Abstract
We set up a formalism, within the antenna subtraction framework, for computing the production of a massive quark-antiquark pair in electron positron collisions at next-to-next-to-leading order in the coupling α s of quantum chromodynamics at the differential level. Our formalism applies to the calculation of any infrared-safe observable. We apply this set-up to the production of top-quark top antiquark pairs in the continuum. We compute the production cross section and several distributions. We determine, in particular, the top-quark forward-backward asymmetry at order α 2 s . Our result agrees with previous computations of this observable.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ECFA/DESY LC Physics Working Group collaboration, J.A. Aguilar-Saavedra et al., TESLA: The superconducting electron positron linear collider with an integrated x-ray laser laboratory. Technical design report. Part 3. Physics at an e + e − linear collider, hep-ph/0106315 [INSPIRE].
H. Baer et al., The International Linear Collider Technical Design Report — Volume 2: Physics, arXiv:1306.6352 [INSPIRE].
TLEP Design Study Working Group collaboration, M. Bicer et al., First Look at the Physics Case of TLEP, JHEP 01 (2014) 164 [arXiv:1308.6176] [INSPIRE].
A. Arbey et al., Physics at the e + e − Linear Collider, Eur. Phys. J. C 75 (2015) 371 [arXiv:1504.01726] [INSPIRE].
M. Vos et al., Top physics at high-energy lepton colliders, arXiv:1604.08122 [INSPIRE].
M. Beneke, Y. Kiyo, P. Marquard, A. Penin, J. Piclum and M. Steinhauser, Next-to-Next-to-Next-to-Leading Order QCD Prediction for the Top Antitop S-Wave Pair Production Cross section Near Threshold in e + e − Annihilation, Phys. Rev. Lett. 115 (2015) 192001 [arXiv:1506.06864] [INSPIRE].
J. Jersak, E. Laermann and P.M. Zerwas, Electroweak Production of Heavy Quarks in e + e − Annihilation, Phys. Rev. D 25 (1982) 1218 [Erratum ibid. D 36 (1987) 310] [INSPIRE].
W. Bernreuther, A. Brandenburg and P. Uwer, Next-to-leading order QCD corrections to three jet cross-sections with massive quarks, Phys. Rev. Lett. 79 (1997) 189 [hep-ph/9703305] [INSPIRE].
A. Brandenburg and P. Uwer, Next-to-leading order QCD corrections and massive quarks in e + e − → three jets, Nucl. Phys. B 515 (1998) 279 [hep-ph/9708350] [INSPIRE].
G. Rodrigo, A. Santamaria and M.S. Bilenky, Do the quark masses run? Extracting \( {\overline{m}}_b\left({m}_Z\right) \) from LEP data, Phys. Rev. Lett. 79 (1997) 193 [hep-ph/9703358] [INSPIRE].
G. Rodrigo, M.S. Bilenky and A. Santamaria, Quark mass effects for jet production in e + e − collisions at the next-to-leading order: Results and applications, Nucl. Phys. B 554 (1999) 257 [hep-ph/9905276] [INSPIRE].
P. Nason and C. Oleari, Next-to-leading order corrections to momentum correlations in \( {Z}^0\to b\overline{b} \), Phys. Lett. B 407 (1997) 57 [hep-ph/9705295] [INSPIRE].
P. Nason and C. Oleari, Next-to-leading order corrections to the production of heavy flavor jets in e + e − collisions, Nucl. Phys. B 521 (1998) 237 [hep-ph/9709360] [INSPIRE].
W. Beenakker, S.C. van der Marck and W. Hollik, e + e − annihilation into heavy fermion pairs at high-energy colliders, Nucl. Phys. B 365 (1991) 24 [INSPIRE].
J. Fleischer, A. Leike, T. Riemann and A. Werthenbach, Electroweak one loop corrections for e + e − annihilation into \( t\overline{t} \) including hard bremsstrahlung, Eur. Phys. J. C 31 (2003) 37 [hep-ph/0302259] [INSPIRE].
