Abstract
We compute the three-loop QCD corrections to the vertex function for the Yukawa coupling of a Higgs boson to a pair of bottom quarks in the limit of vanishing quark masses. This QCD form factor is a crucial ingredient to third-order QCD corrections for the production of Higgs bosons in bottom quark fusion, and for the fully differential decay rate of Higgs bosons to bottom quarks. The infrared pole structure of the form factors agrees with the prediction from infrared factorization in QCD.
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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].
C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order, Nucl. Phys. B 724 (2005) 197 [hep-ph/0501130] [INSPIRE].
M. Grazzini, NNLO predictions for the Higgs boson signal in the H → W W → ℓνℓν and H →ZZ →4ℓ decay channels, JHEP 02 (2008) 043 [arXiv:0801.3232] [INSPIRE].
S. Bühler, F. Herzog, A. Lazopoulos and R. Müller, The fully differential hadronic production of a Higgs boson via bottom quark fusion at NNLO, JHEP 07 (2012) 115 [arXiv:1204.4415] [INSPIRE].
G. Ferrera, M. Grazzini and F. Tramontano, Associated WH production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 107 (2011) 152003 [arXiv:1107.1164] [INSPIRE].
G. Ferrera, M. Grazzini and F. Tramontano, Higher-order QCD effects for associated WH production and decay at the LHC, JHEP 04 (2014) 039 [arXiv:1312.1669] [INSPIRE].
T. Figy, C. Oleari and D. Zeppenfeld, Next-to-leading order jet distributions for Higgs boson production via weak boson fusion, Phys. Rev. D 68 (2003) 073005 [hep-ph/0306109] [INSPIRE].
K. Arnold et al., VBFNLO: a parton level Monte Carlo for processes with electroweak bosons, Comput. Phys. Commun. 180 (2009) 1661 [arXiv:0811.4559] [INSPIRE].
F. Campanario, T.M. Figy, S. Plätzer and M. Sjödahl, Electroweak Higgs Boson Plus Three Jet Production at Next-to-Leading-Order QCD, Phys. Rev. Lett. 111 (2013) 211802 [arXiv:1308.2932] [INSPIRE].
W. Beenakker, S. Dittmaier, M. Krämer, B. Plumper, M. Spira and P.M. Zerwas, NLO QCD corrections to ttH production in hadron collisions, Nucl. Phys. B 653 (2003) 151 [hep-ph/0211352] [INSPIRE].
S. Dawson, C. Jackson, L.H. Orr, L. Reina and D. Wackeroth, Associated Higgs production with top quarks at the large hadron collider: NLO QCD corrections, Phys. Rev. D 68 (2003) 034022 [hep-ph/0305087] [INSPIRE].
R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, R. Pittau and P. Torrielli, Scalar and pseudoscalar Higgs production in association with a top-antitop pair, Phys. Lett. B 701 (2011) 427 [arXiv:1104.5613] [INSPIRE].
K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser, Hadronic Higgs decay to order α 4 s , Phys. Rev. Lett. 79 (1997) 353 [hep-ph/9705240] [INSPIRE].
P.A. Baikov, K.G. Chetyrkin and J.H. Kuhn, Scalar correlator at O(α 4 s ), Higgs decay into b-quarks and bounds on the light quark masses, Phys. Rev. Lett. 96 (2006) 012003 [hep-ph/0511063] [INSPIRE].
C. Anastasiou, F. Herzog and A. Lazopoulos, The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD, JHEP 03 (2012) 035 [arXiv:1110.2368] [INSPIRE].
G. Ferrera, M. Grazzini and F. Tramontano, Associated ZH production at hadron colliders: the fully differential NNLO QCD calculation, arXiv:1407.4747 [INSPIRE].
D. Dicus, T. Stelzer, Z. Sullivan and S. Willenbrock, Higgs boson production in association with bottom quarks at next-to-leading order, Phys. Rev. D 59 (1999) 094016 [hep-ph/9811492] [INSPIRE].
F. Maltoni, Z. Sullivan and S. Willenbrock, Higgs-boson production via bottom-quark fusion, Phys. Rev. D 67 (2003) 093005 [hep-ph/0301033] [INSPIRE].
R.V. Harlander and W.B. Kilgore, Higgs boson production in bottom quark fusion at next-to-next-to leading order, Phys. Rev. D 68 (2003) 013001 [hep-ph/0304035] [INSPIRE].
R.V. Harlander, A. Tripathi and M. Wiesemann, Higgs production in bottom quark annihilation: transverse momentum distribution at NNLO+NNLL, arXiv:1403.7196 [INSPIRE].
