Abstract
We present details of the calculation of the pp → W(→ lν)γ process at next-to-next-to-leading order in QCD, calculated using the jettiness slicing method. The calculation is based entirely on analytic amplitudes. Because of the radiation zero, the NLO QCD contribution from the gq channel is as important as the contribution from the Born \( q\overline{q} \) process, disrupting the normal counting of leading and sub-leading contributions. We also assess the importance of electroweak (EW) corrections, including the EW corrections to both the six-parton channel 0 → \( \overline{u} d\nu {e}^{+}\gamma g \) and the five-parton channel 0 → \( \overline{u} d\nu {e}^{+}\gamma \). Previous experimental results have been shown to agree with theoretical predictions, taking into account the large experimental errors. With the advent of run II data from the LHC, the statistical errors on the data will decrease, and will be competitive with the error on theoretical predictions for the first time. We present numerical results for \( \sqrt{s} \) = 7 and 13 TeV. Analytic results for the one-loop six-parton QCD amplitude and the tree-level seven-parton QCD amplitude are presented in appendices.
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K.O. Mikaelian, M.A. Samuel and D. Sahdev, The magnetic moment of weak bosons produced in pp and \( p\overline{p} \) collisions, Phys. Rev. Lett. 43 (1979) 746 [INSPIRE].
R.W. Brown, D. Sahdev and K.O. Mikaelian, W±Z0 and W±γ pair production in neutrino e, pp, and \( p\overline{p} \) collisions, Phys. Rev. D 20 (1979) 1164 [INSPIRE].
C.J. Goebel, F. Halzen and J.P. Leveille, Angular zeros of Brown, Mikaelian, Sahdev, and Samuel and the factorization of tree amplitudes in gauge theories, Phys. Rev. D 23 (1981) 2682 [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
R.W. Brown and S.G. Naculich, BCJ relations from a new symmetry of gauge-theory amplitudes, JHEP 10 (2016) 130 [arXiv:1608.04387] [INSPIRE].
J. Smith, D. Thomas and W.L. van Neerven, QCD corrections to the reaction \( p\overline{p} \) → WγX, Z. Phys. C 44 (1989) 267 [INSPIRE].
J. Ohnemus, Order αs calculations of hadronic W±γ and Zγ production, Phys. Rev. D 47 (1993) 940 [INSPIRE].
U. Baur, T. Han and J. Ohnemus, QCD corrections to hadronic Wγ production with nonstandard WWγ couplings, Phys. Rev. D 48 (1993) 5140 [hep-ph/9305314] [INSPIRE].
L.J. Dixon, Z. Kunszt and A. Signer, Helicity amplitudes for O(αs) production of W+W−, W±Z, ZZ, W±γ, or Zγ pairs at hadron colliders, Nucl. Phys. B 531 (1998) 3 [hep-ph/9803250] [INSPIRE].
J.M. Campbell, R.K. Ellis and C. Williams, Vector boson pair production at the LHC, JHEP 07 (2011) 018 [arXiv:1105.0020] [INSPIRE].
L. Barze et al., W γ production in hadronic collisions using the POWHEG+MiNLO method, JHEP 12 (2014) 039 [arXiv:1408.5766] [INSPIRE].
M. Grazzini, S. Kallweit and D. Rathlev, Wγ and Zγ production at the LHC in NNLO QCD, PoS RADCOR2015 (2016) 074 [arXiv:1601.06751] [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].
M. Grazzini, S. Kallweit and M. Wiesemann, Fully differential NNLO computations with MATRIX, Eur. Phys. J. C 78 (2018) 537 [arXiv:1711.06631] [INSPIRE].
F. Cascioli, P. Maierhofer and S. Pozzorini, Scattering amplitudes with open loops, Phys. Rev. Lett. 108 (2012) 111601 [arXiv:1111.5206] [INSPIRE].
E. Accomando, A. Denner and S. Pozzorini, Electroweak correction effects in gauge boson pair production at the CERN LHC, Phys. Rev. D 65 (2002) 073003 [hep-ph/0110114] [INSPIRE].
A. Denner, S. Dittmaier, M. Hecht and C. Pasold, NLO QCD and electroweak corrections to W + γ production with leptonic W-boson decays, JHEP 04 (2015) 018 [arXiv:1412.7421] [INSPIRE].
M. Grazzini, S. Kallweit, J.M. Lindert, S. Pozzorini and M. Wiesemann, NNLO QCD + NLO EW with Matrix+OpenLoops: precise predictions for vector-boson pair production, JHEP 02 (2020) 087 [arXiv:1912.00068] [INSPIRE].
