Wilson coefficients for Higgs boson production and decoupling relations to Oαs4$$ \mathcal{O}\left({\alpha}_s^4\right) $$

A bstractAn 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.

[1]  V. Ravindran,et al.  Two-loop massless QCD corrections to the g + g → H + H four-point amplitude , 2018, Journal of High Energy Physics.

[2]  Michael Spira,et al.  Effective multi-Higgs couplings to gluons , 2016, 1607.05548.

[3]  C. Anastasiou,et al.  High precision determination of the gluon fusion Higgs boson cross-section at the LHC , 2016, 1602.00695.

[4]  J. Kuhn,et al.  The $\beta$-function of Quantum Chromodynamics and the effective Higgs-gluon-gluon coupling in five-loop order , 2016 .

[5]  M. Zoller.  On the renormalization of operator products: the scalar gluonic case , 2016, 1601.08094.

[6]  J. T. Childers,et al.  Searches for heavy long-lived charged particles with the ATLAS detector in proton-proton collisions at s=8$$ \sqrt{s}=8 $$ TeV , 2014, 1411.6795.

[7]  Takahiro Ueda,et al.  FORM version 4.2 , 2017, ArXiv.

[8]  Results and techniques of multi-loop calculations , 2002, hep-ph/0201075.

[9]  Michael Spira,et al.  Soft gluon radiation in Higgs boson production at the LHC , 1996, hep-ph/9611272.

[10]  J.A.M. Vermaseren,et al.  The 4-loop quark mass anomalous dimension and the invariant quark mass , 1997, hep-ph/9703284.

[11]  R. N. Lee.  LiteRed 1.4: a powerful tool for reduction of multiloop integrals , 2013, 1310.1145.

[12]  Yasuhiro Okada,et al.  Effective gauge theory and the effect of heavy quarks in Higgs boson decays , 1983 .

[13]  Y. Schroder,et al.  High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles , 2005 .

[14]  C. Sturm,et al.  QCD decoupling at four loops , 2005, hep-ph/0512060.

[15]  B. Kniehl,et al.  Decoupling relations to O(a s 3) and their connection to low-energy theorems , 1998 .

[16]  K. Melnikov,et al.  Virtual corrections to Higgs boson pair production in the large top quark mass limit , 2014, 1408.2422.

[17]  I. Terekhov,et al.  Application of the DRA method to the calculation of the four-loop QED-type tadpoles , 2010, 1010.6117.

[18]  R. N. Lee.  Presenting LiteRed: a tool for the Loop InTEgrals REDuction , 2012, 1212.2685.

[19]  M. Steinhauser,et al.  Decoupling of heavy quarks at four loops and effective Higgs-fermion coupling , 2015, 1502.04719.

[20]  The three-loop relation between the and the pole quark masses , 1999, hep-ph/9912391.

[21]  B. Ruijl,et al.  The five-loop beta function of Yang-Mills theory with fermions , 2017, 1701.01404.

[22]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[23]  The relation between the $\bar{\rm MS}$ and the on-shell quark mass at order $\alpha_s^3$ , 1999, hep-ph/9911434.

[24]  T. V. Ritbergen,et al.  GROUP THEORY FACTORS FOR FEYNMAN DIAGRAMS , 1998, hep-ph/9802376.

[25]  M. Steinhauser,et al.  Simultaneous decoupling of bottom and charm quarks , 2011, 1107.5970.

[26]  M. Steinhauser.  MATAD: a program package for the computation of MAssive TADpoles , 2000 .

[27]  K. G. Chetyrkin.  Quark Mass Anomalous Dimension to alpha_s**4 , 1997 .

[28]  P. Nogueira.  Automatic Feynman graph generation , 1993 .

[29]  M. Steinhauser,et al.  Four-loop decoupling relations for the strong coupling , 2005, hep-ph/0512058.

[30]  A. Maier,et al.  The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge , 2017, Journal of High Energy Physics.

[31]  Gorjan Alagic,et al.  #p , 2019, Quantum information & computation.

[32]  M. Zoller.  OPE of the energy-momentum tensor correlator and the gluon condensate operator in massless QCD to three-loop order , 2014, 1407.6921.

[33]  K. Chetyrkin,et al.  Five-Loop Running of the QCD Coupling Constant. , 2016, Physical review letters.

[34]  P. Zerwas,et al.  Production of Higgs bosons in proton colliders: QCD corrections , 1991 .

[35]  T. Seidensticker.  Automatic application of successive asymptotic expansions of Feynman diagrams , 1999, hep-ph/9905298.

[36]  P. Zerwas,et al.  Production of Higgs bosons in proton colliders , 1991 .

[37]  B. Mistlberger.  Higgs boson production at hadron colliders at N3LO in QCD , 2018, Journal of High Energy Physics.

[38]  K. Chetyrkin,et al.  OPE of the energy-momentum tensor correlator in massless QCD , 2012, 1209.1516.

[39]  M. Czakon,et al.  The Four-loop QCD beta-function and anomalous dimensions , 2004, hep-ph/0411261.

[40]  A. V. Smirnov,et al.  FIRE5: A C++ implementation of Feynman Integral REduction , 2014, Comput. Phys. Commun..