Abstract
We consider the class of inclusive hadron collider processes in which one or more energetic jets are produced, possibly accompanied by colourless particles. We provide a general formulation of a slicing scheme for this class of processes, by identifying the various contributions that need to be computed up to next-to-leading order (NLO) in QCD perturbation theory. We focus on two novel observables, the one-jet resolution variable ∆Et and the n-jet resolution variable \( {k}_T^{\textrm{ness}} \), and explicitly compute all the ingredients needed to carry out NLO computations using these variables. We contrast the behaviour of these variables when the slicing parameter becomes small. In the case of \( {k}_T^{\textrm{ness}} \) we also present results for the hadroproduction of multiple jets.
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G. Heinrich, Collider Physics at the Precision Frontier, Phys. Rept. 922 (2021) 1 [arXiv:2009.00516] [INSPIRE].
A. Huss, J. Huston, S. Jones and M. Pellen, Les Houches 2021 — physics at TeV colliders: report on the standard model precision wishlist, J. Phys. G 50 (2023) 043001 [arXiv:2207.02122] [INSPIRE].
W.J. Torres Bobadilla et al., May the four be with you: Novel IR-subtraction methods to tackle NNLO calculations, Eur. Phys. J. C 81 (2021) 250 [arXiv:2012.02567] [INSPIRE].
R. Gavin, Y. Li, F. Petriello and S. Quackenbush, FEWZ 2.0: A code for hadronic Z production at next-to-next-to-leading order, Comput. Phys. Commun. 182 (2011) 2388 [arXiv:1011.3540] [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].
S. Camarda et al., DYTurbo: Fast predictions for Drell-Yan processes, Eur. Phys. J. C 80 (2020) 251 [Erratum ibid. 80 (2020) 440] [arXiv:1910.07049] [INSPIRE].
S. Catani et al., Top-quark pair production at the LHC: Fully differential QCD predictions at NNLO, JHEP 07 (2019) 100 [arXiv:1906.06535] [INSPIRE].
J. Campbell and T. Neumann, Precision Phenomenology with MCFM, JHEP 12 (2019) 034 [arXiv:1909.09117] [INSPIRE].
J.M. Campbell, R.K. Ellis and S. Seth, Non-local slicing approaches for NNLO QCD in MCFM, JHEP 06 (2022) 002 [arXiv:2202.07738] [INSPIRE].
K. Fabricius, I. Schmitt, G. Kramer and G. Schierholz, Higher Order Perturbative QCD Calculation of Jet Cross-Sections in e+e− Annihilation, Z. Phys. C 11 (1981) 315 [INSPIRE].
G. Kramer and B. Lampe, Jet Cross-Sections in e+e− Annihilation, Fortsch. Phys. 37 (1989) 161 [INSPIRE].
W.T. Giele and E.W.N. Glover, Higher order corrections to jet cross-sections in e+e− annihilation, Phys. Rev. D 46 (1992) 1980 [INSPIRE].
W.T. Giele, E.W.N. Glover and D.A. Kosower, Higher order corrections to jet cross-sections in hadron colliders, Nucl. Phys. B 403 (1993) 633 [hep-ph/9302225] [INSPIRE].
S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett. 98 (2007) 222002 [hep-ph/0703012] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, N-Jettiness: An Inclusive Event Shape to Veto Jets, Phys. Rev. Lett. 105 (2010) 092002 [arXiv:1004.2489] [INSPIRE].
M. Grazzini, NNLO predictions for the Higgs boson signal in the H → WW → lνlν and H → ZZ → 4l decay channels, JHEP 02 (2008) 043 [arXiv:0801.3232] [INSPIRE].
S. Catani et al., Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 103 (2009) 082001 [arXiv:0903.2120] [INSPIRE].
G. Ferrera, M. Grazzini and F. Tramontano, Associated WH production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 107 (2011) 152003 [arXiv:1107.1164] [INSPIRE].
