Abstract
We present a subtraction method utilizing the N -jettiness observable, T N , to perform QCD calculations for arbitrary processes at next-to-next-to-leading order (NNLO). Our method employs soft-collinear effective theory (SCET) to determine the IR singular contributions of N -jet cross sections for T N → 0, and uses these to construct suitable T N -subtractions. The construction is systematic and economic, due to being based on a physical observable. The resulting NNLO calculation is fully differential and in a form directly suitable for combining with resummation and parton showers. We explain in detail the application to processes with an arbitrary number of massless partons at lepton and hadron colliders together with the required external inputs in the form of QCD amplitudes and lower-order calculations. We provide explicit expressions for the T N -subtractions at NLO and NNLO. The required ingredients are fully known at NLO, and at NNLO for processes with two external QCD partons. The remaining NNLO ingredient for three or more external partons can be obtained numerically with existing NNLO techniques. As an example, we employ our results to obtain the NNLO rapidity spectrum for Drell-Yan and gluon-fusion Higgs production. We discuss aspects of numerical accuracy and convergence and the practical implementation. We also discuss and comment on possible extensions, such as more-differential subtractions, necessary steps for going to N3LO, and the treatment of massive quarks.
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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.L. Mangano, P. Nason and G. Ridolfi, Heavy quark correlations in hadron collisions at next-to-leading order, Nucl. Phys. B 373 (1992) 295 [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 [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].
G. Somogyi, Z. Trócsányi and V. Del Duca, A subtraction scheme for computing QCD jet cross sections at NNLO: Regularization of doubly-real emissions, JHEP 01 (2007) 070 [hep-ph/0609042] [INSPIRE].
G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: Regularization of real-virtual emission, JHEP 01 (2007) 052 [hep-ph/0609043] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [INSPIRE].
A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP 04 (2007) 016 [hep-ph/0612257] [INSPIRE].
J. Currie, E.W.N. Glover and S. Wells, Infrared Structure at NNLO Using Antenna Subtraction, JHEP 04 (2013) 066 [arXiv:1301.4693] [INSPIRE].
S. Weinzierl, Subtraction terms at NNLO, JHEP 03 (2003) 062 [hep-ph/0302180] [INSPIRE].
S. Frixione and M. Grazzini, Subtraction at NNLO, JHEP 06 (2005) 010 [hep-ph/0411399] [INSPIRE].
G. Somogyi, Z. Trócsányi and V. Del Duca, Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements, JHEP 06 (2005) 024 [hep-ph/0502226] [INSPIRE].
G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: Integrating the subtraction terms. I, JHEP 08 (2008) 042 [arXiv:0807.0509] [INSPIRE].
U. Aglietti, V. Del Duca, C. Duhr, G. Somogyi and Z. Trócsányi, Analytic integration of real-virtual counterterms in NNLO jet cross sections. I, JHEP 09 (2008) 107 [arXiv:0807.0514] [INSPIRE].
P. Bolzoni, S.-O. Moch, G. Somogyi and Z. Trócsányi, Analytic integration of real-virtual counterterms in NNLO jet cross sections. II, JHEP 08 (2009) 079 [arXiv:0905.4390] [INSPIRE].
P. Bolzoni, G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the iterated singly-unresolved subtraction terms, JHEP 01 (2011) 059 [arXiv:1011.1909] [INSPIRE].
V. Del Duca, G. Somogyi and Z. Trócsányi, Integration of collinear-type doubly unresolved counterterms in NNLO jet cross sections, JHEP 06 (2013) 079 [arXiv:1301.3504] [INSPIRE].
G. Somogyi, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the doubly unresolved subtraction terms, JHEP 04 (2013) 010 [arXiv:1301.3919] [INSPIRE].
V. Del Duca, C. Duhr, G. Somogyi, F. Tramontano and Z. Trócsányi, Higgs boson decay into b-quarks at NNLO accuracy, JHEP 04 (2015) 036 [arXiv:1501.07226] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Infrared structure of e + e − → 2 jets at NNLO, Nucl. Phys. B 691 (2004) 195 [hep-ph/0403057] [INSPIRE].
A. Daleo, A. Gehrmann-De Ridder, T. Gehrmann and G. Luisoni, Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, JHEP 01 (2010) 118 [arXiv:0912.0374] [INSPIRE].
E.W. Nigel Glover and J. Pires, Antenna subtraction for gluon scattering at NNLO, JHEP 06 (2010) 096 [arXiv:1003.2824] [INSPIRE].
