Abstract
An important ingredient for the calculation of Higgs boson properties in the infinite top quark mass limit is the knowledge of the effective coupling between the Higgs bosons and gluons, i.e. the Wilson coefficients CH and CHH for one and two Higgs bosons, respectively. In this work we calculate for the first time CHH to four loops in a direct, diagrammatic way, discussing in detail all issues arising due to the renormalization of operator products. Furthermore, we also calculate the Wilson coefficient CH for the coupling of a single Higgs boson to gluons as well as all four loop decoupling relations in QCD with general SU(Nc) colour factors. The latter are related to CH and CHH via low-energy theorems, which are used to obtain five-loop results for the Wilson coefficients.
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References
K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser, Decoupling relations to O(α 3S ) and their connection to low-energy theorems, Nucl. Phys. B 510 (1998) 61 [hep-ph/9708255] [INSPIRE].
M. Spira, Effective Multi-Higgs Couplings to Gluons, JHEP 10 (2016) 026 [arXiv:1607.05548] [INSPIRE].
T. Inami, T. Kubota and Y. Okada, Effective Gauge Theory and the Effect of Heavy Quarks in Higgs Boson Decays, Z. Phys. C 18 (1983) 69 [INSPIRE].
A. Djouadi, M. Spira and P.M. Zerwas, Production of Higgs bosons in proton colliders: QCD corrections, Phys. Lett. B 264 (1991) 440 [INSPIRE].
K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser, Hadronic Higgs decay to order α 4S , Phys. Rev. Lett. 79 (1997) 353 [hep-ph/9705240] [INSPIRE].
M. Steinhauser, Results and techniques of multiloop calculations, Phys. Rept. 364 (2002) 247 [hep-ph/0201075] [INSPIRE].
M. Krämer, E. Laenen and M. Spira, Soft gluon radiation in Higgs boson production at the LHC, Nucl. Phys. B 511 (1998) 523 [hep-ph/9611272] [INSPIRE].
T. van Ritbergen, J.A.M. Vermaseren and S.A. Larin, The Four loop β-function in quantum chromodynamics, Phys. Lett. B 400 (1997) 379 [hep-ph/9701390] [INSPIRE].
M. Czakon, The Four-loop QCD β-function and anomalous dimensions, Nucl. Phys. B 710 (2005) 485 [hep-ph/0411261] [INSPIRE].
Y. Schröder and M. Steinhauser, Four-loop decoupling relations for the strong coupling, JHEP 01 (2006) 051 [hep-ph/0512058] [INSPIRE].
K.G. Chetyrkin, J.H. Kuhn and C. Sturm, QCD decoupling at four loops, Nucl. Phys. B 744 (2006) 121 [hep-ph/0512060] [INSPIRE].
K. Chetyrkin, P. Baikov and J. Kühn, Multiloop Renormalization Group: new results, PoS(LL2016)010.
P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Five-Loop Running of the QCD coupling constant, Phys. Rev. Lett. 118 (2017) 082002 [arXiv:1606.08659] [INSPIRE].
F. Herzog, B. Ruijl, T. Ueda, J.A.M. Vermaseren and A. Vogt, The five-loop β-function of Yang-Mills theory with fermions, JHEP 02 (2017) 090 [arXiv:1701.01404] [INSPIRE].
T. Luthe, A. Maier, P. Marquard and Y. Schröder, The five-loop β-function for a general gauge group and anomalous dimensions beyond Feynman gauge, JHEP 10 (2017) 166 [arXiv:1709.07718] [INSPIRE].
J. Grigo, K. Melnikov and M. Steinhauser, Virtual corrections to Higgs boson pair production in the large top quark mass limit, Nucl. Phys. B 888 (2014) 17 [arXiv:1408.2422] [INSPIRE].
K.G. Chetyrkin, Four-loop renormalization of QCD: Full set of renormalization constants and anomalous dimensions, Nucl. Phys. B 710 (2005) 499 [hep-ph/0405193] [INSPIRE].
K.G. Chetyrkin and M. Steinhauser, Short distance mass of a heavy quark at order α 3s , Phys. Rev. Lett. 83 (1999) 4001 [hep-ph/9907509] [INSPIRE].
K.G. Chetyrkin and M. Steinhauser, The Relation between the MS-bar and the on-shell quark mass at order α 3s , Nucl. Phys. B 573 (2000) 617 [hep-ph/9911434] [INSPIRE].
K. Melnikov and T.v. Ritbergen, The Three loop relation between the MS-bar and the pole quark masses, Phys. Lett. B 482 (2000) 99 [hep-ph/9912391] [INSPIRE].