T. Hahn, W. Hollik, A. Lorca, T. Riemann and A. Werthenbach, O(α) electroweak corrections to the processes e + e − → τ − τ + , \( c\overline{c},b\overline{b},t\overline{t} \) : A comparison, hep-ph/0307132 [INSPIRE].
P.H. Khiem et al., Full \( \mathcal{O}\left(\alpha \right) \) electroweak radiative corrections to \( {e}^{+}{e}^{-}\to t\overline{t}\gamma \) with GRACE-Loop, Eur. Phys. J. C 73 (2013) 2400 [arXiv:1211.1112] [INSPIRE].
B. Chokoufé Nejad, W. Kilian, J.M. Lindert, S. Pozzorini, J. Reuter and C. Weiss, NLO QCD Predictions for off-shell \( t\overline{t} \) and \( t\overline{t}H \) Production and Decay at a Linear Collider, arXiv:1609.03390 [INSPIRE].
S.G. Gorishnii, A.L. Kataev and S.A. Larin, Three Loop Corrections of Order O(M 2) to the Correlator of Electromagnetic Quark Currents, Nuovo Cim. A 92 (1986) 119 [INSPIRE].
K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, Three loop polarization function and O(α 2 S ) corrections to the production of heavy quarks, Nucl. Phys. B 482 (1996) 213 [hep-ph/9606230] [INSPIRE].
K.G. Chetyrkin, R. Harlander, J.H. Kuhn and M. Steinhauser, Mass corrections to the vector current correlator, Nucl. Phys. B 503 (1997) 339 [hep-ph/9704222] [INSPIRE].
K.G. Chetyrkin, A.H. Hoang, J.H. Kuhn, M. Steinhauser and T. Teubner, Massive quark production in electron positron annihilation to order O(α 2 S ), Eur. Phys. J. C 2 (1998) 137 [hep-ph/9711327] [INSPIRE].
Y. Kiyo, A. Maier, P. Maierhofer and P. Marquard, Reconstruction of heavy quark current correlators at O(α 2 S ), Nucl. Phys. B 823 (2009) 269 [arXiv:0907.2120] [INSPIRE].
O. Dekkers and W. Bernreuther, The real-virtual antenna functions for \( S\to Q\overline{Q}X \) at NNLO QCD, Phys. Lett. B 738 (2014) 325 [arXiv:1409.3124] [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].
D.A. Kosower, Antenna factorization of gauge theory amplitudes, Phys. Rev. D 57 (1998) 5410 [hep-ph/9710213] [INSPIRE].
D.A. Kosower, Antenna factorization in strongly ordered limits, Phys. Rev. D 71 (2005) 045016 [hep-ph/0311272] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [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].
A. Gehrmann-De Ridder and M. Ritzmann, NLO Antenna Subtraction with Massive Fermions, JHEP 07 (2009) 041 [arXiv:0904.3297] [INSPIRE].
G. Abelof and A. Gehrmann-De Ridder, Antenna subtraction for the production of heavy particles at hadron colliders, JHEP 04 (2011) 063 [arXiv:1102.2443] [INSPIRE].
G. Abelof and A. Gehrmann-De Ridder, Double real radiation corrections to \( t\overline{t} \) production at the LHC: the all-fermion processes, JHEP 04 (2012) 076 [arXiv:1112.4736] [INSPIRE].
G. Abelof, O. Dekkers and A. Gehrmann-De Ridder, Antenna subtraction with massive fermions at NNLO: Double real initial-final configurations, JHEP 12 (2012) 107 [arXiv:1210.5059] [INSPIRE].
G. Abelof, A. Gehrmann-De Ridder, P. Maierhofer and S. Pozzorini, NNLO QCD subtraction for top-antitop production in the \( q\overline{q} \) channel, JHEP 08 (2014) 035 [arXiv:1404.6493] [INSPIRE].
G. Abelof and A. Gehrmann-De Ridder, Light fermionic NNLO QCD corrections to top-antitop production in the quark-antiquark channel, JHEP 12 (2014) 076 [arXiv:1409.3148] [INSPIRE].
