Abstract
The ambiguity in the choice of a renormalization scheme and scale for the top-quark mass leads to an additional source of theoretical uncertainty in the calculation of the Higgs boson production cross section via gluon fusion. These uncertainties were found to be dominant in the case of off-shell Higgs production at next-to-leading order in QCD for large values of the Higgs virtuality \( {m}_H^{\ast } \). In this work, we study the uncertainties related to the top-quark mass definition up to next-to-next-to-leading order (NNLO) in QCD. We include the full top-quark mass dependence up to three loops in the virtual corrections, and evaluate the real contributions in the soft limit, therefore obtaining the so-called soft-virtual (SV) approximation. We construct NNLOSV predictions for off-shell Higgs boson production renormalizing the top-quark mass within both the on-shell (OS) and the \( \overline{\mathrm{MS}} \) schemes, and study in detail the differences between them. While the differences between the two schemes are sizeable, we find that the predictions are always compatible within scale uncertainties. We also observe that the difference between renormalization schemes is largely reduced when increasing the order of the perturbative expansion. We analyze the quality of the convergence of the perturbative series in both schemes, and find that at large invariant masses the \( \overline{\mathrm{MS}} \) results present much larger corrections than their OS counterparts. We also comment on the more complicated case of Higgs boson pair production.
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F. Englert and R. Brout, Broken symmetry and the mass of gauge vector mesons, Phys. Rev. Lett. 13 (1964) 321 [INSPIRE].
P.W. Higgs, Broken symmetries, massless particles and gauge fields, Phys. Lett. 12 (1964) 132 [INSPIRE].
P.W. Higgs, Broken symmetries and the masses of gauge bosons, Phys. Rev. Lett. 13 (1964) 508 [INSPIRE].
G.S. Guralnik, C.R. Hagen and T.W.B. Kibble, Global conservation laws and massless particles, Phys. Rev. Lett. 13 (1964) 585 [INSPIRE].
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
F. Caola and K. Melnikov, Constraining the Higgs boson width with ZZ production at the LHC, Phys. Rev. D 88 (2013) 054024 [arXiv:1307.4935] [INSPIRE].
ATLAS collaboration, Constraints on off-shell Higgs boson production and the Higgs boson total width in ZZ → 4ℓ and ZZ → 2ℓ2ν final states with the ATLAS detector, Phys. Lett. B 786 (2018) 223 [arXiv:1808.01191] [INSPIRE].
CMS collaboration, Measurements of the Higgs boson width and anomalous HVV couplings from on-shell and off-shell production in the four-lepton final state, Phys. Rev. D 99 (2019) 112003 [arXiv:1901.00174] [INSPIRE].
J. Alison et al., Higgs boson potential at colliders: status and perspectives, Rev. Phys. 5 (2020) 100045 [arXiv:1910.00012] [INSPIRE].
D. Graudenz, M. Spira and P.M. Zerwas, QCD corrections to Higgs boson production at proton proton colliders, Phys. Rev. Lett. 70 (1993) 1372 [INSPIRE].
M. Spira, A. Djouadi, D. Graudenz and P.M. Zerwas, Higgs boson production at the LHC, Nucl. Phys. B 453 (1995) 17 [hep-ph/9504378] [INSPIRE].
M. Czakon, R.V. Harlander, J. Klappert and M. Niggetiedt, Exact top-quark mass dependence in hadronic Higgs production, Phys. Rev. Lett. 127 (2021) 162002 [arXiv:2105.04436] [INSPIRE].
C. Anastasiou, C. Duhr, F. Dulat, F. Herzog and B. Mistlberger, Higgs boson gluon-fusion production in QCD at three loops, Phys. Rev. Lett. 114 (2015) 212001 [arXiv:1503.06056] [INSPIRE].
B. Mistlberger, Higgs boson production at hadron colliders at N3LO in QCD, JHEP 05 (2018) 028 [arXiv:1802.00833] [INSPIRE].
M. Bonvini and S. Marzani, Resummed Higgs cross section at N3LL, JHEP 09 (2014) 007 [arXiv:1405.3654] [INSPIRE].
T. Schmidt and M. Spira, Higgs boson production via gluon fusion: soft-gluon resummation including mass effects, Phys. Rev. D 93 (2016) 014022 [arXiv:1509.00195] [INSPIRE].
G. Das, S. Moch and A. Vogt, Approximate four-loop QCD corrections to the Higgs-boson production cross section, Phys. Lett. B 807 (2020) 135546 [arXiv:2004.00563] [INSPIRE].
A.H. Ajjath, P. Mukherjee, V. Ravindran, A. Sankar and S. Tiwari, Resummed Higgs boson cross section at next-to SV to NNLO + \( \overline{\mathrm{NNLL}} \), Eur. Phys. J. C 82 (2022) 774 [arXiv:2109.12657] [INSPIRE].
J. Baglio, F. Campanario, S. Glaus, M. Mühlleitner, M. Spira and J. Streicher, Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme, Eur. Phys. J. C 79 (2019) 459 [arXiv:1811.05692] [INSPIRE].