P. Marquard, L. Mihaila, J.H. Piclum and M. Steinhauser, Relation between the pole and the minimally subtracted mass in dimensional regularization and dimensional reduction to three-loop order, Nucl. Phys. B 773 (2007) 1 [hep-ph/0702185] [INSPIRE].
K.G. Chetyrkin, Quark mass anomalous dimension to O(α 4S ), Phys. Lett. B 404 (1997) 161 [hep-ph/9703278] [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].
A.G. Grozin et al., Simultaneous decoupling of bottom and charm quarks, JHEP 09 (2011) 066 [arXiv:1107.5970] [INSPIRE].
V.P. Spiridonov, Anomalous Dimension of G 2μν and β Function, IYaI-P-0378 [INSPIRE].
M.F. Zoller, On the renormalization of operator products: the scalar gluonic case, JHEP 04 (2016) 165 [arXiv:1601.08094] [INSPIRE].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
R. Harlander, T. Seidensticker and M. Steinhauser, Corrections of O(αα s) to the decay of the Z boson into bottom quarks, Phys. Lett. B 426 (1998) 125 [hep-ph/9712228] [INSPIRE].
T. Seidensticker, Automatic application of successive asymptotic expansions of Feynman diagrams, in 6th International Workshop on New Computing Techniques in Physics Research: Software Engineering, Artificial Intelligence Neural Nets, Genetic Algorithms, Symbolic Algebra, Automatic Calculation (AIHENP 99), Heraklion, Crete, Greece, April 12–16, 1999 (1999) [hep-ph/9905298] [INSPIRE].
B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE].
T. van Ritbergen, A.N. Schellekens and J.A.M. Vermaseren, Group theory factors for Feynman diagrams, Int. J. Mod. Phys. A 14 (1999) 41 [hep-ph/9802376] [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
A.V. Smirnov, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun. 189 (2015) 182 [arXiv:1408.2372] [INSPIRE].
R.N. Lee and I.S. Terekhov, Application of the DRA method to the calculation of the four-loop QED-type tadpoles, JHEP 01 (2011) 068 [arXiv:1010.6117] [INSPIRE].
Y. Schröder and A. Vuorinen, High-precision ϵ-expansions of single-mass-scale four-loop vacuum bubbles, JHEP 06 (2005) 051 [hep-ph/0503209] [INSPIRE].
K.G. Chetyrkin, M. Faisst, C. Sturm and M. Tentyukov, epsilon-finite basis of master integrals for the integration-by-parts method, Nucl. Phys. B 742 (2006) 208 [hep-ph/0601165] [INSPIRE].
R.N. Lee, private communication.
M. Steinhauser, MATAD: A Program package for the computation of MAssive TADpoles, Comput. Phys. Commun. 134 (2001) 335 [hep-ph/0009029] [INSPIRE].
T. Liu and M. Steinhauser, Decoupling of heavy quarks at four loops and effective Higgs-fermion coupling, Phys. Lett. B 746 (2015) 330 [arXiv:1502.04719] [INSPIRE].
M.F. Zoller and K.G. Chetyrkin, OPE of the energy-momentum tensor correlator in massless QCD, JHEP 12 (2012) 119 [arXiv:1209.1516] [INSPIRE].
M.F. Zoller, OPE of the energy-momentum tensor correlator and the gluon condensate operator in massless QCD to three-loop order, JHEP 10 (2014) 169 [arXiv:1407.6921] [INSPIRE].
C. Anastasiou et al., High precision determination of the gluon fusion Higgs boson cross-section at the LHC, JHEP 05 (2016) 058 [arXiv:1602.00695] [INSPIRE].
B. Mistlberger, Higgs boson production at hadron colliders at N 3 LO in QCD, JHEP 05 (2018) 028 [arXiv:1802.00833] [INSPIRE].
P. Banerjee, S. Borowka, P.K. Dhani, T. Gehrmann and V. Ravindran, Two-loop massless QCD corrections to the g + g → H + H four-point amplitude, submitted to JHEP (2018) [arXiv:1809.05388] [INSPIRE].
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Gerlach, M., Herren, F. & Steinhauser, M. Wilson coefficients for Higgs boson production and decoupling relations to \( \mathcal{O}\left({\alpha}_s^4\right) \). J. High Energ. Phys. 2018, 141 (2018). https://doi.org/10.1007/JHEP11(2018)141
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DOI: https://doi.org/10.1007/JHEP11(2018)141