R.V. Harlander, K.J. Ozeren and M. Wiesemann, Higgs plus jet production in bottom quark annihilation at next-to-leading order, Phys. Lett. B 693 (2010) 269 [arXiv:1007.5411] [INSPIRE].
R. Harlander and M. Wiesemann, Jet-veto in bottom-quark induced Higgs production at next-to-next-to-leading order, JHEP 04 (2012) 066 [arXiv:1111.2182] [INSPIRE].
V. Ravindran, Higher-order threshold effects to inclusive processes in QCD, Nucl. Phys. B 752 (2006) 173 [hep-ph/0603041] [INSPIRE].
W. Bernreuther, R. Bonciani, T. Gehrmann, R. Heinesch, P. Mastrolia and E. Remiddi, Decays of scalar and pseudoscalar Higgs bosons into fermions: two-loop QCD corrections to the Higgs-quark-antiquark amplitude, Phys. Rev. D 72 (2005) 096002 [hep-ph/0508254] [INSPIRE].
S. Catani, The Singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
G.F. Sterman and M.E. Tejeda-Yeomans, Multiloop amplitudes and resummation, Phys. Lett. B 552 (2003) 48 [hep-ph/0210130] [INSPIRE].
S. Moch, J.A.M. Vermaseren and A. Vogt, The quark form-factor at higher orders, JHEP 08 (2005) 049 [hep-ph/0507039] [INSPIRE].
T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett. 102 (2009) 162001 [arXiv:0901.0722] [INSPIRE].
E. Gardi and L. Magnea, Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, JHEP 03 (2009) 079 [arXiv:0901.1091] [INSPIRE].
T. Ahmed, M. Mahakhud, P. Mathews, N. Rana and V. Ravindran, Two-loop QCD corrections to Higgs → b + \( \overline{b} \) + g amplitude, JHEP 08 (2014) 075 [arXiv:1405.2324] [INSPIRE].
C. Anastasiou, C. Duhr, F. Dulat and B. Mistlberger, Soft triple-real radiation for Higgs production at N3LO, JHEP 07 (2013) 003 [arXiv:1302.4379] [INSPIRE].
C. Duhr and T. Gehrmann, The two-loop soft current in dimensional regularization, Phys. Lett. B 727 (2013) 452 [arXiv:1309.4393] [INSPIRE].
Y. Li and H.X. Zhu, Single soft gluon emission at two loops, JHEP 11 (2013) 080 [arXiv:1309.4391] [INSPIRE].
C. Anastasiou, C. Duhr, F. Dulat, F. Herzog and B. Mistlberger, Real-virtual contributions to the inclusive Higgs cross-section at N 3 LO, JHEP 12 (2013) 088 [arXiv:1311.1425] [INSPIRE].
Y. Li, A. von Manteuffel, R.M. Schabinger and H.X. Zhu, N 3 LO Higgs and Drell-Yan production at threshold: the one-loop two-emission contribution, Phys. Rev. D 90 (2014) 053006 [arXiv:1404.5839] [INSPIRE].
M. Höschele, J. Hoff and T. Ueda, Adequate bases of phase space master integrals for gg → h at NNLO and beyond, JHEP 09 (2014) 116 [arXiv:1407.4049] [INSPIRE].
C. Anastasiou et al., Higgs boson gluon-fusion production at threshold in N 3 LO QCD, Phys. Lett. B 737 (2014) 325 [arXiv:1403.4616] [INSPIRE].
T. Ahmed, M. Mahakhud, N. Rana and V. Ravindran, Drell-Yan production at threshold in N 3 LO QCD, Phys. Rev. Lett. 113 (2014) 112002 [arXiv:1404.0366] [INSPIRE].
S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Threshold resummation at N 3 LL accuracy and soft-virtual cross sections at N 3 LO, arXiv:1405.4827 [INSPIRE].
P.A. Baikov, K.G. Chetyrkin, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Quark and gluon form factors to three loops, Phys. Rev. Lett. 102 (2009) 212002 [arXiv:0902.3519] [INSPIRE].
T. Gehrmann, E.W.N. Glover, T. Huber, N. Ikizlerli and C. Studerus, Calculation of the quark and gluon form factors to three loops in QCD, JHEP 06 (2010) 094 [arXiv:1004.3653] [INSPIRE].
T. Gehrmann, E.W.N. Glover, T. Huber, N. Ikizlerli and C. Studerus, The quark and gluon form factors to three loops in QCD through to O(ϵ 2), JHEP 11 (2010) 102 [arXiv:1010.4478] [INSPIRE].