G. Ferrera, M. Grazzini and F. Tramontano, Associated ZH production at hadron colliders: the fully differential NNLO QCD calculation, Phys. Lett. B 740 (2015) 51 [arXiv:1407.4747] [INSPIRE].
G. Ferrera, G. Somogyi and F. Tramontano, Associated production of a Higgs boson decaying into bottom quarks at the LHC in full NNLO QCD, Phys. Lett. B 780 (2018) 346 [arXiv:1705.10304] [INSPIRE].
D. de Florian et al., Differential Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD, JHEP 09 (2016) 151 [arXiv:1606.09519] [INSPIRE].
S. Catani et al., Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, Phys. Rev. Lett. 108 (2012) 072001 [Erratum ibid. 117 (2016) 089901] [arXiv:1110.2375] [INSPIRE].
M. Grazzini, S. Kallweit, D. Rathlev and A. Torre, Zγ production at hadron colliders in NNLO QCD, Phys. Lett. B 731 (2014) 204 [arXiv:1309.7000] [INSPIRE].
M. Grazzini, S. Kallweit and D. Rathlev, Wγ and Zγ production at the LHC in NNLO QCD, JHEP 07 (2015) 085 [arXiv:1504.01330] [INSPIRE].
F. Cascioli et al., ZZ production at hadron colliders in NNLO QCD, Phys. Lett. B 735 (2014) 311 [arXiv:1405.2219] [INSPIRE].
M. Grazzini, S. Kallweit and D. Rathlev, ZZ production at the LHC: fiducial cross sections and distributions in NNLO QCD, Phys. Lett. B 750 (2015) 407 [arXiv:1507.06257] [INSPIRE].
T. Gehrmann et al., W+W− Production at Hadron Colliders in Next to Next to Leading Order QCD, Phys. Rev. Lett. 113 (2014) 212001 [arXiv:1408.5243] [INSPIRE].
M. Grazzini et al., W+W− production at the LHC: fiducial cross sections and distributions in NNLO QCD, JHEP 08 (2016) 140 [arXiv:1605.02716] [INSPIRE].
M. Grazzini, S. Kallweit, D. Rathlev and M. Wiesemann, W±Z production at hadron colliders in NNLO QCD, Phys. Lett. B 761 (2016) 179 [arXiv:1604.08576] [INSPIRE].
M. Grazzini, S. Kallweit, D. Rathlev and M. Wiesemann, W±Z production at the LHC: fiducial cross sections and distributions in NNLO QCD, JHEP 05 (2017) 139 [arXiv:1703.09065] [INSPIRE].
J. Gaunt, M. Stahlhofen, F.J. Tackmann and J.R. Walsh, N-jettiness Subtractions for NNLO QCD Calculations, JHEP 09 (2015) 058 [arXiv:1505.04794] [INSPIRE].
R. Boughezal et al., Color singlet production at NNLO in MCFM, Eur. Phys. J. C 77 (2017) 7 [arXiv:1605.08011] [INSPIRE].
J.M. Campbell, R.K. Ellis, Y. Li and C. Williams, Predictions for diphoton production at the LHC through NNLO in QCD, JHEP 07 (2016) 148 [arXiv:1603.02663] [INSPIRE].
G. Heinrich et al., NNLO predictions for Z-boson pair production at the LHC, JHEP 03 (2018) 142 [arXiv:1710.06294] [INSPIRE].
J.M. Campbell, T. Neumann and C. Williams, Zγ Production at NNLO Including Anomalous Couplings, JHEP 11 (2017) 150 [arXiv:1708.02925] [INSPIRE].
S. Catani et al., Diphoton production at the LHC: a QCD study up to NNLO, JHEP 04 (2018) 142 [arXiv:1802.02095] [INSPIRE].
S. Abreu et al., Quark and gluon two-loop beam functions for leading-jet pT and slicing at NNLO, JHEP 04 (2023) 127 [arXiv:2207.07037] [INSPIRE].