R. Boughezal et al., Color singlet production at NNLO in MCFM, Eur. Phys. J. C 77 (2017) 7 [arXiv:1605.08011] [INSPIRE].
J.M. Campbell, T. Neumann and C. Williams, Zγ production at NNLO including anomalous couplings, JHEP 11 (2017) 150 [arXiv:1708.02925] [INSPIRE].
R. Boughezal et al., Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, Phys. Rev. Lett. 116 (2016) 152001 [arXiv:1512.01291] [INSPIRE].
J.M. Campbell, R.K. Ellis and S. Seth, H + 1 jet production revisited, JHEP 10 (2019) 136 [arXiv:1906.01020] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, One loop amplitudes for e+e− to four partons, Nucl. Phys. B 513 (1998) 3 [hep-ph/9708239] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103] [INSPIRE].
D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [arXiv:0704.1835] [INSPIRE].
P. Mastrolia, Double-cut of scattering amplitudes and Stokes’ theorem, Phys. Lett. B 678 (2009) 246 [arXiv:0905.2909] [INSPIRE].
G. Laurentis and D. Maître, Extracting analytical one-loop amplitudes from numerical evaluations, JHEP 07 (2019) 123 [arXiv:1904.04067] [INSPIRE].
CDF collaboration, Measurement of W-γ couplings with CDF in \( p\overline{p} \) collisions at \( \sqrt{s} \) = 1.8 TeV, Phys. Rev. Lett. 74 (1995) 1936 [INSPIRE].
D0 collaboration, Measurement of the WWγ gauge boson couplings in \( p\overline{p} \) collisions at \( \sqrt{s} \) = 1.8 TeV, Phys. Rev. Lett. 75 (1995) 1034 [hep-ex/9505007] [INSPIRE].
CDF collaboration, Measurement of Wγ and Zγ production in \( p\overline{p} \) collisions at \( \sqrt{s} \) = 1.96 TeV, Phys. Rev. Lett. 94 (2005) 041803 [hep-ex/0410008] [INSPIRE].
D0 collaboration, Measurement of the p-\( \overline{p} \) → Wγ + X cross section at \( \sqrt{s} \) = 1.96 TeV and WWγ anomalous coupling limits, Phys. Rev. D 71 (2005) 091108 [hep-ex/0503048] [INSPIRE].
D0 collaboration, Wγ production and limits on anomalous WWγ couplings in \( p\overline{p} \) collisions, Phys. Rev. Lett. 107 (2011) 241803 [arXiv:1109.4432] [INSPIRE].
CMS collaboration, Measurement of the Wγ production cross section in proton-proton collisions at \( \sqrt{s} \) = 13 TeV and constraints on effective field theory coefficients, Phys. Rev. Lett. 126 (2021) 252002 [arXiv:2102.02283] [INSPIRE].
U. Baur and E.L. Berger, Probing the WWγ vertex at the Tevatron collider, Phys. Rev. D 41 (1990) 1476 [INSPIRE].
U. Baur and D. Zeppenfeld, Measuring the WWγ vertex in single W production at ep colliders, Nucl. Phys. B 325 (1989) 253 [INSPIRE].
U. Baur and E.L. Berger, Probing the weak boson sector in Zγ production at hadron colliders, Phys. Rev. D 47 (1993) 4889 [INSPIRE].
CMS collaboration, Measurement of Wγ and Zγ production in pp collisions at \( \sqrt{s} \) = 7 TeV, Phys. Lett. B 701 (2011) 535 [arXiv:1105.2758] [INSPIRE].
ATLAS collaboration, Measurement of Wγ and Zγ production in proton-proton collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS detector, JHEP 09 (2011) 072 [arXiv:1106.1592] [INSPIRE].
ATLAS collaboration, Measurement of Wγ and Zγ production cross sections in pp collisions at \( \sqrt{s} \) = 7 TeV and limits on anomalous triple gauge couplings with the ATLAS detector, Phys. Lett. B 717 (2012) 49 [arXiv:1205.2531] [INSPIRE].
J.M. Campbell and R.K. Ellis, MCFM for the Tevatron and the LHC, Nucl. Phys. B Proc. Suppl. 205-206 (2010) 10 [arXiv:1007.3492] [INSPIRE].
CMS collaboration, Measurement of the Wγ and Zγ inclusive cross sections in pp collisions at \( \sqrt{s} \) = 7 TeV and limits on anomalous triple gauge boson couplings, Phys. Rev. D 89 (2014) 092005 [arXiv:1308.6832] [INSPIRE].
J.M. Campbell and R.K. Ellis, An update on vector boson pair production at hadron colliders, Phys. Rev. D 60 (1999) 113006 [hep-ph/9905386] [INSPIRE].
J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].
