We present the CoLoRFulNNLO method to compute higher order radiative corrections to jet cross sections in perturbative QCD. We apply our method to the computation of event shape observables in electron-positron collisions at NNLO accuracy and validate our code by comparing our predictions to previous results in the literature. We also calculate for the first time jet cone energy fraction at NNLO.
, Studies of QCD at ${\rm e}^ + {\rm e}^-$ centre-of-mass energies between 91 and 209 GeV, 10.1140/epjc/s2004-01891-4
, A study of the energy evolution of event shape distributions and their means with the DELPHI detector at LEP, 10.1140/epjc/s2003-01198-0
Achard P., Adriani O., Aguilar-Benitez M., Alcaraz J., Alemanni G., Allaby J., Aloisio A., Alviggi M.G., Anderhub H., Andreev V.P., Anselmo F., Arefiev A., Azemoon T., Aziz T., Bagnaia P., Bajo A., Baksay G., Baksay L., Baldew S.V., Banerjee S., Banerjee Sw., Barczyk A., Barillère R., Bartalini P., Basile M., Batalova N., Battiston R., Bay A., Becattini F., Becker U., Behner F., Bellucci L., Berbeco R., Berdugo J., Berges P., Bertucci B., Betev B.L., Biasini M., Biglietti M., Biland A., Blaising J.J., Blyth S.C., Bobbink G.J., Böhm A., Boldizsar L., Borgia B., Bottai S., Bourilkov D., Bourquin M., Braccini S., Branson J.G., Brochu F., Burger J.D., Burger W.J., Cai X.D., Capell M., Cara Romeo G., Carlino G., Cartacci A., Casaus J., Cavallari F., Cavallo N., Cecchi C., Cerrada M., Chamizo M., Chang Y.H., Chemarin M., Chen A., Chen G., Chen G.M., Chen H.F., Chen H.S., Chiefari G., Cifarelli L., Cindolo F., Clare I., Clare R., Coignet G., Colino N., Costantini S., de la Cruz B., Cucciarelli S., van Dalen J.A., de Asmundis R., Déglon P., Debreczeni J., Degré A., Dehmelt K., Deiters K., della Volpe D., Delmeire E., Denes P., De Notaristefani F., De Salvo A., Diemoz M., Dierckxsens M., Dionisi C., Dittmar M., Doria A., Dova M.T., Duchesneau D., Duda M., Echenard B., Eline A., El Hage A., El Mamouni H., Engler A., Eppling F.J., Extermann P., Falagan M.A., Falciano S., Favara A., Fay J., Fedin O., Felcini M., Ferguson T., Fesefeldt H., Fiandrini E., Field J.H., Filthaut F., Fisher P.H., Fisher W., Fisk I., Forconi G., Freudenreich K., Furetta C., Galaktionov Yu., Ganguli S.N., Garcia-Abia P., Gataullin M., Gentile S., Giagu S., Gong Z.F., Grenier G., Grimm O., Gruenewald M.W., Guida M., Gupta V.K., Gurtu A., Gutay L.J., Haas D., Hatzifotiadou D., Hebbeker T., Hervé A., Hirschfelder J., Hofer H., Hohlmann M., Holzner G., Hou S.R., Hu Y., Jin B.N., Jones L.W., de Jong P., Josa-Mutuberría I., Kaur M., Kienzle-Focacci M.N., Kim J.K., Kirkby J., Kittel W., Klimentov A., König A.C., Kopal M., Koutsenko V., Kräber M., Kraemer R.W., Krüger A., Kunin A., Ladron de Guevara P., Laktineh I., Landi G., Lebeau M., Lebedev A., Lebrun P., Lecomte P., Lecoq P., Le Coultre P., Le Goff J.M., Leiste R., Levtchenko M., Levtchenko P., Li C., Likhoded S., Lin C.H., Lin W.T., Linde F.L., Lista L., Liu Z.A., Lohmann W., Longo E., Lu Y.S., Luci C., Luminari L., Lustermann W., Ma W.G., Malgeri L., Malinin A., Maña C., Mangeol D., Mans J., Martin J.P., Marzano F., Mazumdar K., McNeil R.R., Mele S., Merola L., Meschini M., Metzger W.J., Mihul A., Milcent H., Mirabelli G., Mnich J., Mohanty G.B., Muanza G.S., Muijs A.J.M., Musicar B., Musy