Abstract
We compute the tree-level current for the emission of a soft quark-antiquark pair in association with a gluon. This soft current is the last missing ingredient to understand the infrared singularities that can arise in next-to-next-to-next-to-leading-order (N3LO) computations in QCD. Its square allows us to understand for the first time the colour correlations induced by the soft emission of a quark pair and a gluon. We find that there are three types of correlations: besides dipole-type correlations that have already appeared in soft limits of tree-level amplitudes, we uncover for the first time also a three-parton correlation involving a totally symmetric structure constant. We also study the behaviour of collinear splitting amplitudes in the triple-soft limit, and we derive the corresponding factorisation formula.
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J.M. Campbell and E.W.N. Glover, Double unresolved approximations to multiparton scattering amplitudes, Nucl. Phys. B 527 (1998) 264 [hep-ph/9710255] [INSPIRE].
S. Catani and M. Grazzini, Collinear factorization and splitting functions for next-to-next-to-leading order QCD calculations, Phys. Lett. B 446 (1999) 143 [hep-ph/9810389] [INSPIRE].
S. Catani and M. Grazzini, Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond, Nucl. Phys. B 570 (2000) 287 [hep-ph/9908523] [INSPIRE].
V. Del Duca, A. Frizzo and F. Maltoni, Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit, Nucl. Phys. B 568 (2000) 211 [hep-ph/9909464] [INSPIRE].
D.A. Kosower, Multiple singular emission in gauge theories, Phys. Rev. D 67 (2003) 116003 [hep-ph/0212097] [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].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
Z. Bern, V. Del Duca and C.R. Schmidt, The Infrared behavior of one loop gluon amplitudes at next-to-next-to-leading order, Phys. Lett. B 445 (1998) 168 [hep-ph/9810409] [INSPIRE].
D.A. Kosower and P. Uwer, One loop splitting amplitudes in gauge theory, Nucl. Phys. B 563 (1999) 477 [hep-ph/9903515] [INSPIRE].
Z. Bern, V. Del Duca, W.B. Kilgore and C.R. Schmidt, The infrared behavior of one loop QCD amplitudes at next-to-next-to leading order, Phys. Rev. D 60 (1999) 116001 [hep-ph/9903516] [INSPIRE].
S. Catani and M. Grazzini, The soft gluon current at one loop order, Nucl. Phys. B 591 (2000) 435 [hep-ph/0007142] [INSPIRE].
O. Braun-White and N. Glover, Decomposition of triple collinear splitting functions, JHEP 09 (2022) 059 [arXiv:2204.10755] [INSPIRE].
F. Caola, A. Chakraborty, G. Gambuti, A. von Manteuffel and L. Tancredi, Three-loop helicity amplitudes for four-quark scattering in massless QCD, JHEP 10 (2021) 206 [arXiv:2108.00055] [INSPIRE].
P. Bargiela, F. Caola, A. von Manteuffel and L. Tancredi, Three-loop helicity amplitudes for diphoton production in gluon fusion, JHEP 02 (2022) 153 [arXiv:2111.13595] [INSPIRE].
F. Caola, A. Chakraborty, G. Gambuti, A. von Manteuffel and L. Tancredi, Three-Loop Gluon Scattering in QCD and the Gluon Regge Trajectory, Phys. Rev. Lett. 128 (2022) 212001 [arXiv:2112.11097] [INSPIRE].
S. Abreu, F. Febres Cordero, H. Ita, B. Page and V. Sotnikov, Leading-color two-loop QCD corrections for three-jet production at hadron colliders, JHEP 07 (2021) 095 [arXiv:2102.13609] [INSPIRE].
S. Abreu, F. Febres Cordero, H. Ita, M. Klinkert, B. Page and V. Sotnikov, Leading-color two-loop amplitudes for four partons and a W boson in QCD, JHEP 04 (2022) 042 [arXiv:2110.07541] [INSPIRE].
S. Badger, H.B. Hartanto and S. Zoia, Two-Loop QCD Corrections to Wbb¯ Production at Hadron Colliders, Phys. Rev. Lett. 127 (2021) 012001 [arXiv:2102.02516] [INSPIRE].
S. Badger, H.B. Hartanto, J. Kryś and S. Zoia, Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC, JHEP 11 (2021) 012 [arXiv:2107.14733] [INSPIRE].
S. Badger, H.B. Hartanto, J. Kryś and S. Zoia, Two-loop leading colour helicity amplitudes for W±γ + j production at the LHC, JHEP 05 (2022) 035 [arXiv:2201.04075] [INSPIRE].
F.A. Dreyer and A. Karlberg, Vector-Boson Fusion Higgs Production at Three Loops in QCD, Phys. Rev. Lett. 117 (2016) 072001 [arXiv:1606.00840] [INSPIRE].
F.A. Dreyer and A. Karlberg, Vector-Boson Fusion Higgs Pair Production at N3LO, Phys. Rev. D 98 (2018) 114016 [arXiv:1811.07906] [INSPIRE].