R. Boughezal, C. Focke, X. Liu and F. Petriello, W-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, Phys. Rev. Lett. 115 (2015) 062002 [arXiv:1504.02131] [INSPIRE].
R. Boughezal et al., Higgs boson production in association with a jet at NNLO using jettiness subtraction, Phys. Lett. B 748 (2015) 5 [arXiv:1505.03893] [INSPIRE].
R. Boughezal et al., Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, Phys. Rev. Lett. 116 (2016) 152001 [arXiv:1512.01291] [INSPIRE].
R. Boughezal, X. Liu and F. Petriello, W-boson plus jet differential distributions at NNLO in QCD, Phys. Rev. D 94 (2016) 113009 [arXiv:1602.06965] [INSPIRE].
S. Catani et al., 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 et al., Bottom-quark production at hadron colliders: fully differential predictions in NNLO QCD, JHEP 03 (2021) 029 [arXiv:2010.11906] [INSPIRE].
S. Catani et al., Higgs Boson Production in Association with a Top-Antitop Quark Pair in Next-to-Next-to-Leading Order QCD, Phys. Rev. Lett. 130 (2023) 111902 [arXiv:2210.07846] [INSPIRE].
L. Buonocore et al., Associated production of a W boson and massive bottom quarks at next-to-next-to-leading order in QCD, Phys. Rev. D 107 (2023) 074032 [arXiv:2212.04954] [INSPIRE].
L. Buonocore et al., Precise Predictions for the Associated Production of a W Boson with a Top-Antitop Quark Pair at the LHC, Phys. Rev. Lett. 131 (2023) 231901 [arXiv:2306.16311] [INSPIRE].
L. Cieri et al., Higgs boson production at the LHC using the qT subtraction formalism at N3LO QCD, JHEP 02 (2019) 096 [arXiv:1807.11501] [INSPIRE].
S. Camarda, L. Cieri and G. Ferrera, Drell-Yan lepton-pair production: qT resummation at N3LL accuracy and fiducial cross sections at N3LO, Phys. Rev. D 104 (2021) L111503 [arXiv:2103.04974] [INSPIRE].
G. Billis et al., Higgs pT Spectrum and Total Cross Section with Fiducial Cuts at Third Resummed and Fixed Order in QCD, Phys. Rev. Lett. 127 (2021) 072001 [arXiv:2102.08039] [INSPIRE].
X. Chen et al., Third-Order Fiducial Predictions for Drell-Yan Production at the LHC, Phys. Rev. Lett. 128 (2022) 252001 [arXiv:2203.01565] [INSPIRE].
T. Neumann and J. Campbell, Fiducial Drell-Yan production at the LHC improved by transverse-momentum resummation at N4LLp+N3LO, Phys. Rev. D 107 (2023) L011506 [arXiv:2207.07056] [INSPIRE].
X. Chen et al., Transverse mass distribution and charge asymmetry in W boson production to third order in QCD, Phys. Lett. B 840 (2023) 137876 [arXiv:2205.11426] [INSPIRE].
S. Alioli et al., Matching Fully Differential NNLO Calculations and Parton Showers, JHEP 06 (2014) 089 [arXiv:1311.0286] [INSPIRE].
S. Höche, Y. Li and S. Prestel, Higgs-boson production through gluon fusion at NNLO QCD with parton showers, Phys. Rev. D 90 (2014) 054011 [arXiv:1407.3773] [INSPIRE].
P.F. Monni et al., MiNNLOPS: a new method to match NNLO QCD to parton showers, JHEP 05 (2020) 143 [Erratum ibid. 02 (2022) 031] [arXiv:1908.06987] [INSPIRE].
J. Mazzitelli et al., Next-to-Next-to-Leading Order Event Generation for Top-Quark Pair Production, Phys. Rev. Lett. 127 (2021) 062001 [arXiv:2012.14267] [INSPIRE].