M., Nagy S., Natale S., Napolitano M., Nessi-Tedaldi F., Newman H., Nisati A., Novak T., Nowak H., Ofierzynski R., Organtini G., Pal I., Palomares C., Paolucci P., Paramatti R., Passaleva G., Patricelli S., Paul T., Pauluzzi M., Paus C., Pauss F., Pedace M., Pensotti S., Perret-Gallix D., Petersen B., Piccolo D., Pierella F., Pioppi M., Piroué P.A., Pistolesi E., Plyaskin V., Pohl M., Pojidaev V., Pothier J., Prokofiev D., Quartieri J., Rahal-Callot G., Rahaman M.A., Raics P., Raja N., Ramelli R., Rancoita P.G., Ranieri R., Raspereza A., Razis P., Ren D., Rescigno M., Reucroft S., Riemann S., Riles K., Roe B.P., Romero L., Rosca A., Rosemann C., Rosenbleck C., Rosier-Lees S., Roth S., Rubio J.A., Ruggiero G., Rykaczewski H., Sakharov A., Saremi S., Sarkar S., Salicio J., Sanchez E., Schäfer C., Schegelsky V., Schopper H., Schotanus D.J., Sciacca C., Servoli L., Shevchenko S., Shivarov N., Shoutko V., Shumilov E., Shvorob A., Son D., Souga C., Spillantini P., Steuer M., Stickland D.P., Stoyanov B., Straessner A., Sudhakar K., Sultanov G., Sun L.Z., Sushkov S., Suter H., Swain J.D., Szillasi Z., Tang X.W., Tarjan P., Tauscher L., Taylor L., Tellili B., Teyssier D., Timmermans C., Ting Samuel C.C., Ting S.M., Tonwar S.C., Tóth J., Tully C., Tung K.L., Ulbricht J., Valente E., Van de Walle R.T., Vasquez R., Veszpremi V., Vesztergombi G., Vetlitsky I., Vicinanza D., Viertel G., Villa S., Vivargent M., Vlachos S., Vodopianov I., Vogel H., Vogt H., Vorobiev I., Vorobyov A.A., Wadhwa M., Wang Q., Wang X.L., Wang Z.M., Weber M., Wilkens H., Wynhoff S., Xia L., Xu Z.Z., Yamamoto J., Yang B.Z., Yang C.G., Yang H.J., Yang M., Yeh S.C., Zalite An., Zalite Yu., Zhang Z.P., Zhao J., Zhu G.Y., Zhu R.Y., Zhuang H.L., Zichichi A., Zimmermann B., Zöller M., Studies of hadronic event structure in e+e- annihilation from 30 to 209GeV with the L3 detector, 10.1016/j.physrep.2004.07.002
, Measurement of event shape distributions and moments in e + e $^-\rightarrow \mathrm{hadrons}$ at 91-209 GeV and a determination of $\ensuremath{\alpha_{\mathrm{s}}}$, 10.1140/epjc/s2005-02120-6
Ridder A. Gehrmann-De, Gehrmann T, Glover E.W.N, Heinrich G, NNLO corrections to event shapes in e+e− annihilation, 10.1088/1126-6708/2007/12/094
Weinzierl Stefan, Event shapes and jet rates in electron-positron annihilation at NNLO, 10.1088/1126-6708/2009/06/041
Del Duca Vittorio, Duhr Claude, Kardos Adam, Somogyi Gábor, Trócsányi Zoltán, Three-Jet Production in Electron-Positron Collisions at Next-to-Next-to-Leading Order Accuracy, 10.1103/physrevlett.117.152004
Signer Adrian, Dixon Lance, Electron-Positron Annihilation into Four Jets at Next-to-Leading Order inαs, 10.1103/physrevlett.78.811
Nagy Zoltán, Trócsányi Zoltán, Next-to-Leading Order Calculation of Four-Jet Shape Variables, 10.1103/physrevlett.79.3604
Campbell J.M., Cullen M.A., Glover E.W.N., Four jet event shapes in electron-positron annihilation, 10.1007/s100529900034
Weinzierl Stefan, Kosower David A., QCD corrections to four-jet production and three-jet structure ine+e−annihilation, 10.1103/physrevd.60.054028
Frederix Rikkert, Frixione Stefano, Melnikov Kirill, Zanderighi Giulia, NLO QCD corrections to five-jet production at LEP and the extraction of α s (M Z ), 10.1007/jhep11(2010)050