G. Abelof, A. Gehrmann-De Ridder and I. Majer, Top quark pair production at NNLO in the quark-antiquark channel, JHEP 12 (2015) 074 [arXiv:1506.04037] [INSPIRE].
W. Bernreuther, C. Bogner and O. Dekkers, The real radiation antenna function for \( S\to Q\overline{Q}q\overline{q} \) at NNLO QCD, JHEP 06 (2011) 032 [arXiv:1105.0530] [INSPIRE].
W. Bernreuther, C. Bogner and O. Dekkers, The real radiation antenna functions for \( S\to Q\overline{Q} gg \) at NNLO QCD, JHEP 10 (2013) 161 [arXiv:1309.6887] [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].
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, D. Heymes and A. Mitov, High-precision differential predictions for top-quark pairs at the LHC, Phys. Rev. Lett. 116 (2016) 082003 [arXiv:1511.00549] [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].
A. von Manteuffel, R.M. Schabinger and H.X. Zhu, The two-loop soft function for heavy quark pair production at future linear colliders, Phys. Rev. D 92 (2015) 045034 [arXiv:1408.5134] [INSPIRE].
G. Abelof and A. Gehrmann-De Ridder, private communication.
S. Weinzierl, NNLO corrections to 2-jet observables in electron-positron annihilation, Phys. Rev. D 74 (2006) 014020 [hep-ph/0606008] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Infrared structure of e + e − → 3 jets at NNLO, JHEP 11 (2007) 058 [arXiv:0710.0346] [INSPIRE].
E.W. Nigel Glover and J. Pires, Antenna subtraction for gluon scattering at NNLO, JHEP 06 (2010) 096 [arXiv:1003.2824] [INSPIRE].
K. Hagiwara, T. Kuruma and Y. Yamada, Three jet distributions from the one loop Zgg vertex at e + e − colliders, Nucl. Phys. B 358 (1991) 80 [INSPIRE].
W. Bernreuther et al., Two-loop QCD corrections to the heavy quark form-factors: The Vector contributions, Nucl. Phys. B 706 (2005) 245 [hep-ph/0406046] [INSPIRE].
W. Bernreuther et al., Two-loop QCD corrections to the heavy quark form-factors: Axial vector contributions, Nucl. Phys. B 712 (2005) 229 [hep-ph/0412259] [INSPIRE].
W. Bernreuther, R. Bonciani, T. Gehrmann, R. Heinesch, T. Leineweber and E. Remiddi, Two-loop QCD corrections to the heavy quark form-factors: Anomaly contributions, Nucl. Phys. B 723 (2005) 91 [hep-ph/0504190] [INSPIRE].
J. Gluza, A. Mitov, S. Moch and T. Riemann, The QCD form factor of heavy quarks at NNLO, JHEP 07 (2009) 001 [arXiv:0905.1137] [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
T. Gehrmann and E. Remiddi, Numerical evaluation of harmonic polylogarithms, Comput. Phys. Commun. 141 (2001) 296 [hep-ph/0107173] [INSPIRE].
D. Maître, HPL, a mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun. 174 (2006) 222 [hep-ph/0507152] [INSPIRE].
J. Blumlein, Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5, Comput. Phys. Commun. 180 (2009) 2218 [arXiv:0901.3106] [INSPIRE].
J. Ablinger, J. Blumlein and C. Schneider, Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials, J. Math. Phys. 52 (2011) 102301 [arXiv:1105.6063] [INSPIRE].
J. Ablinger, J. Blümlein and C. Schneider, Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms, J. Math. Phys. 54 (2013) 082301 [arXiv:1302.0378] [INSPIRE].
A. Czarnecki and K. Melnikov, Two loop QCD corrections to the heavy quark pair production cross-section in e + e − annihilation near the threshold, Phys. Rev. Lett. 80 (1998) 2531 [hep-ph/9712222] [INSPIRE].
