Abstract
We present a calculation of the NLO QCD corrections to the loop-induced production of a photon pair through gluon fusion, including massive top quarks at two loops, where the two-loop integrals are calculated numerically. Matching the fixed-order NLO results to a threshold expansion, we obtain accurate results around the top quark pair production threshold. We analyse how the top quark threshold corrections affect distributions of the photon pair invariant mass and comment on the possibility of determining the top quark mass from precision measurements of the diphoton invariant mass spectrum.
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CMS collaboration, Measurement of differential cross sections for the production of a pair of isolated photons in pp collisions at \( \sqrt{s} \) = 7 TeV, Eur. Phys. J.C 74 (2014) 3129 [arXiv:1405.7225] [INSPIRE].
ATLAS collaboration, Measurements of integrated and differential cross sections for isolated photon pair production in pp collisions at \( \sqrt{s} \) = 8 TeV with the ATLAS detector, Phys. Rev.D 95 (2017) 112005 [arXiv:1704.03839] [INSPIRE].
D.A. Dicus and S.S.D. Willenbrock, Photon Pair Production and the Intermediate Mass Higgs Boson, Phys. Rev.D 37 (1988) 1801 [INSPIRE].
L.J. Dixon and M.S. Siu, Resonance continuum interference in the diphoton Higgs signal at the LHC, Phys. Rev. Lett.90 (2003) 252001 [hep-ph/0302233] [INSPIRE].
S.P. Martin, Shift in the LHC Higgs Diphoton Mass Peak from Interference with Background, Phys. Rev.D 86 (2012) 073016 [arXiv:1208.1533] [INSPIRE].
D. de Florian, N. Fidanza, R.J. Hernández-Pinto, J. Mazzitelli, Y. Rotstein Habarnau and G.F.R. Sborlini, A complete \( O\left({\alpha}_S^2\right) \)calculation of the signal-background interference for the Higgs diphoton decay channel, Eur. Phys. J.C 73 (2013) 2387 [arXiv:1303.1397] [INSPIRE].
S.P. Martin, Interference of Higgs Diphoton Signal and Background in Production with a Jet at the LHC, Phys. Rev.D 88 (2013) 013004 [arXiv:1303.3342] [INSPIRE].
L.J. Dixon and Y. Li, Bounding the Higgs Boson Width Through Interferometry, Phys. Rev. Lett.111 (2013) 111802 [arXiv:1305.3854] [INSPIRE].
J. Campbell, M. Carena, R. Harnik and Z. Liu, Interference in the gg → h → γγ On-Shell Rate and the Higgs Boson Total Width, Phys. Rev. Lett.119 (2017) 181801 [arXiv:1704.08259] [INSPIRE].
L. Cieri, F. Coradeschi, D. de Florian and N. Fidanza, Transverse-momentum resummation for the signal-background interference in the H → γγ channel at the LHC, Phys. Rev.D 96 (2017) 054003 [arXiv:1706.07331] [INSPIRE].
ATLAS collaboration, Search for resonances in diphoton events at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, JHEP09 (2016) 001 [arXiv:1606.03833] [INSPIRE].
CMS collaboration, Search for physics beyond the standard model in high-mass diphoton events from proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Phys. Rev.D 98 (2018) 092001 [arXiv:1809.00327] [INSPIRE].
S.R. Dugad, P. Jain, S. Mitra, P. Sanyal and R.K. Verma, The top threshold effect in the γγ production at the LHC, Eur. Phys. J.C 78 (2018) 715 [arXiv:1605.07360] [INSPIRE].
S. Kawabata and H. Yokoya, Top-quark mass from the diphoton mass spectrum, Eur. Phys. J.C 77 (2017) 323 [arXiv:1607.00990] [INSPIRE].
T. Binoth, J.P. Guillet, E. Pilon and M. Werlen, A Full next-to-leading order study of direct photon pair production in hadronic collisions, Eur. Phys. J.C 16 (2000) 311 [hep-ph/9911340] [INSPIRE].
C. Balázs, E.L. Berger, P.M. Nadolsky and C.P. Yuan, Calculation of prompt diphoton production cross-sections at Tevatron and LHC energies, Phys. Rev.D 76 (2007) 013009 [arXiv:0704.0001] [INSPIRE].