Becker Sebastian, Götz Daniel, Reuschle Christian, Schwan Christopher, Weinzierl Stefan, Next-to-Leading-Order Results for Five, Six, and Seven Jets in Electron-Positron Annihilation, 10.1103/physrevlett.108.032005
Catani S., Trentadue L., Turnock G., Webber B.R., Resummation of large logarithms in e+e− event shape distributions, 10.1016/0550-3213(93)90271-p
Banfi Andrea, Salam Gavin P, Zanderighi Giulia, Principles of general final-state resummation and automated implementation, 10.1088/1126-6708/2005/03/073
Banfi Andrea, McAslan Heather, Monni Pier Francesco, Zanderighi Giulia, A general method for the resummation of event-shape distributions in e
+
e
− annihilation, 10.1007/jhep05(2015)102
Chien Yang-ting, Schwartz Matthew D., Resummation of heavy jet mass and comparison to LEP data, 10.1007/jhep08(2010)058
Hoang André H., Kolodrubetz Daniel W., Mateu Vicent, Stewart Iain W., C-parameter distribution atN3LL′including power corrections, 10.1103/physrevd.91.094017
Binoth T., Heinrich G., An automatized algorithm to compute infrared divergent multi-loop integrals, 10.1016/s0550-3213(00)00429-6
Binoth T., Heinrich G., Numerical evaluation of phase space integrals by sector decomposition, 10.1016/j.nuclphysb.2004.06.005
Anastasiou Charalampos, Melnikov Kirill, Petriello Frank, A new method for real radiation at next-to-next-to-leading order, 10.1103/physrevd.69.076010
Anastasiou Charalampos, Herzog Franz, Lazopoulos Achilleas, On the factorization of overlapping singularities at NNLO, 10.1007/jhep03(2011)038
Weinzierl Stefan, Subtraction terms for one-loop amplitudes with one unresolved parton, 10.1088/1126-6708/2003/07/052
Catani Stefano, Grazzini Massimiliano, Next-to-Next-to-Leading-Order Subtraction Formalism in Hadron Collisions and its Application to Higgs-Boson Production at the Large Hadron Collider, 10.1103/physrevlett.98.222002
Daleo Alejandro, Gehrmann-De Ridder Aude, Gehrmann Thomas, Luisoni Gionata, Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, 10.1007/jhep01(2010)118
Gehrmann Thomas, Monni Pier Francesco, Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, 10.1007/jhep12(2011)049
Boughezal Radja, Gehrmann-De Ridder Aude, Ritzmann Mathias, Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours, 10.1007/jhep02(2011)098
Gehrmann-De Ridder A., Gehrmann T., Ritzmann M., Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations, 10.1007/jhep10(2012)047
Currie James, Glover E. W. N., Wells Steven, Infrared structure at NNLO using antenna subtraction, 10.1007/jhep04(2013)066
Czakon M., Double-real radiation in hadronic top quark pair production as a proof of a certain concept, 10.1016/j.nuclphysb.2011.03.020
Czakon M., Heymes D., Four-dimensional formulation of the sector-improved residue subtraction scheme, 10.1016/j.nuclphysb.2014.11.006
Boughezal Radja, Melnikov Kirill, Petriello Frank, Subtraction scheme for next-to-next-to-leading order computations, 10.1103/physrevd.85.034025
Somogyi Gábor, Trócsányi Zoltán, Duca Vittorio Del, Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements, 10.1088/1126-6708/2005/06/024
G. Somogyi, Acta physica et chimica Debrecina, XL, 101 (2006)
Somogyi Gábor, Trócsányi Zoltán, Duca Vittorio Del, A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of doubly-real emissions, 10.1088/1126-6708/2007/01/070