R. Boughezal, A. Gehrmann-De Ridder and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours, JHEP 02 (2011) 098 [arXiv:1011.6631] [INSPIRE].
T. Gehrmann and P.F. Monni, Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, JHEP 12 (2011) 049 [arXiv:1107.4037] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations, JHEP 10 (2012) 047 [arXiv:1207.5779] [INSPIRE].
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].
C. Anastasiou, K. Melnikov and F. Petriello, A new method for real radiation at NNLO, Phys. Rev. D 69 (2004) 076010 [hep-ph/0311311] [INSPIRE].
T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys. B 693 (2004) 134 [hep-ph/0402265] [INSPIRE].
M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B 693 (2010) 259 [arXiv:1005.0274] [INSPIRE].
M. Czakon, Double-real radiation in hadronic top quark pair production as a proof of a certain concept, Nucl. Phys. B 849 (2011) 250 [arXiv:1101.0642] [INSPIRE].
R. Boughezal, K. Melnikov and F. Petriello, A subtraction scheme for NNLO computations, Phys. Rev. D 85 (2012) 034025 [arXiv:1111.7041] [INSPIRE].
M. Brucherseifer, F. Caola and K. Melnikov, \( O\left({\alpha}_{{}^s}^2\right) \) corrections to fully-differential top quark decays, JHEP 04 (2013) 059 [arXiv:1301.7133] [INSPIRE].
R. Boughezal, F. Caola, K. Melnikov, F. Petriello and M. Schulze, Higgs boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, JHEP 06 (2013) 072 [arXiv:1302.6216] [INSPIRE].
M. Czakon, P. Fiedler and A. Mitov, Total Top-Quark Pair-Production Cross section at Hadron Colliders Through \( O\left(\alpha \frac{4}{S}\right) \), Phys. Rev. Lett. 110 (2013) 252004 [arXiv:1303.6254] [INSPIRE].
M. Czakon and D. Heymes, Four-dimensional formulation of the sector-improved residue subtraction scheme, Nucl. Phys. B 890 (2014) 152 [arXiv:1408.2500] [INSPIRE].
R. Boughezal, F. Caola, K. Melnikov, F. Petriello and M. Schulze, Higgs boson production in association with a jet at next-to-next-to-leading order, Phys. Rev. Lett. 115 (2015) 082003 [arXiv:1504.07922] [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].
S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 103 (2009) 082001 [arXiv:0903.2120] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, Phys. Rev. Lett. 108 (2012) 072001 [arXiv:1110.2375] [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].
F. Cascioli, T. Gehrmann, M. Grazzini, S. Kallweit, P. Maierhöfer, A. von Manteuffel et al., ZZ production at hadron colliders in NNLO QCD, Phys. Lett. B 735 (2014) 311 [arXiv:1405.2219] [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, 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].
H.X. Zhu, C.S. Li, H.T. Li, D.Y. Shao and L.L. Yang, Transverse-momentum resummation for top-quark pairs at hadron colliders, Phys. Rev. Lett. 110 (2013) 082001 [arXiv:1208.5774] [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].
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].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Factorization at the LHC: From PDFs to Initial State Jets, Phys. Rev. D 81 (2010) 094035 [arXiv:0910.0467] [INSPIRE].
T.T. Jouttenus, I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, The Soft Function for Exclusive N-Jet Production at Hadron Colliders, Phys. Rev. D 83 (2011) 114030 [arXiv:1102.4344] [INSPIRE].
C.W. Bauer, S. Fleming and M.E. Luke, Summing Sudakov logarithms in B → X sγ in effective field theory, Phys. Rev. D 63 (2000) 014006 [hep-ph/0005275] [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 and I.W. Stewart, Invariant operators in collinear effective theory, Phys. Lett. B 516 (2001) 134 [hep-ph/0107001] [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, S. Fleming, D. Pirjol, I.Z. Rothstein and I.W. Stewart, 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].
J.R. Gaunt, M. Stahlhofen and F.J. Tackmann, The Quark Beam Function at Two Loops, JHEP 04 (2014) 113 [arXiv:1401.5478] [INSPIRE].
J. Gaunt, M. Stahlhofen and F.J. Tackmann, The Gluon Beam Function at Two Loops, JHEP 08 (2014) 020 [arXiv:1405.1044] [INSPIRE].
