NNLO QCD subtraction for top-antitop production in the qq̄ channel

We present the computation of the double real and real-virtual contributions to top-antitop pair production in the quark-antiquark channel at leading colour. The TeX → TeX amplitudes contributing to the real-virtual part are computed with OpenLoops, and their numerical stability in the soft and collinear regions is found to be sufficiently high to perform a realistic NNLO calculation in double precision. The subtraction terms required at real-real and real-virtual levels are constructed within the antenna subtraction formalism extended to deal with the presence of coloured massive final state particles. We show that those subtraction terms approximate the real-real and real-virtual matrix elements in all their singular limits. DOI: https://doi.org/10.1007/JHEP08(2014)035 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-108245 Journal Article Published Version The following work is licensed under a Creative Commons: Attribution 4.0 International (CC BY 4.0) License. Originally published at: Abelof, Gabriel; Gehrmann-De Ridder, Aude; Maierhoefer, Philipp; Pozzorini, Stefano (2014). NNLO QCD subtraction for top-antitop production in the qq̄ channel. Journal of High Energy Physics:035. DOI: https://doi.org/10.1007/JHEP08(2014)035 J H E P 0 8 ( 2 0 1 4 ) 0 3 5 Published for SISSA by Springer Received: May 6, 2014 Accepted: July 15, 2014 Published: August 6, 2014 NNLO QCD subtraction for top-antitop production in the qq̄ channel Gabriel Abelof,a Aude Gehrmann-De Ridder,b,c Philipp Maierhöferc and Stefano Pozzorinic Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208, U.S.A. Institute for Theoretical Physics, ETH, CH-8093 Zürich, Switzerland Physics Institute, University of Zürich, Winterthurerstrasse 190, CH-8057, Zürich E-mail: gabriel.abelof@northwestern.edu, gehra@itp.phys.ethz.ch, philipp@physik.uzh.ch, pozzorin@physik.uzh.ch Abstract: We present the computation of the double real and real-virtual contributions to top-antitop pair production in the quark-antiquark channel at leading colour. The qq̄ → tt̄g amplitudes contributing to the real-virtual part are computed with OpenLoops, and their numerical stability in the soft and collinear regions is found to be sufficiently high to perform a realistic NNLO calculation in double precision. The subtraction terms required at real-real and real-virtual levels are constructed within the antenna subtraction formalism extended to deal with the presence of coloured massive final state particles. We show that those subtraction terms approximate the real-real and real-virtual matrix elements in all their singular limits. We present the computation of the double real and real-virtual contributions to top-antitop pair production in the quark-antiquark channel at leading colour. The qq̄ → tt̄g amplitudes contributing to the real-virtual part are computed with OpenLoops, and their numerical stability in the soft and collinear regions is found to be sufficiently high to perform a realistic NNLO calculation in double precision. The subtraction terms required at real-real and real-virtual levels are constructed within the antenna subtraction formalism extended to deal with the presence of coloured massive final state particles. We show that those subtraction terms approximate the real-real and real-virtual matrix elements in all their singular limits.

[1]  Ansgar Denner,et al.  Collier: A fortran-based complex one-loop library in extended regularizations , 2016, Comput. Phys. Commun..

[2]  F. Siegert,et al.  Next-to-leading order QCD predictions for top-quark pair production with up to two jets merged with a parton shower , 2014, 1402.6293.

[3]  A. Denner,et al.  COLLIER -- A fortran-library for one-loop integrals , 2014, 1407.0087.

[4]  D. Rathlev,et al.  ZZ production at hadron colliders in NNLO QCD , 2014, 1604.08576.

[5]  E. Glover,et al.  NNLO QCD corrections to jet production at hadron colliders from gluon scattering , 2013, 1310.3993.

[6]  A. Mitov,et al.  Total top-quark pair-production cross section at hadron colliders through O(αS(4)). , 2013, Physical review letters.

[7]  A. Gehrmann-De Ridder,et al.  Second-order QCD corrections to jet production at hadron colliders: the all-gluon contribution. , 2013, Physical review letters.

[8]  E. Glover,et al.  Infrared structure at NNLO using antenna subtraction , 2013, 1301.4693.

[9]  J. G. Korner,et al.  s ) results for heavy quark pair production in quark{antiquark collisions: The one-loop squared contributions , 2013 .