S. Alioli et al., Matching NNLO predictions to parton showers using N3LL color-singlet transverse momentum resummation in geneva, Phys. Rev. D 104 (2021) 094020 [arXiv:2102.08390] [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Resummed event shapes at hadron-hadron colliders, JHEP 08 (2004) 062 [hep-ph/0407287] [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Phenomenology of event shapes at hadron colliders, JHEP 06 (2010) 038 [arXiv:1001.4082] [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].
S. Catani and M.H. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [hep-ph/9605323] [INSPIRE].
S. Catani, S. Dittmaier, M.H. Seymour and Z. Trocsanyi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B 627 (2002) 189 [hep-ph/0201036] [INSPIRE].
S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys. B 467 (1996) 399 [hep-ph/9512328] [INSPIRE].
S. Frixione, A general approach to jet cross-sections in QCD, Nucl. Phys. B 507 (1997) 295 [hep-ph/9706545] [INSPIRE].
M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].
C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [INSPIRE].
C.W. Bauer et al., Hard scattering factorization from effective field theory, Phys. Rev. D 66 (2002) 014017 [hep-ph/0202088] [INSPIRE].
M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power, Nucl. Phys. B 643 (2002) 431 [hep-ph/0206152] [INSPIRE].
M. Beneke and T. Feldmann, Multipole expanded soft collinear effective theory with nonAbelian gauge symmetry, Phys. Lett. B 553 (2003) 267 [hep-ph/0211358] [INSPIRE].
L. Buonocore et al., Effective transverse momentum in multiple jet production at hadron colliders, Phys. Rev. D 106 (2022) 014008 [arXiv:2201.11519] [INSPIRE].
J.C. Collins and F.V. Tkachov, Breakdown of dimensional regularization in the Sudakov problem, Phys. Lett. B 294 (1992) 403 [hep-ph/9208209] [INSPIRE].
M. Beneke, Lectures on “Soft-Collinear Effective Theory”, in proceedings of the Helmholtz International Summer School on Heavy Quark Physics Moscow, Dubna, Russian Federation, June 9–10 (2005).
J. Collins, Foundations of perturbative QCD, Cambridge University Press (2013) [https://doi.org/10.1017/9781009401845].
M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
V.A. Smirnov, Applied asymptotic expansions in momenta and masses, Springer Tracts Mod. Phys. 177 (2002) 1 [INSPIRE].
A. Mukherjee and W. Vogelsang, Jet production in (un)polarized pp collisions: dependence on jet algorithm, Phys. Rev. D 86 (2012) 094009 [Erratum ibid. 107 (2023) 119901] [arXiv:1209.1785] [INSPIRE].
S. Catani, M. Grazzini and A. Torre, Transverse-momentum resummation for heavy-quark hadroproduction, Nucl. Phys. B 890 (2014) 518 [arXiv:1408.4564] [INSPIRE].
L. Buonocore, M. Grazzini, J. Haag and L. Rottoli, Transverse-momentum resummation for boson plus jet production at hadron colliders, Eur. Phys. J. C 82 (2022) 27 [arXiv:2110.06913] [INSPIRE].
S. Catani, S. Devoto, M. Grazzini and J. Mazzitelli, Soft-parton contributions to heavy-quark production at low transverse momentum, JHEP 04 (2023) 144 [arXiv:2301.11786] [INSPIRE].
D. Bertolini et al., Soft Functions for Generic Jet Algorithms and Observables at Hadron Colliders, JHEP 07 (2017) 099 [arXiv:1704.08262] [INSPIRE].
Z. Kunszt, A. Signer and Z. Trocsanyi, Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross-sections of multiparton processes, Nucl. Phys. B 420 (1994) 550 [hep-ph/9401294] [INSPIRE].
Y.-T. Chien et al., Recoil-free azimuthal angle for precision boson-jet correlation, Phys. Lett. B 815 (2021) 136124 [arXiv:2005.12279] [INSPIRE].
S. Catani, Y.L. Dokshitzer, M.H. Seymour and B.R. Webber, Longitudinally invariant Kt clustering algorithms for hadron hadron collisions, Nucl. Phys. B 406 (1993) 187 [INSPIRE].