C.W. Bauer, F.J. Tackmann, J.R. Walsh and S. Zuberi, Factorization and Resummation for Dijet Invariant Mass Spectra, Phys. Rev. D 85 (2012) 074006 [arXiv:1106.6047] [INSPIRE].
M. Procura, W.J. Waalewijn and L. Zeune, Resummation of Double-Differential Cross sections and Fully-Unintegrated Parton Distribution Functions, JHEP 02 (2015) 117 [arXiv:1410.6483] [INSPIRE].
A.J. Larkoski, I. Moult and D. Neill, Toward Multi-Differential Cross sections: Measuring Two Angularities on a Single Jet, JHEP 09 (2014) 046 [arXiv:1401.4458] [INSPIRE].
A.J. Larkoski, I. Moult and D. Neill, Non-Global Logarithms, Factorization and the Soft Substructure of Jets, arXiv:1501.04596 [INSPIRE].
T.T. Jouttenus, I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Jet mass spectra in Higgs boson plus one jet at next-to-next-to-leading logarithmic order, Phys. Rev. D 88 (2013) 054031 [arXiv:1302.0846] [INSPIRE].
S. Alioli, C.W. Bauer, C. Berggren, F.J. Tackmann, J.R. Walsh and S. Zuberi, Matching Fully Differential NNLO Calculations and Parton Showers, JHEP 06 (2014) 089 [arXiv:1311.0286] [INSPIRE].
S. Alioli, C.W. Bauer, C.J. Berggren, A. Hornig, F.J. Tackmann, C.K. Vermilion et al., Combining Higher-Order Resummation with Multiple NLO Calculations and Parton Showers in GENEVA, JHEP 09 (2013) 120 [arXiv:1211.7049] [INSPIRE].
S. Gangal, M. Stahlhofen and F.J. Tackmann, Rapidity-Dependent Jet Vetoes, Phys. Rev. D 91 (2015) 054023 [arXiv:1412.4792] [INSPIRE].
J. Gao, C.S. Li and H.X. Zhu, Top Quark Decay at Next-to-Next-to Leading Order in QCD, Phys. Rev. Lett. 110 (2013) 042001 [arXiv:1210.2808] [INSPIRE].
J. Gao and H.X. Zhu, Electroweak prodution of top-quark pairs in e + e − annihilation at NNLO in QCD: the vector contributions, Phys. Rev. D 90 (2014) 114022 [arXiv:1408.5150] [INSPIRE].
J. Gao and H.X. Zhu, Top Quark Forward-Backward Asymmetry in e + e − Annihilation at Next-to-Next-to-Leading Order in QCD, Phys. Rev. Lett. 113 (2014) 262001 [arXiv:1410.3165] [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, C. Focke, W. Giele, X. Liu and F. Petriello, Higgs boson production in association with a jet at NNLO using jettiness subtraction, Phys. Lett. B 748 (2015) 5 [arXiv:1505.03893] [INSPIRE].
Z. Ligeti, I.W. Stewart and F.J. Tackmann, Treating the b quark distribution function with reliable uncertainties, Phys. Rev. D 78 (2008) 114014 [arXiv:0807.1926] [INSPIRE].
K.S.M. Lee and I.W. Stewart, Factorization for power corrections to B → X sγ and \( B\to {X}_{\mathrm{u}}\ell \overline{\nu} \) ,Nucl. Phys. B 721(2005) 325 [hep-ph/0409045] [INSPIRE].
S.M. Freedman, Subleading Corrections To Thrust Using Effective Field Theory, arXiv:1303.1558 [INSPIRE].
S.M. Freedman and R. Goerke, Renormalization of Subleading Dijet Operators in Soft-Collinear Effective Theory, Phys. Rev. D 90 (2014) 114010 [arXiv:1408.6240] [INSPIRE].
D. Kolodrubetz, Subleading SCET helicity operators, talk presented at SCET 2015 workshop, Santa Fe, New Mexico U.S.A., 25-27 March 2015.
J. Thaler and K. Van Tilburg, Identifying Boosted Objects with N-subjettiness, JHEP 03 (2011) 015 [arXiv:1011.2268] [INSPIRE].
J. Thaler and K. Van Tilburg, Maximizing Boosted Top Identification by Minimizing N-subjettiness, JHEP 02 (2012) 093 [arXiv:1108.2701] [INSPIRE].
J.R. Gaunt, Glauber Gluons and Multiple Parton Interactions, JHEP 07 (2014) 110 [arXiv:1405.2080] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Combining Fixed-Order Helicity Amplitudes With Resummation Using SCET, arXiv:1211.2305 [INSPIRE].