[10]  W. Bernreuther,et al.  The real radiation antenna functions for S ! Q ¯ Qgg at NNLO QCD , 2013 .

[11]  A. Ridder,et al.  Antenna subtraction with massive fermions at NNLO: double real initial-final configurations , 2012, 1210.5059.

[12]  Atlas Collaboration.  Measurements of top quark pair relative differential cross-sections with ATLAS in pp collisions at sqrt(s) = 7 TeV , 2012, 1207.5644.

[13]  A. Mitov,et al.  NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels , 2012, 1207.0236.

[14]  A. Gehrmann-De Ridder,et al.  Double virtual corrections for gluon scattering at NNLO , 2012, 1211.2710.

[15]  T. Gehrmann,et al.  Real-virtual corrections for gluon scattering at NNLO , 2011, 1112.3613.

[16]  F Cascioli,et al.  Scattering amplitudes with open loops. , 2011, Physical review letters.

[17]  A. Ridder,et al.  Double real radiation corrections to tt̄ production at the LHC : the all-fermion processes , 2012 .

[18]  A. Ridder,et al.  Double real radiation corrections to t ¯ t production at the LHC: the gg → t ¯ tq ¯ q channel , 2012 .

[19]  K. Melnikov,et al.  Subtraction scheme for next-to-next-to-leading order computations , 2011, 1111.7041.

[20]  A. Mitov,et al.  The singular behavior of one-loop massive QCD amplitudes with one external soft gluon , 2011, 1107.4384.

[21]  A. Gehrmann-De Ridder,et al.  Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations , 2011, 1207.5779.

[22]  P. Monni,et al.  Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations , 2011, 1107.4037.

[23]  F. Maltoni,et al.  MadGraph 5: going beyond , 2011, 1106.0522.

[24]  A. Gehrmann-De Ridder,et al.  Antenna subtraction for the production of heavy particles at hadron colliders , 2011, 1102.2443.

[25]  S. Badger,et al.  One-Loop Helicity Amplitudes for tt Production at Hadron Colliders , 2011, 1101.5947.

[26]  M. Czakon.  Double-real radiation in hadronic top quark pair production as a proof of a certain concept , 2011, 1101.0642.

[27]  R. Bonciani,et al.  Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel , 2010, 1011.6661.

[28]  C. Anastasiou,et al.  On the factorization of overlapping singularities at NNLO , 2010, 1011.4867.

[29]  A. Denner,et al.  Scalar one-loop 4-point integrals , 2010, 1005.2076.

[30]  R. Boughezal,et al.  Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours , 2010, 1011.6631.

[31]  P. Mastrolia,et al.  Scattering amplitudes from unitarity-based reduction algorithm at the integrand-level , 2010, 1006.0710.

[32]  M. Czakon.  A novel subtraction scheme for double-real radiation at NNLO , 2010, 1005.0274.

[33]  E. Glover,et al.  Antenna subtraction for gluon scattering at NNLO , 2010, 1003.2824.

[34]  G. Luisoni,et al.  Antenna subtraction at NNLO with hadronic initial states: initial-final configurations , 2009, 0912.0374.

[35]  R. Bonciani,et al.  Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel , 2009, 0906.3671.

[36]  A. Ridder,et al.  NLO antenna subtraction with massive fermions , 2009, 0904.3297.

[37]  R. Pittau,et al.  Feynman rules for the rational part of the QCD 1-loop amplitudes , 2009, 0903.0356.

[38]  B. Kniehl,et al.  Heavy quark pair production in gluon fusion at next-to-next-to-leading O ( α s 4 ) order: One-loop squared contributions , 2008, 0809.3980.

[39]  C. Anastasiou,et al.  One-loop gluon amplitude for heavy-quark production at next-to-next-to-leading order , 2008, 0809.1355.

[40]  R. Bonciani,et al.  Two-loop fermionic corrections to heavy-quark pair production: the quark-antiquark channel , 2008, 0806.2301.

[41]  M. Czakon.  Tops from light quarks : Full mass dependence at two-loops in QCD , 2008, 0803.1400.

[42]  Costas G. Papadopoulos,et al.  CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes , 2007, 0711.3596.

[43]  T. Gehrmann,et al.  Antenna subtraction with hadronic initial states , 2006, hep-ph/0612257.