J. Baglio et al., Higgs-pair production via gluon fusion at hadron colliders: NLO QCD corrections, JHEP 04 (2020) 181 [arXiv:2003.03227] [INSPIRE].
S. Amoroso et al., Les Houches 2019. Physics at TeV colliders: Standard Model working group report, in 11th Les Houches workshop on physics at TeV colliders: PhysTeV Les Houches, (2020) [arXiv:2003.01700] [INSPIRE].
M.L. Czakon and M. Niggetiedt, Exact quark-mass dependence of the Higgs-gluon form factor at three loops in QCD, JHEP 05 (2020) 149 [arXiv:2001.03008] [INSPIRE].
F. Dulat, A. Lazopoulos and B. Mistlberger, iHixs 2 — inclusive Higgs cross sections, Comput. Phys. Commun. 233 (2018) 243 [arXiv:1802.00827] [INSPIRE].
M. Spira, HIGLU and HDECAY: programs for Higgs boson production at the LHC and Higgs boson decay widths, Nucl. Instrum. Meth. A 389 (1997) 357 [hep-ph/9610350] [INSPIRE].
D. de Florian and J. Mazzitelli, A next-to-next-to-leading order calculation of soft-virtual cross sections, JHEP 12 (2012) 088 [arXiv:1209.0673] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Threshold resummation at N3LL accuracy and soft-virtual cross sections at N3LO, Nucl. Phys. B 888 (2014) 75 [arXiv:1405.4827] [INSPIRE].
S. Catani, D. de Florian and M. Grazzini, Higgs production in hadron collisions: soft and virtual QCD corrections at NNLO, JHEP 05 (2001) 025 [hep-ph/0102227] [INSPIRE].
N. Gray, D.J. Broadhurst, W. Grafe and K. Schilcher, Three loop relation of quark (modified) \( \overline{\mathrm{MS}} \) and pole masses, Z. Phys. C 48 (1990) 673 [INSPIRE].
J. Fleischer, F. Jegerlehner, O.V. Tarasov and O.L. Veretin, Two loop QCD corrections of the massive fermion propagator, Nucl. Phys. B 539 (1999) 671 [Erratum ibid. 571 (2000) 511] [hep-ph/9803493] [INSPIRE].
S. Catani, S. Devoto, M. Grazzini, S. Kallweit and J. Mazzitelli, Top-quark pair hadroproduction at NNLO: differential predictions with the \( \overline{\mathrm{MS}} \) mass, JHEP 08 (2020) 027 [arXiv:2005.00557] [INSPIRE].
J. Butterworth et al., PDF4LHC recommendations for LHC run II, J. Phys. G 43 (2016) 023001 [arXiv:1510.03865] [INSPIRE].
M. Dowling and S.-O. Moch, Differential distributions for top-quark hadro-production with a running mass, Eur. Phys. J. C 74 (2014) 3167 [arXiv:1305.6422] [INSPIRE].
T. Liu and A.A. Penin, High-energy limit of QCD beyond the Sudakov approximation, Phys. Rev. Lett. 119 (2017) 262001 [arXiv:1709.01092] [INSPIRE].
T. Liu and A. Penin, High-energy limit of mass-suppressed amplitudes in gauge theories, JHEP 11 (2018) 158 [arXiv:1809.04950] [INSPIRE].
C. Anastasiou and A. Penin, Light quark mediated Higgs boson threshold production in the next-to-leading logarithmic approximation, JHEP 07 (2020) 195 [Erratum ibid. 01 (2021) 164] [arXiv:2004.03602] [INSPIRE].
J. Baglio, F. Campanario, S. Glaus, M. Mühlleitner, J. Ronca and M. Spira, gg → HH: combined uncertainties, Phys. Rev. D 103 (2021) 056002 [arXiv:2008.11626] [INSPIRE].
S. Borowka et al., Higgs boson pair production in gluon fusion at next-to-leading order with full top-quark mass dependence, Phys. Rev. Lett. 117 (2016) 012001 [Erratum ibid. 117 (2016) 079901] [arXiv:1604.06447] [INSPIRE].
M. Grazzini et al., Higgs boson pair production at NNLO with top quark mass effects, JHEP 05 (2018) 059 [arXiv:1803.02463] [INSPIRE].
J. Davies, G. Mishima, M. Steinhauser and D. Wellmann, Double Higgs boson production at NLO in the high-energy limit: complete analytic results, JHEP 01 (2019) 176 [arXiv:1811.05489] [INSPIRE].
L. Chen et al., ZH production in gluon fusion at NLO in QCD, JHEP 08 (2022) 056 [arXiv:2204.05225] [INSPIRE].
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Mazzitelli, J. NNLO study of top-quark mass renormalization scheme uncertainties in Higgs boson production. J. High Energ. Phys. 2022, 65 (2022). https://doi.org/10.1007/JHEP09(2022)065
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DOI: https://doi.org/10.1007/JHEP09(2022)065