S.D. Ellis and D.E. Soper, Successive combination jet algorithm for hadron collisions, Phys. Rev. D 48 (1993) 3160 [hep-ph/9305266] [INSPIRE].
J.C. Collins, D.E. Soper and G.F. Sterman, Transverse Momentum Distribution in Drell-Yan Pair and W and Z Boson Production, Nucl. Phys. B 250 (1985) 199 [INSPIRE].
J. Butterworth et al., PDF4LHC recommendations for LHC Run II, J. Phys. G 43 (2016) 023001 [arXiv:1510.03865] [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-kt jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].
F. Cascioli, P. Maierhöfer and S. Pozzorini, Scattering Amplitudes with Open Loops, Phys. Rev. Lett. 108 (2012) 111601 [arXiv:1111.5206] [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. Buccioni et al., OpenLoops 2, Eur. Phys. J. C 79 (2019) 866 [arXiv:1907.13071] [INSPIRE].
S. Actis et al., 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].
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].
S. Catani and B.R. Webber, Infrared safe but infinite: Soft gluon divergences inside the physical region, JHEP 10 (1997) 005 [hep-ph/9710333] [INSPIRE].
NNPDF collaboration, Parton distributions from high-precision collider data, Eur. Phys. J. C 77 (2017) 663 [arXiv:1706.00428] [INSPIRE].
S. Catani and M. Grazzini, QCD transverse-momentum resummation in gluon fusion processes, Nucl. Phys. B 845 (2011) 297 [arXiv:1011.3918] [INSPIRE].
X.-D. Ji, J.-P. Ma and F. Yuan, QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum, Phys. Rev. D 71 (2005) 034005 [hep-ph/0404183] [INSPIRE].
J.-Y. Chiu et al., Soft-Collinear Factorization and Zero-Bin Subtractions, Phys. Rev. D 79 (2009) 053007 [arXiv:0901.1332] [INSPIRE].
T. Becher and G. Bell, Analytic Regularization in Soft-Collinear Effective Theory, Phys. Lett. B 713 (2012) 41 [arXiv:1112.3907] [INSPIRE].
J.-Y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, A formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory, JHEP 05 (2012) 084 [arXiv:1202.0814] [INSPIRE].
M.G. Echevarria, I. Scimemi and A. Vladimirov, Universal transverse momentum dependent soft function at NNLO, Phys. Rev. D 93 (2016) 054004 [arXiv:1511.05590] [INSPIRE].
Y. Li, D. Neill and H.X. Zhu, An exponential regulator for rapidity divergences, Nucl. Phys. B 960 (2020) 115193 [arXiv:1604.00392] [INSPIRE].
J. Chay and C. Kim, Consistent treatment of rapidity divergence in soft-collinear effective theory, JHEP 03 (2021) 300 [arXiv:2008.00617] [INSPIRE].
S. Catani and P.K. Dhani, Collinear functions for QCD resummations, JHEP 03 (2023) 200 [arXiv:2208.05840] [INSPIRE].
C.W. Bauer, A.V. Manohar and P.F. Monni, Disentangling observable dependence in SCETI and SCETII anomalous dimensions: angularities at two loops, JHEP 07 (2021) 214 [arXiv:2012.09213] [INSPIRE].
Acknowledgments
This work is supported in part by the Swiss National Science Foundation (SNSF) under contracts 200020_188464 and PZ00P2_201878 and by the UZH Forschungskredit Grant FK-22-099. We would like to thank Stefano Catani for helpful discussions. We are grateful to Stefan Kallweit for his support in the implementation of \( {k}_T^{\textrm{ness}} \) in Matrix and for comments on the manuscript.
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Buonocore, L., Grazzini, M., Haag, J. et al. Exploring slicing variables for jet processes. J. High Energ. Phys. 2023, 193 (2023). https://doi.org/10.1007/JHEP12(2023)193
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DOI: https://doi.org/10.1007/JHEP12(2023)193