSPIRE]. - [15]S.D. Ellis, Z. Kunszt and D.E. Soper,
*Two jet production in hadron collisions at order α*_{s}^{3}*in QCD*,*Phys. Rev. Lett.***69**(1992) 1496 [INSPIRE]. - [16]W.T. Giele, E.W.N. Glover and D.A. Kosower,
*The Two-Jet Differential Cross Section at*\( \mathcal{O}\left({\alpha}_s^3\right) \)*in Hadron Collisions*,*Phys. Rev. Lett.***73**(1994) 2019 [hep-ph/9403347] [INSPIRE]. - [17]Z. Nagy,
*Three jet cross-sections in hadron hadron collisions at next-to-leading order*,*Phys. Rev. Lett.***88**(2002) 122003 [hep-ph/0110315] [INSPIRE]. - [18]S. Alioli, K. Hamilton, P. Nason, C. Oleari and E. Re,
*Jet pair production in POWHEG*,*JHEP***04**(2011) 081 [arXiv:1012.3380] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [19]S. Höche and M. Schönherr,
*Uncertainties in next-to-leading order plus parton shower matched simulations of inclusive jet and dijet production*,*Phys. Rev.***D 86**(2012) 094042 [arXiv:1208.2815] [INSPIRE]. - [20]S. Dittmaier, A. Huss and C. Speckner,
*Weak radiative corrections to dijet production at hadron colliders*,*JHEP***11**(2012) 095 [arXiv:1210.0438] [INSPIRE].ADSCrossRefGoogle Scholar - [21]J.M. Campbell, D. Wackeroth and J. Zhou,
*Study of weak corrections to Drell-Yan, top-quark pair and dijet production at high energies with MCFM*,*Phys. Rev.***D 94**(2016) 093009 [arXiv:1608.03356] [INSPIRE]. - [22]R. Frederix, S. Frixione, V. Hirschi, D. Pagani, H.-S. Shao and M. Zaro,
*The complete NLO corrections to dijet hadroproduction*,*JHEP***04**(2017) 076 [arXiv:1612.06548] [INSPIRE].ADSCrossRefGoogle Scholar - [23]X. Liu, S.-O. Moch and F. Ringer,
*Phenomenology of single-inclusive jet production with jet radius and threshold resummation*,*Phys. Rev.***D 97**(2018) 056026 [arXiv:1801.07284] [INSPIRE]. - [24]E.W. Nigel Glover and J. Pires,
*Antenna subtraction for gluon scattering at NNLO*,*JHEP***06**(2010) 096 [arXiv:1003.2824] [INSPIRE].CrossRefzbMATHGoogle Scholar - [25]A. Gehrmann-De Ridder, E.W.N. Glover and J. Pires,
*Real-Virtual corrections for gluon scattering at NNLO*,*JHEP***02**(2012) 141 [arXiv:1112.3613] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [26]A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and J. Pires,
*Double Virtual corrections for gluon scattering at NNLO*,*JHEP***02**(2013) 026 [arXiv:1211.2710] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar - [27]J. Currie, E.W.N. Glover and S. Wells,
*Infrared Structure at NNLO Using Antenna Subtraction*,*JHEP***04**(2013) 066 [arXiv:1301.4693] [INSPIRE].ADSCrossRefGoogle Scholar - [28]A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and J. Pires,
*Second order QCD corrections to jet production at hadron colliders: the all-gluon contribution*,*Phys. Rev. Lett.***110**(2013) 162003 [arXiv:1301.7310] [INSPIRE].ADSCrossRefGoogle Scholar - [29]J. Currie, A. Gehrmann-De Ridder, E.W.N. Glover and J. Pires,
*NNLO QCD corrections to jet production at hadron colliders from gluon scattering*,*JHEP***01**(2014) 110 [arXiv:1310.3993] [INSPIRE].ADSCrossRefGoogle Scholar - [30]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]. - [31]J. Currie, A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover, A. Huss and J. Pires,
*Precise predictions for dijet production at the LHC*,*Phys. Rev. Lett.***119**(2017) 152001 [arXiv:1705.10271] [INSPIRE].ADSCrossRefGoogle Scholar - [32]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]. - [33]O.V. Tarasov, A.A. Vladimirov and A.Y. Zharkov,
*The Gell-Mann-Low Function of QCD in the Three Loop Approximation*,*Phys. Lett.***B 93**(1980) 429 [INSPIRE]. - [34]S.A. Larin and J.A.M. Vermaseren,
*The Three loop QCD β-function and anomalous dimensions*,*Phys. Lett.***B 303**(1993) 334 [hep-ph/9302208] [INSPIRE]. - [35]G. Altarelli and G. Parisi,
*Asymptotic Freedom in Parton Language*,*Nucl. Phys.***B 126**(1977) 298 [INSPIRE]. - [36]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]. - [37]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]. - [38]M. Dasgupta, F.A. Dreyer, G.P. Salam and G. Soyez,
*Inclusive jet spectrum for small-radius jets*,*JHEP***06**(2016) 057 [arXiv:1602.01110] [INSPIRE].ADSCrossRefGoogle Scholar - [39]M. Cacciari, G.P. Salam and G. Soyez,
*The Catchment Area of Jets*,*JHEP***04**(2008) 005 [arXiv:0802.1188] [INSPIRE].ADSCrossRefGoogle Scholar - [40]M. Cacciari, G.P. Salam and G. Soyez,
*The anti-k*_{t}*jet clustering algorithm*,*JHEP***04**(2008) 063 [arXiv:0802.1189] [INSPIRE]. - [41]J. Butterworth et al.,
*PDF4LHC recommendations for LHC Run II*,*J. Phys.***G 43**(2016) 023001 [arXiv:1510.03865] [INSPIRE]. - [42]L.A. Harland-Lang, A.D. Martin and R.S. Thorne,
*The Impact of LHC Jet Data on the MMHT PDF Fit at NNLO*,*Eur. Phys. J.***C 78**(2018) 248 [arXiv:1711.05757] [INSPIRE].