I. Moult, I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Employing Helicity Amplitudes for Resummation, DESY 15-065 [arXiv:1508.02397] [INSPIRE].
R. Kelley and M.D. Schwartz, 1-loop matching and NNLL resummation for all partonic 2 to 2 processes in QCD, Phys. Rev. D 83 (2011) 045022 [arXiv:1008.2759] [INSPIRE].
T. Becher, G. Bell, C. Lorentzen and S. Marti, Transverse-momentum spectra of electroweak bosons near threshold at NNLO, JHEP 02 (2014) 004 [arXiv:1309.3245] [INSPIRE].
I. Moult and I.W. Stewart, Jet Vetoes interfering with H → W W , JHEP 09 (2014) 129 [arXiv:1405.5534] [INSPIRE].
A. Broggio, A. Ferroglia, B.D. Pecjak and Z. Zhang, NNLO hard functions in massless QCD, JHEP 12 (2014) 005 [arXiv:1409.5294] [INSPIRE].
A.V. Manohar and I.W. Stewart, The Zero-Bin and Mode Factorization in Quantum Field Theory, Phys. Rev. D 76 (2007) 074002 [hep-ph/0605001] [INSPIRE].
R. Boughezal, X. Liu and F. Petriello, N -jettiness soft function at next-to-next-to-leading order, Phys. Rev. D 91 (2015) 094035 [arXiv:1504.02540] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, The Quark Beam Function at NNLL, JHEP 09 (2010) 005 [arXiv:1002.2213] [INSPIRE].
C.F. Berger, C. Marcantonini, I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Higgs Production with a Central Jet Veto at NNLL+NNLO, JHEP 04 (2011) 092 [arXiv:1012.4480] [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].
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].
S. Moch, J.A.M. Vermaseren and A. Vogt, The quark form-factor at higher orders, JHEP 08 (2005) 049 [hep-ph/0507039] [INSPIRE].
S. Moch, J.A.M. Vermaseren and A. Vogt, Three-loop results for quark and gluon form-factors, Phys. Lett. B 625 (2005) 245 [hep-ph/0508055] [INSPIRE].
T. Becher, M. Neubert and B.D. Pecjak, Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering, JHEP 01 (2007) 076 [hep-ph/0607228] [INSPIRE].
T. Becher and M.D. Schwartz, Direct photon production with effective field theory, JHEP 02 (2010) 040 [arXiv:0911.0681] [INSPIRE].
P.A. Baikov, K.G. Chetyrkin, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Quark and gluon form factors to three loops, Phys. Rev. Lett. 102 (2009) 212002 [arXiv:0902.3519] [INSPIRE].
T. Gehrmann, E.W.N. Glover, T. Huber, N. Ikizlerli and C. Studerus, Calculation of the quark and gluon form factors to three loops in QCD, JHEP 06 (2010) 094 [arXiv:1004.3653] [INSPIRE].
A. Jain, M. Procura and W.J. Waalewijn, Fully-Unintegrated Parton Distribution and Fragmentation Functions at Perturbative k T , JHEP 04 (2012) 132 [arXiv:1110.0839] [INSPIRE].
J.C. Collins, T.C. Rogers and A.M. Stasto, Fully unintegrated parton correlation functions and factorization in lowest-order hard scattering, Phys. Rev. D 77 (2008) 085009 [arXiv:0708.2833] [INSPIRE].
T.C. Rogers, Next-to-Leading Order Hard Scattering Using Fully Unintegrated Parton Distribution Functions, Phys. Rev. D 78 (2008) 074018 [arXiv:0807.2430] [INSPIRE].
J.R. Gaunt and M. Stahlhofen, The Fully-Differential Quark Beam Function at NNLO, JHEP 12 (2014) 146 [arXiv:1409.8281] [INSPIRE].
R. Frederix, S. Frixione, F. Maltoni and T. Stelzer, Automation of next-to-leading order computations in QCD: The FKS subtraction, JHEP 10 (2009) 003 [arXiv:0908.4272] [INSPIRE].
S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP 06 (2010) 043 [arXiv:1002.2581] [INSPIRE].
C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD, Phys. Rev. Lett. 91 (2003) 182002 [hep-ph/0306192] [INSPIRE].
C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, High precision QCD at hadron colliders: Electroweak gauge boson rapidity distributions at NNLO, Phys. Rev. D 69 (2004) 094008 [hep-ph/0312266] [INSPIRE].