Z. Bern, A. De Freitas and L.J. Dixon, Two loop amplitudes for gluon fusion into two photons, JHEP09 (2001) 037 [hep-ph/0109078] [INSPIRE].
Z. Bern, L.J. Dixon and C. Schmidt, Isolating a light Higgs boson from the diphoton background at the CERN LHC, Phys. Rev.D 66 (2002) 074018 [hep-ph/0206194] [INSPIRE].
J.M. Campbell, R.K. Ellis and C. Williams, Vector boson pair production at the LHC, JHEP07 (2011) 018 [arXiv:1105.0020] [INSPIRE].
F. Maltoni, M.K. Mandal and X. Zhao, Top-quark effects in diphoton production through gluon fusion at next-to-leading order in QCD, Phys. Rev.D 100 (2019) 071501 [arXiv:1812.08703] [INSPIRE].
M. Czakon, Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD, Phys. Lett.B 664 (2008) 307 [arXiv:0803.1400] [INSPIRE].
M.K. Mandal and X. Zhao, Evaluating multi-loop Feynman integrals numerically through differential equations, JHEP03 (2019) 190 [arXiv:1812.03060] [INSPIRE].
S. Caron-Huot and J.M. Henn, Iterative structure of finite loop integrals, JHEP06 (2014) 114 [arXiv:1404.2922] [INSPIRE].
M. Becchetti and R. Bonciani, Two-Loop Master Integrals for the Planar QCD Massive Corrections to Di-photon and Di-jet Hadro-production, JHEP01 (2018) 048 [arXiv:1712.02537] [INSPIRE].
A. von Manteuffel and L. Tancredi, A non-planar two-loop three-point function beyond multiple polylogarithms, JHEP06 (2017) 127 [arXiv:1701.05905] [INSPIRE].
J. Broedel, C. Duhr, F. Dulat, B. Penante and L. Tancredi, Elliptic polylogarithms and Feynman parameter integrals, JHEP05 (2019) 120 [arXiv:1902.09971] [INSPIRE].
U. Aglietti, R. Bonciani, G. Degrassi and A. Vicini, Analytic Results for Virtual QCD Corrections to Higgs Production and Decay, JHEP01 (2007) 021 [hep-ph/0611266] [INSPIRE].
C. Anastasiou, S. Beerli, S. Bucherer, A. Daleo and Z. Kunszt, Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop, JHEP01 (2007) 082 [hep-ph/0611236] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, Phys. Rev. Lett.108 (2012) 072001 [Erratum ibid.117 (2016) 089901] [arXiv:1110.2375] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at the LHC: a QCD study up to NNLO, JHEP04 (2018) 142 [arXiv:1802.02095] [INSPIRE].
J.M. Campbell, R.K. Ellis, Y. Li and C. Williams, Predictions for diphoton production at the LHC through NNLO in QCD, JHEP07 (2016) 148 [arXiv:1603.02663] [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].
L. Chen, A prescription for projectors to compute helicity amplitudes in D dimensions, arXiv:1904.00705 [INSPIRE].
T. Ahmed, A.H. Ajjath, L. Chen, P.K. Dhani, P. Mukherjee and V. Ravindran, Polarised Amplitudes and Soft-Virtual Cross Sections for \( b\overline{b} \)→ ZH at NNLO in QCD, JHEP01 (2020) 030 [arXiv:1910.06347] [INSPIRE].
R. Karplus and M. Neuman, The scattering of light by light, Phys. Rev.83 (1951) 776 [INSPIRE].
Z. Bern, A. De Freitas, L.J. Dixon, A. Ghinculov and H.L. Wong, QCD and QED corrections to light by light scattering, JHEP11 (2001) 031 [hep-ph/0109079] [INSPIRE].
T. Binoth, E.W.N. Glover, P. Marquard and J.J. van der Bij, Two loop corrections to light by light scattering in supersymmetric QED, JHEP05 (2002) 060 [hep-ph/0202266] [INSPIRE].