W.A. Bardeen, A.J. Buras, D.W. Duke and T. Muta, Deep Inelastic Scattering Beyond the Leading Order in Asymptotically Free Gauge Theories, Phys. Rev. D 18 (1978) 3998 [INSPIRE].
D.J. Gross and F. Wilczek, Ultraviolet Behavior of Nonabelian Gauge Theories, Phys. Rev. Lett. 30 (1973) 1343 [INSPIRE].
H.D. Politzer, Reliable Perturbative Results for Strong Interactions?, Phys. Rev. Lett. 30 (1973) 1346 [INSPIRE].
W.E. Caswell, Asymptotic Behavior of Nonabelian Gauge Theories to Two Loop Order, Phys. Rev. Lett. 33 (1974) 244 [INSPIRE].
D.R.T. Jones, Two Loop Diagrams in Yang-Mills Theory, Nucl. Phys. B 75 (1974) 531 [INSPIRE].
E. Egorian and O.V. Tarasov, Two Loop Renormalization of the QCD in an Arbitrary Gauge, Teor. Mat. Fiz. 41 (1979) 26 [INSPIRE].
O.V. Tarasov, A.A. Vladimirov and A.Y. Zharkov, The Gell-Mann-Low Function of QCD in the Three Loop Approximation, Phys. Lett. B 93 (1980) 429 [INSPIRE].
S.A. Larin and J.A.M. Vermaseren, The Three loop QCD β-function and anomalous dimensions, Phys. Lett. B 303 (1993) 334 [hep-ph/9302208] [INSPIRE].
J.A.M. Vermaseren, S.A. Larin and T. van Ritbergen, The four loop quark mass anomalous dimension and the invariant quark mass, Phys. Lett. B 405 (1997) 327 [hep-ph/9703284] [INSPIRE].
K.G. Chetyrkin, Quark mass anomalous dimension to O(α 4 s ), Phys. Lett. B 404 (1997) 161 [hep-ph/9703278] [INSPIRE].
M. Czakon, The Four-loop QCD β-function and anomalous dimensions, Nucl. Phys. B 710 (2005) 485 [hep-ph/0411261] [INSPIRE].
T. Gehrmann, T. Huber and D. Maître, Two-loop quark and gluon form-factors in dimensional regularisation, Phys. Lett. B 622 (2005) 295 [hep-ph/0507061] [INSPIRE].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
K.G. Chetyrkin and F.V. Tkachov, Integration by Parts: The Algorithm to Calculate β-functions in 4 Loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [INSPIRE].
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
C. Anastasiou and A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations, JHEP 07 (2004) 046 [hep-ph/0404258] [INSPIRE].
A.V. Smirnov, Algorithm FIRE — Feynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].
C. Studerus, Reduze-Feynman Integral Reduction in C++, Comput. Phys. Commun. 181 (2010) 1293 [arXiv:0912.2546] [INSPIRE].
A. von Manteuffel and C. Studerus, Reduze 2 — Distributed Feynman Integral Reduction, arXiv:1201.4330 [INSPIRE].
T. Gehrmann, G. Heinrich, T. Huber and C. Studerus, Master integrals for massless three-loop form-factors: one-loop and two-loop insertions, Phys. Lett. B 640 (2006) 252 [hep-ph/0607185] [INSPIRE].
G. Heinrich, T. Huber and D. Maître, Master integrals for fermionic contributions to massless three-loop form-factors, Phys. Lett. B 662 (2008) 344 [arXiv:0711.3590] [INSPIRE].
G. Heinrich, T. Huber, D.A. Kosower and V.A. Smirnov, Nine-Propagator Master Integrals for Massless Three-Loop Form Factors, Phys. Lett. B 678 (2009) 359 [arXiv:0902.3512] [INSPIRE].
R.N. Lee, A.V. Smirnov and V.A. Smirnov, Analytic Results for Massless Three-Loop Form Factors, JHEP 04 (2010) 020 [arXiv:1001.2887] [INSPIRE].
T. Becher, M. Neubert and B.D. Pecjak, Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering, JHEP 01 (2007) 076 [hep-ph/0607228] [INSPIRE].
T. Becher and M. Neubert, On the Structure of Infrared Singularities of Gauge-Theory Amplitudes, JHEP 06 (2009) 081 [Erratum ibid. 1311 (2013) 024] [arXiv:0903.1126] [INSPIRE].
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Gehrmann, T., Kara, D. The \( Hb\overline{b} \) form factor to three loops in QCD. J. High Energ. Phys. 2014, 174 (2014). https://doi.org/10.1007/JHEP09(2014)174
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DOI: https://doi.org/10.1007/JHEP09(2014)174