M. Beneke, A. Signer and V.A. Smirnov, Two loop correction to the leptonic decay of quarkonium, Phys. Rev. Lett. 80 (1998) 2535 [hep-ph/9712302] [INSPIRE].
A.H. Hoang, Two loop corrections to the electromagnetic vertex for energies close to threshold, Phys. Rev. D 56 (1997) 7276 [hep-ph/9703404] [INSPIRE].
W. Bernreuther et al., Two-Parton Contribution to the Heavy-Quark Forward-Backward Asymmetry in NNLO QCD, Nucl. Phys. B 750 (2006) 83 [hep-ph/0604031] [INSPIRE].
J. Jersak, E. Laermann and P.M. Zerwas, QCD Corrected Forward Backward Asymmetry of Quark Jets in e + e − Annihilation, Phys. Lett. 98B (1981) 363 [INSPIRE].
A.B. Arbuzov, D. Yu. Bardin and A. Leike, Analytic final state corrections with cut for e + e − → massive fermions, Mod. Phys. Lett. A 7 (1992) 2029 [Erratum ibid. A 9 (1994) 1515] [INSPIRE].
A. Djouadi, B. Lampe and P.M. Zerwas, A note on the QCD corrections to forward-backward asymmetries of heavy quark jets in Z decays, Z. Phys. C 67 (1995) 123 [hep-ph/9411386] [INSPIRE].
D.Y. Bardin, et al., ZFITTER v.6.21: A semianalytical program for fermion pair production in e + e − annihilation, Comput. Phys. Commun. 133 (2001) 229 [hep-ph/9908433] [INSPIRE].
G. Altarelli and B. Lampe, Second order QCD corrections to heavy quark forward-backward asymmetries, Nucl. Phys. B 391 (1993) 3 [INSPIRE].
V. Ravindran and W.L. van Neerven, Second order QCD corrections to the forward-backward asymmetry in e + e − collisions, Phys. Lett. B 445 (1998) 214 [hep-ph/9809411] [INSPIRE].
S. Catani and M.H. Seymour, Corrections of O(α 2 S ) to the forward backward asymmetry, JHEP 07 (1999) 023 [hep-ph/9905424] [INSPIRE].
S. Weinzierl, The forward-backward asymmetry at NNLO revisited, Phys. Lett. B 644 (2007) 331 [hep-ph/0609021] [INSPIRE].
K. Waninger, Die Vorwärts-Rückwärts-Asymmetrie für schwere Quarks zur Ordnung α 2 s , Ph.D. Thesis, RWTH Aachen University, Germany (2011).
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].
R. Kleiss, W.J. Stirling and S.D. Ellis, A New Monte Carlo Treatment of Multiparticle Phase Space at High-energies, Comput. Phys. Commun. 40 (1986) 359 [INSPIRE].
E. Devetak, A. Nomerotski and M. Peskin, Top quark anomalous couplings at the International Linear Collider, Phys. Rev. D 84 (2011) 034029 [arXiv:1005.1756] [INSPIRE].
R. Röntsch and M. Schulze, Probing top-Z dipole moments at the LHC and ILC, JHEP 08 (2015) 044 [arXiv:1501.05939] [INSPIRE].
P.H. Khiem, E. Kou, Y. Kurihara and F. Le Diberder, Probing New Physics using top quark polarization in the \( {e}^{+}{e}^{-}\to t\overline{t} \) process at future Linear Colliders, arXiv:1503.04247 [INSPIRE].
P. Janot, Top-quark electroweak couplings at the FCC-ee, JHEP 04 (2015) 182 [arXiv:1503.01325] [INSPIRE].
M.S. Amjad et al., A precise characterisation of the top quark electro-weak vertices at the ILC, Eur. Phys. J. C 75 (2015) 512 [arXiv:1505.06020] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1610.07897
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Chen, L., Dekkers, O., Heisler, D. et al. Top-quark pair production at next-to-next-to-leading order QCD in electron positron collisions. J. High Energ. Phys. 2016, 98 (2016). https://doi.org/10.1007/JHEP12(2016)098
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2016)098