Z. Bern and A.G. Morgan, Massive loop amplitudes from unitarity, Nucl. Phys.B 467 (1996) 479 [hep-ph/9511336] [INSPIRE].
C. Bernicot, Light-light amplitude from generalized unitarity in massive QED, arXiv:0804.0749 [INSPIRE].
S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys.B 467 (1996) 399 [hep-ph/9512328] [INSPIRE].
P. Nason, A New method for combining NLO QCD with shower Monte Carlo algorithms, JHEP11 (2004) 040 [hep-ph/0409146] [INSPIRE].
S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with Parton Shower simulations: the POWHEG method, JHEP11 (2007) 070 [arXiv:0709.2092] [INSPIRE].
S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP06 (2010) 043 [arXiv:1002.2581] [INSPIRE].
S.P. Jones, Automation of 2-loop Amplitude Calculations, PoS(LL2016)069 [arXiv:1608.03846] [INSPIRE].
A. von Manteuffel and C. Studerus, Reduze 2 — Distributed Feynman Integral Reduction, arXiv:1201.4330 [INSPIRE].
M. Argeri et al., Magnus and Dyson Series for Master Integrals, JHEP03 (2014) 082 [arXiv:1401.2979] [INSPIRE].
A. von Manteuffel, E. Panzer and R.M. Schabinger, A quasi-finite basis for multi-loop Feynman integrals, JHEP02 (2015) 120 [arXiv:1411.7392] [INSPIRE].
S. Borowka et al., pySecDec: a toolbox for the numerical evaluation of multi-scale integrals, Comput. Phys. Commun.222 (2018) 313 [arXiv:1703.09692] [INSPIRE].
S. Borowka, G. Heinrich, S. Jahn, S.P. Jones, M. Kerner and J. Schlenk, A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec, Comput. Phys. Commun.240 (2019) 120 [arXiv:1811.11720] [INSPIRE].
G. Luisoni, P. Nason, C. Oleari and F. Tramontano, HW±/HZ + 0 and 1 jet at NLO with the POWHEG BOX interfaced to GoSam and their merging within MiNLO, JHEP10 (2013) 083 [arXiv:1306.2542] [INSPIRE].
G. Cullen et al., Automated One-Loop Calculations with GoSam, Eur. Phys. J.C 72 (2012) 1889 [arXiv:1111.2034] [INSPIRE].
G. Cullen et al., GOSAM-2.0: a tool for automated one-loop calculations within the Standard Model and beyond, Eur. Phys. J.C 74 (2014) 3001 [arXiv:1404.7096] [INSPIRE].
W.E. Caswell and G.P. Lepage, Effective Lagrangians for Bound State Problems in QED, QCD and Other Field Theories, Phys. Lett.B 167 (1986) 437 [INSPIRE].
G.T. Bodwin, E. Braaten and G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev.D 51 (1995) 1125 [Erratum ibid.D 55 (1997) 5853] [hep-ph/9407339] [INSPIRE].
A. Pineda and J. Soto, Effective field theory for ultrasoft momenta in NRQCD and NRQED, Nucl. Phys. Proc. Suppl.64 (1998) 428 [hep-ph/9707481] [INSPIRE].
M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys.B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
K. Melnikov, M. Spira and O.I. Yakovlev, Threshold effects in two photon decays of Higgs particles, Z. Phys.C 64 (1994) 401 [hep-ph/9405301] [INSPIRE].
K. Melnikov and O.I. Yakovlev, Top near threshold: All αscorrections are trivial, Phys. Lett.B 324 (1994) 217 [hep-ph/9302311] [INSPIRE].
W. Fischler, Quark-anti-Quark Potential in QCD, Nucl. Phys.B 129 (1977) 157 [INSPIRE].
A. Billoire, How Heavy Must Be Quarks in Order to Build Coulombic \( q\overline{q} \)Bound States, Phys. Lett.B 92 (1980) 343 [INSPIRE].
M. Beneke, A Quark mass definition adequate for threshold problems, Phys. Lett.B 434 (1998) 115 [hep-ph/9804241] [INSPIRE].