[44]  R. Pittau,et al.  Reducing full one-loop amplitudes to scalar integrals at the integrand level , 2006, hep-ph/0609007.

[45]  A. Denner,et al.  Reduction schemes for one-loop tensor integrals , 2005, hep-ph/0509141.

[46]  T. Gehrmann,et al.  Antenna subtraction at NNLO , 2005, hep-ph/0505111.

[47]  S. Badger,et al.  Two-loop splitting functions in QCD , 2004, hep-ph/0405236.

[48]  L. Dixon,et al.  Two-loop g→gg splitting amplitudes in QCD , 2004, hep-ph/0404293.

[49]  T. Gehrmann,et al.  Infrared structure of e+ e- ---> 2 jets at NNLO , 2004, 0710.0346.

[50]  T. Binoth,et al.  Numerical evaluation of phase space integrals by sector decomposition , 2004, hep-ph/0402265.

[51]  D. Florian,et al.  The triple collinear limit of one-loop QCD amplitudes , 2003, hep-ph/0312067.

[52]  C. Anastasiou,et al.  A new method for real radiation at NNLO , 2003, hep-ph/0311311.

[53]  S. Weinzierl.  Subtraction terms for one-loop amplitudes with one unresolved parton , 2003, hep-ph/0306248.

[54]  D. Kosower.  All-orders singular emission in gauge theories. , 2003, Physical review letters.

[55]  D. Kosower.  Multiple singular emission in gauge theories , 2002, hep-ph/0212097.

[56]  Z. Trocsanyi,et al.  The Dipole Formalism for Next-to-Leading Order QCD Calculations with Massive Partons , 2002, hep-ph/0201036.

[57]  D. Florian,et al.  The structure of large logarithmic corrections at small transverse momentum in hadronic collisions , 2001, hep-ph/0108273.

[58]  Z. Trocsanyi,et al.  One-loop Singular Behaviour of QCD and SUSY QCD Amplitudes with Massive Partons , 2000, hep-ph/0011222.

[59]  M. Grazzini,et al.  The soft-gluon current at one-loop order☆ , 2000, hep-ph/0007142.

[60]  T. Binoth,et al.  An automatized algorithm to compute infrared divergent multi-loop integrals , 2000, hep-ph/0004013.

[61]  C. Schmidt,et al.  Infrared behavior of one-loop QCD amplitudes at next-to-next-to-leading order , 1999, hep-ph/9903516.

[62]  P. Uwer,et al.  One-loop splitting amplitudes in gauge theory , 1999, hep-ph/9903515.

[63]  D. Kosower.  All order collinear behavior in gauge theories , 1999, hep-ph/9901201.

[64]  C. Schmidt,et al.  The infrared behavior of one-loop gluon amplitudes at next-to-next-to-leading order , 1998, hep-ph/9810409.

[65]  J. Campbell,et al.  DOUBLE UNRESOLVED APPROXIMATIONS TO MULTIPARTON SCATTERING AMPLITUDES , 1997, hep-ph/9710255.

[66]  S. Frixione.  A general approach to jet cross sections in QCD , 1997, hep-ph/9706545.

[67]  D. Graudenz,et al.  HIGGS BOSON PRODUCTION AT THE LHC , 1995, hep-ph/9504378.

[68]  L. Dixon,et al.  One-loop n-point gauge theory amplitudes, unitarity and collinear limits , 1994, hep-ph/9403226.

[69]  P. Nogueira.  Automatic Feynman graph generation , 1993 .

[70]  S. Dawson,et al.  The one particle inclusive differential cross section for heavy quark production in hadronic collisions , 1989 .

[71]  W. Beenakker,et al.  QCD Corrections to Heavy Quark Production in p anti-p Collisions , 1989 .

[72]  W. Giele,et al.  Multiple soft gluon radiation in parton processes , 1989 .

[73]  Beenakker,et al.  QCD corrections to heavy-quark production in pp-bar collisions. , 1989, Physical review. D, Particles and fields.

[74]  S. D. Ellis,et al.  A New Monte Carlo Treatment of Multiparticle Phase Space at High-energies , 1986 .

[75]  G. Parisi,et al.  Asymptotic Freedom in Parton Language , 1977 .