C. Anastasiou, K. Melnikov and F. Petriello, Higgs boson production at hadron colliders: Differential cross sections through next-to-next-to-leading order, Phys. Rev. Lett. 93 (2004) 262002 [hep-ph/0409088] [INSPIRE].
C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order, Nucl. Phys. B 724 (2005) 197 [hep-ph/0501130] [INSPIRE].
M. Grazzini, NNLO predictions for the Higgs boson signal in the H → W W → ℓνℓν and H →ZZ →4ℓ decay channels,JHEP 02 (2008) 043[arXiv:0801.3232] [INSPIRE].
J. Gao et al., CT10 next-to-next-to-leading order global analysis of QCD, Phys. Rev. D 89 (2014) 033009 [arXiv:1302.6246] [INSPIRE].
J.M. Campbell and R.K. Ellis, Next-to-leading order corrections to W + 2 jet and Z + 2 jet production at hadron colliders, Phys. Rev. D 65 (2002) 113007 [hep-ph/0202176] [INSPIRE].
J.M. Campbell and R.K. Ellis, MCFM for the Tevatron and the LHC, Nucl. Phys. Proc. Suppl. 205-206 (2010) 10 [arXiv:1007.3492] [INSPIRE].
A.K. Leibovich, Z. Ligeti and M.B. Wise, Comment on quark masses in SCET, Phys. Lett. B 564 (2003) 231 [hep-ph/0303099] [INSPIRE].
S. Fleming, A.H. Hoang, S. Mantry and I.W. Stewart, Jets from massive unstable particles: Top-mass determination, Phys. Rev. D 77 (2008) 074010 [hep-ph/0703207] [INSPIRE].
S. Fleming, A.H. Hoang, S. Mantry and I.W. Stewart, Top Jets in the Peak Region: Factorization Analysis with NLL Resummation, Phys. Rev. D 77 (2008) 114003 [arXiv:0711.2079] [INSPIRE].
A. Jain, I. Scimemi and I.W. Stewart, Two-loop Jet-Function and Jet-Mass for Top Quarks, Phys. Rev. D 77 (2008) 094008 [arXiv:0801.0743] [INSPIRE].
S. Gritschacher, A. Hoang, I. Jemos and P. Pietrulewicz, Two loop soft function for secondary massive quarks, Phys. Rev. D 89 (2014) 014035 [arXiv:1309.6251] [INSPIRE].
P. Pietrulewicz, S. Gritschacher, A.H. Hoang, I. Jemos and V. Mateu, Variable Flavor Number Scheme for Final State Jets in Thrust, Phys. Rev. D 90 (2014) 114001 [arXiv:1405.4860] [INSPIRE].
S. Fleming, A.K. Leibovich and T. Mehen, Resumming the color octet contribution to e+e− → J/ψ+ X, Phys. Rev. D 68 (2003) 094011 [hep-ph/0306139] [INSPIRE].
C.W. Bauer and A.V. Manohar, Shape function effects in B → X s γ and \( B\to {X}_ul\overline{\nu} \) decays, Phys. Rev. D 70 (2004) 034024 [hep-ph/0312109] [INSPIRE].
T. Becher and M. Neubert, Toward a NNLO calculation of the \( \overline{B}\to {X}_s\gamma \) decay rate with a cut on photon energy. II. Two-loop result for the jet function, Phys. Lett. B 637 (2006) 251 [hep-ph/0603140] [INSPIRE].
T. Becher and G. Bell, The gluon jet function at two-loop order, Phys. Lett. B 695 (2011) 252 [arXiv:1008.1936] [INSPIRE].
P.F. Monni, T. Gehrmann and G. Luisoni, Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region, JHEP 08 (2011) 010 [arXiv:1105.4560] [INSPIRE].
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 O(α 2 s ) Dijet Soft Function, JHEP 08 (2011) 054 [arXiv:1105.4628] [INSPIRE].
D. Kang, O.Z. Labun and C. Lee, Equality of hemisphere soft functions for e + e − , DIS and pp collisions at O(α 2 s ), Phys. Lett. B 748 (2015) 45 [arXiv:1504.04006] [INSPIRE].
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Gaunt, J.R., Stahlhofen, M., Tackmann, F.J. et al. N-jettiness subtractions for NNLO QCD calculations. J. High Energ. Phys. 2015, 58 (2015). https://doi.org/10.1007/JHEP09(2015)058
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DOI: https://doi.org/10.1007/JHEP09(2015)058