A.H. Hoang and T. Teubner, Top quark pair production at threshold: Complete next-to-next-to-leading order relativistic corrections, Phys. Rev.D 58 (1998) 114023 [hep-ph/9801397] [INSPIRE].
M. Beneke, A. Signer and V.A. Smirnov, A Two loop application of the threshold expansion: The Bottom quark mass from \( b\overline{b} \)production, in Radiative corrections: Application of quantum field theory to phenomenology. Proceedings of 4th International Symposium, RADCOR’98, Barcelona Spain (1998), pg. 223 [hep-ph/9906476] [INSPIRE].
A.H. Hoang, A.V. Manohar, I.W. Stewart and T. Teubner, The Threshold \( t\overline{t} \)cross-section at NNLL order, Phys. Rev.D 65 (2002) 014014 [hep-ph/0107144] [INSPIRE].
A. Petrelli, M. Cacciari, M. Greco, F. Maltoni and M.L. Mangano, NLO production and decay of quarkonium, Nucl. Phys.B 514 (1998) 245 [hep-ph/9707223] [INSPIRE].
K. Hagiwara, Y. Sumino and H. Yokoya, Bound-state Effects on Top Quark Production at Hadron Colliders, Phys. Lett.B 666 (2008) 71 [arXiv:0804.1014] [INSPIRE].
Y. Kiyo, J.H. Kuhn, S. Moch, M. Steinhauser and P. Uwer, Top-quark pair production near threshold at LHC, Eur. Phys. J.C 60 (2009) 375 [arXiv:0812.0919] [INSPIRE].
A.H. Hoang and C.J. Reisser, Electroweak absorptive parts in NRQCD matching conditions, Phys. Rev.D 71 (2005) 074022 [hep-ph/0412258] [INSPIRE].
Y. Kiyo, A. Pineda and A. Signer, New determination of inclusive electromagnetic decay ratios of heavy quarkonium from QCD, Nucl. Phys.B 841 (2010) 231 [arXiv:1006.2685] [INSPIRE].
J. Butterworth et al., PDF4LHC recommendations for LHC Run II, J. Phys.G 43 (2016) 023001 [arXiv:1510.03865] [INSPIRE].
S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev.D 93 (2016) 033006 [arXiv:1506.07443] [INSPIRE].
L.A. Harland-Lang, A.D. Martin, P. Motylinski and R.S. Thorne, Parton distributions in the LHC era: MMHT 2014 PDFs, Eur. Phys. J.C 75 (2015) 204 [arXiv:1412.3989] [INSPIRE].
NNPDF collaboration, Parton distributions for the LHC Run II, JHEP04 (2015) 040 [arXiv:1410.8849] [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].
J. Campbell and T. Neumann, Precision Phenomenology with MCFM, JHEP12 (2019) 034 [arXiv:1909.09117] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys.B 44 (1972) 189 [INSPIRE].
ATLAS collaboration, Electron and photon energy calibration with the ATLAS detector using LHC Run 1 data, Eur. Phys. J.C 74 (2014) 3071 [arXiv:1407.5063] [INSPIRE].
CMS collaboration, Performance of Photon Reconstruction and Identification with the CMS Detector in Proton-Proton Collisions at \( \sqrt{s} \) = 8 TeV, 2015 JINST10 P08010 [arXiv:1502.02702] [INSPIRE].
M. Jezabek and J.H. Kuhn, QCD Corrections to Semileptonic Decays of Heavy Quarks, Nucl. Phys.B 314 (1989) 1 [INSPIRE].
ATLAS collaboration, Measurement of the top-quark decay width in top-quark pair events in the dilepton channel at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, ATLAS-CONF-2019-038 (2019).
ATLAS and CMS collaborations, Top Quark Mass Measurements in ATLAS and CMS, in 12th International Workshop on Top Quark Physics (TOP2019), Beijing China (2019) [arXiv:1911.09437] [INSPIRE].
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Chen, L., Heinrich, G., Jahn, S. et al. Photon pair production in gluon fusion: top quark effects at NLO with threshold matching. J. High Energ. Phys. 2020, 115 (2020). https://doi.org/10.1007/JHEP04(2020)115
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DOI: https://doi.org/10.1007/JHEP04(2020)115