Somogyi Gábor, Trócsányi Zoltán, A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of real-virtual emission, 10.1088/1126-6708/2007/01/052
Somogyi Gábor, Trócsányi Zoltán, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the subtraction terms I, 10.1088/1126-6708/2008/08/042
Aglietti Ugo, Duca Vittorio Del, Duhr Claude, Somogyi Gábor, Trócsányi Zoltán, Analytic integration of real-virtual counterterms in NNLO jet cross sections I, 10.1088/1126-6708/2008/09/107
Somogyi Gábor, Subtraction with hadronic initial states at NLO: an NNLO-compatible scheme, 10.1088/1126-6708/2009/05/016
Bolzoni Paolo, Moch Sven-Olaf, Somogyi Gábor, Trócsányi Zoltán, Analytic integration of real-virtual counterterms in NNLO jet cross sections II, 10.1088/1126-6708/2009/08/079
Bolzoni Paolo, Somogyi Gábor, Trócsányi Zoltán, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the iterated singly-unresolved subtraction terms, 10.1007/jhep01(2011)059
Del Duca Vittorio, Somogyi Gábor, Trócsányi Zoltán, Integration of collinear-type doubly unresolved counterterms in NNLO jet cross sections, 10.1007/jhep06(2013)079
Somogyi Gábor, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the doubly unresolved subtraction terms, 10.1007/jhep04(2013)010
Boughezal Radja, Focke Christfried, Liu Xiaohui, Petriello Frank, W-Boson Production in Association with a Jet at Next-to-Next-to-Leading Order in Perturbative QCD, 10.1103/physrevlett.115.062002
Gaunt Jonathan R., Stahlhofen Maximilian, Tackmann Frank J., Walsh Jonathan R., N-jettiness subtractions for NNLO QCD calculations, 10.1007/jhep09(2015)058
Catani Stefano, Grazzini Massimiliano, Collinear factorization and splitting functions for next-to-next-to-leading order QCD calculations, 10.1016/s0370-2693(98)01513-5
Del Duca Vittorio, Frizzo Alberto, Maltoni Fabio, Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit, 10.1016/s0550-3213(99)00657-4
Catani Stefano, Grazzini Massimiliano, Infrared factorization of tree-level QCD amplitudes at the next-to-next-to-leading order and beyond, 10.1016/s0550-3213(99)00778-6
Bern Zvi, Dixon Lance, Kosower David A., One-loop amplitudes for e+e− to four partons, 10.1016/s0550-3213(97)00703-7
Bern Zvi, Del Duca Vittorio, Kilgore William B., Schmidt Carl R., Infrared behavior of one-loop QCD amplitudes at next-to-next-to-leading order, 10.1103/physrevd.60.116001
Del Duca Vittorio, Duhr Claude, Somogyi Gábor, Tramontano Francesco, Trócsányi Zoltán, Higgs boson decay into b-quarks at NNLO accuracy, 10.1007/jhep04(2015)036
Catani S., Seymour M.H., A general algorithm for calculating jet cross sections in NLO QCD, 10.1016/s0550-3213(96)00589-5
Frixione S., Kunszt Z., Signer A., Three-jet cross sections to next-to-leading order, 10.1016/0550-3213(96)00110-1
Nagy Zoltan, Trócsányi Zoltan, Calculation of QCD jet cross sections at next-to-leading order, 10.1016/s0550-3213(96)00657-8
Hagiwara K., Zeppenfeld D., Amplitudes for multi-parton processes involving a current at e+e−, e±p, and hadron colliders, 10.1016/0550-3213(89)90397-0
Berends F.A., Giele W.T., Kuijf H., Exact expressions for processes involving a vector boson and up to five partons, 10.1016/0550-3213(89)90242-3
Falck N.K., Graudenz D., Kramer G., Cross section for five-jet production in e+e− annihilation, 10.1016/0550-3213(89)90331-3