F. Dulat, B. Mistlberger and A. Pelloni, Precision predictions at N3LO for the Higgs boson rapidity distribution at the LHC, Phys. Rev. D 99 (2019) 034004 [arXiv:1810.09462] [INSPIRE].
L.-B. Chen, H.T. Li, H.-S. Shao and J. Wang, Higgs boson pair production via gluon fusion at N3LO in QCD, Phys. Lett. B 803 (2020) 135292 [arXiv:1909.06808] [INSPIRE].
X. Chen, T. Gehrmann, E.W.N. Glover, A. Huss, B. Mistlberger and A. Pelloni, Fully Differential Higgs Boson Production to Third Order in QCD, Phys. Rev. Lett. 127 (2021) 072002 [arXiv:2102.07607] [INSPIRE].
X. Chen, T. Gehrmann, N. Glover, A. Huss, T.-Z. Yang and H.X. Zhu, Dilepton Rapidity Distribution in Drell-Yan Production to Third Order in QCD, Phys. Rev. Lett. 128 (2022) 052001 [arXiv:2107.09085] [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].
V. Del Duca, C. Duhr, R. Haindl, A. Lazopoulos and M. Michel, Tree-level splitting amplitudes for a quark into four collinear partons, JHEP 02 (2020) 189 [arXiv:1912.06425] [INSPIRE].
V. Del Duca, C. Duhr, R. Haindl, A. Lazopoulos and M. Michel, Tree-level splitting amplitudes for a gluon into four collinear partons, JHEP 10 (2020) 093 [arXiv:2007.05345] [INSPIRE].
S. Catani, D. de Florian and G. Rodrigo, The Triple collinear limit of one loop QCD amplitudes, Phys. Lett. B 586 (2004) 323 [hep-ph/0312067] [INSPIRE].
S. Badger, F. Buciuni and T. Peraro, One-loop triple collinear splitting amplitudes in QCD, JHEP 09 (2015) 188 [arXiv:1507.05070] [INSPIRE].
M. Czakon and S. Sapeta, Complete collection of one-loop triple-collinear splitting operators for dimensionally-regulated QCD, JHEP 07 (2022) 052 [arXiv:2204.11801] [INSPIRE].
C. Duhr, T. Gehrmann and M. Jaquier, Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO, JHEP 02 (2015) 077 [arXiv:1411.3587] [INSPIRE].
Y. Li and H.X. Zhu, Single soft gluon emission at two loops, JHEP 11 (2013) 080 [arXiv:1309.4391] [INSPIRE].
C. Duhr and T. Gehrmann, The two-loop soft current in dimensional regularization, Phys. Lett. B 727 (2013) 452 [arXiv:1309.4393] [INSPIRE].
L.J. Dixon, E. Herrmann, K. Yan and H.X. Zhu, Soft gluon emission at two loops in full color, JHEP 05 (2020) 135 [arXiv:1912.09370] [INSPIRE].
Y.J. Zhu, Double soft current at one-loop in QCD, arXiv:2009.08919 [INSPIRE].
S. Catani and L. Cieri, Multiple soft radiation at one-loop order and the emission of a soft quark–antiquark pair, Eur. Phys. J. C 82 (2022) 97 [arXiv:2108.13309] [INSPIRE].
S. Catani, D. Colferai and A. Torrini, Triple (and quadruple) soft-gluon radiation in QCD hard scattering, JHEP 01 (2020) 118 [arXiv:1908.01616] [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. 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
A. Bassetto, M. Ciafaloni and G. Marchesini, Jet Structure and Infrared Sensitive Quantities in Perturbative QCD, Phys. Rept. 100 (1983) 201 [INSPIRE].
S. Catani, New Techniques for Calculating Higher-Order QCD Corrections, in Proceedings, Workshop on New Techniques for Calculating Higher Order QCD Corrections, Zurich, Switzerland, 1992.
S. Catani, D. de Florian and G. Rodrigo, Space-like (versus time-like) collinear limits in QCD: Is factorization violated?, JHEP 07 (2012) 026 [arXiv:1112.4405] [INSPIRE].
D. Amati, R. Petronzio and G. Veneziano, Relating Hard QCD Processes Through Universality of Mass Singularities. 2, Nucl. Phys. B 146 (1978) 29 [INSPIRE].
D. Amati, R. Petronzio and G. Veneziano, Relating Hard QCD Processes Through Universality of Mass Singularities, Nucl. Phys. B 140 (1978) 54 [INSPIRE].
R.K. Ellis, H. Georgi, M. Machacek, H.D. Politzer and G.G. Ross, Factorization and the Parton Model in QCD, Phys. Lett. B 78 (1978) 281 [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].
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ArXiv ePrint: 2206.01584
On leave from INFN, Laboratori Nazionali di Frascati, Italy. (Vittorio Del Duca)
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Del Duca, V., Duhr, C., Haindl, R. et al. Tree-level soft emission of a quark pair in association with a gluon. J. High Energ. Phys. 2023, 40 (2023). https://doi.org/10.1007/JHEP01(2023)040
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DOI: https://doi.org/10.1007/JHEP01(2023)040