R. Frederix and S. Frixione, Merging meets matching in MC@NLO, JHEP 12 (2012) 061 [arXiv:1209.6215] [INSPIRE].
T. Gehrmann and L. Tancredi, Two-loop QCD helicity amplitudes for \( q\overline{q} \) → W±γ and \( q\overline{q} \) → Z0γ, JHEP 02 (2012) 004 [arXiv:1112.1531] [INSPIRE].
T. Matsuura, S.C. van der Marck and W.L. van Neerven, The calculation of the second order soft and virtual contributions to the Drell-Yan cross-section, Nucl. Phys. B 319 (1989) 570 [INSPIRE].
S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [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].
J.M. Campbell, R.K. Ellis, Y. Li and C. Williams, Predictions for diphoton production at the LHC through NNLO in QCD, JHEP 07 (2016) 148 [arXiv:1603.02663] [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].
R. Boughezal, K. Melnikov and F. Petriello, A subtraction scheme for NNLO computations, Phys. Rev. D 85 (2012) 034025 [arXiv:1111.7041] [INSPIRE].
J. Gaunt, M. Stahlhofen, F.J. Tackmann and J.R. Walsh, N-jettiness subtractions for NNLO QCD calculations, JHEP 09 (2015) 058 [arXiv:1505.04794] [INSPIRE].
A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, PTEP 2020 (2020) 083C01 [INSPIRE].
S. Frixione, Isolated photons in perturbative QCD, Phys. Lett. B 429 (1998) 369 [hep-ph/9801442] [INSPIRE].
F. Siegert, A practical guide to event generation for prompt photon production with Sherpa, J. Phys. G 44 (2017) 044007 [arXiv:1611.07226] [INSPIRE].
X. Chen, T. Gehrmann, N. Glover, M. Höfer and A. Huss, Isolated photon and photon+jet production at NNLO QCD accuracy, JHEP 04 (2020) 166 [arXiv:1904.01044] [INSPIRE].
J. Campbell and T. Neumann, Precision phenomenology with MCFM, JHEP 12 (2019) 034 [arXiv:1909.09117] [INSPIRE].
A. Behring et al., Mixed QCD-electroweak corrections to W-boson production in hadron collisions, Phys. Rev. D 103 (2021) 013008 [arXiv:2009.10386] [INSPIRE].
L. Buonocore, M. Grazzini, S. Kallweit, C. Savoini and F. Tramontano, Mixed QCD-EW corrections to pp → ℓνℓ + X at the LHC, Phys. Rev. D 103 (2021) 114012 [arXiv:2102.12539] [INSPIRE].
E. Accomando, A. Denner and C. Meier, Electroweak corrections to Wγ and Zγ production at the LHC, Eur. Phys. J. C 47 (2006) 125 [hep-ph/0509234] [INSPIRE].
A. Manohar, P. Nason, G.P. Salam and G. Zanderighi, How bright is the proton? A precise determination of the photon parton distribution function, Phys. Rev. Lett. 117 (2016) 242002 [arXiv:1607.04266] [INSPIRE].
A.V. Manohar, P. Nason, G.P. Salam and G. Zanderighi, The photon content of the proton, JHEP 12 (2017) 046 [arXiv:1708.01256] [INSPIRE].
S. Actis, A. Denner, L. Hofer, J.-N. Lang, A. Scharf and S. Uccirati, RECOLA: REcursive Computation of One-Loop Amplitudes, Comput. Phys. Commun. 214 (2017) 140 [arXiv:1605.01090] [INSPIRE].
A. Denner, J.-N. Lang and S. Uccirati, RECOLA2: REcursive Computation of One-Loop Amplitudes 2, Comput. Phys. Commun. 224 (2018) 346 [arXiv:1711.07388] [INSPIRE].
M. Bahr et al., HERWIG++ physics and manual, Eur. Phys. J. C 58 (2008) 639 [arXiv:0803.0883] [INSPIRE].
NNPDF collaboration, Parton distributions with QED corrections, Nucl. Phys. B 877 (2013) 290 [arXiv:1308.0598] [INSPIRE].
T. Becher and T. Neumann, Fiducial qT resummation of color-singlet processes at N3LL+NNLO, JHEP 03 (2021) 199 [arXiv:2009.11437] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to five gluon amplitudes, Phys. Rev. Lett. 70 (1993) 2677 [hep-ph/9302280] [INSPIRE].
R.K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP 02 (2008) 002 [arXiv:0712.1851] [INSPIRE].
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Campbell, J.M., De Laurentis, G., Ellis, R.K. et al. The pp → W(→ lν) + γ process at next-to-next-to-leading order. J. High Energ. Phys. 2021, 79 (2021). https://doi.org/10.1007/JHEP07(2021)079
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DOI: https://doi.org/10.1007/JHEP07(2021)079