Garland L.W., Gehrmann T., Glover E.W.N., Koukoutsakis A., Remiddi E., The two-loop QCD matrix element for e+e−→3 jets, 10.1016/s0550-3213(02)00057-3
Garland L.W., Gehrmann T., Glover E.W.N., Koukoutsakis A., Remiddi E., Two-loop QCD helicity amplitudes for e+e−→3 jets, 10.1016/s0550-3213(02)00627-2
Nagy Zoltán, Trócsányi Zoltán, Next-to-leading order calculation of four-jet observables in electron-positron annihilation, 10.1103/physrevd.59.014020
Nagy Zoltán, Trócsányi Zoltán, Erratum: Next-to-leading order calculation of four-jet observables in electron-positron annihilation [Phys. Rev. D59, 014020 (1999)], 10.1103/physrevd.62.099902
Brandt S., Peyrou Ch., Sosnowski R., Wroblewski A., The principal axis of jets — an attempt to analyse high-energy collisions as two-body processes, 10.1016/0031-9163(64)91176-x
Donoghue John F., Low F. E., Pi So-Young, Tensor analysis of hadronic jets in quantum chromodynamics, 10.1103/physrevd.20.2759
Brown N., Stirling W.J., Jet cross sections at leading double logarithm in e+e− annihilation, 10.1016/0370-2693(90)90502-w
Catani S., Dokshitzer Yu.L., Olsson M., Turnock G., Webber B.R., New clustering algorithm for multijet cross sections in e+e− annihilation, 10.1016/0370-2693(91)90196-w
Brown N., Stirling W. J., Finding jets and summing soft gluons: a new algorithm, 10.1007/bf01559740
Bethke S., Kunszt Z., Soper D.E., Stirling W.J., New jet cluster algorithms: next-to-leading order QCD and hadronization corrections, 10.1016/0550-3213(92)90289-n
, Abreu et al. P., Consistent measurements of $\alpha_s$ from precise oriented event shape distributions, 10.1007/s100520000354
Z. Kunszt, Z Physics at LEP 1, 1, 373 (1989)
Dine Michael, Sapirstein Jonathan, Higher-Order Quantum Chromodynamic Corrections ine+e−Annihilation, 10.1103/physrevlett.43.668
Chetyrkin K.G., Kataev A.L., Tkachov F.V., Higher-order corrections to in quantum chromodynamics, 10.1016/0370-2693(79)90596-3
Celmaster William, Gonsalves Richard J., Analytic Calculation of Higher-Order Quantum-Chromodynamic Corrections ine+e−Annihilation, 10.1103/physrevlett.44.560
Tarasov O.V., Vladimirov A.A., Zharkov A.Yu., The gell-mann-low function of QCD in the three-loop approximation, 10.1016/0370-2693(80)90358-5
Gehrmann-De Ridder A., Gehrmann T., Glover E.W.N., Heinrich G., EERAD3: Event shapes and jet rates in electron–positron annihilation at order
α
s
3
, 10.1016/j.cpc.2014.07.024
Catani Stefano, Webber Bryan R, Infrared safe but infinite: soft-gluon divergences inside the physical region, 10.1088/1126-6708/1997/10/005
Weinzierl Stefan, Jet algorithms in electron–positron annihilation: perturbative higher order predictions, 10.1140/epjc/s10052-011-1565-x
Weinzierl Stefan, Erratum to: Jet algorithms in electron–positron annihilation: perturbative higher order predictions, 10.1140/epjc/s10052-011-1717-z
Alwall J., Frederix R., Frixione S., Hirschi V., Maltoni F., Mattelaer O., Shao H.-S., Stelzer T., Torrielli P., Zaro M., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, 10.1007/jhep07(2014)079
Becher Thomas, Schwartz Matthew D, A precise determination of αsfrom LEP thrust data using effective field theory, 10.1088/1126-6708/2008/07/034
Bibliographic reference
Duhr, Claude ; et. al. Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions. In: Physical review. D, Particles and fields, Vol. D94, p. 074019 (2016)