Results and Techniques of Multi-Loop Calculations

Abstract

In this review some recent multi-loop results obtained in the framework of perturbative Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED) are discussed. After reviewing the most advanced techniques used for the computation of renormalization group functions, we consider the decoupling of heavy quarks. In particular, an effective method for the evaluation of the decoupling constants is presented and explicit results are given. Furthermore the connection to observables involving a scalar Higgs boson is worked out in detail. We review the radiative corrections of a Higgs boson into gluons and quarks and present explicit results up to order ${\alpha }_s^4$ and ${\alpha }_s^3$, respectively. In this review special emphasis is put on the applications of asymptotic expansions. A method is described which combines expansion terms of different kinematical regions with the help of conformal mapping and Padé approximation. This method allows us to proceed beyond the present scope of exact multi-loop calculations. As far as physical processes are concerned, we review the computation of three-loop current correlators in QCD taking into account the full mass-dependence. In a further application four-loop diagrams are considered which contribute to the order ${\alpha }^2$ QED corrections to the $\mu$ decay. Finally the calculation of the three-loop relation between the $\overline{\mathrm{MS}}$ and on-shell quark mass definitions is presented. To complete the presentation, some technical details are presented in the Appendix, where also explicit analytical results are listed.

125 pages, to appear in Physics Reports, eqs. (4.11), (4.77), (4.79) and (C.3) corrected, references and note added

References in corpus (4)

• Higgs production in hadron collisions: soft and virtual QCD corrections at NNLO
• Soft and virtual corrections to pp -> H + X at NNLO
• Heavy-light current correlators at order ${\alpha }_s^2$ in QCD and HQET
• Semileptonic b --> u decays: lepton invariant mass spectrum

Cited by in corpus (65)

• Higgs boson production in bottom quark fusion at next-to-next-to-leading order
• Four-Loop Decoupling Relations for the Strong Coupling
• Dark Matter through the Higgs portal
• Finite top quark mass effects in NNLO Higgs boson production at LHC
• Infrared singularities of QCD amplitudes with massive partons
• Numerical evaluation of multi-loop integrals by sector decomposition
• Top mass effects in Higgs production at next-to-next-to-leading order QCD: virtual corrections
• Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Four-Particle Phase Space Integrals in Massless QCD
• Virtual corrections to Higgs boson pair production in the large top quark mass limit
• From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions
• The Hunt for New Physics at the Large Hadron Collider
• Three-loop matching of the dipole operators for b -> s gamma and b -> s g
• Virtual three-loop corrections to Higgs boson production in gluon fusion for finite top quark mass
• Five-loop renormalisation of QCD in covariant gauges
• All-Purpose Numerical Evaluation of One-Loop Multi-Leg Feynman Diagrams
• Rhad: A program for the evaluation of the hadronic R-ratio in the perturbative regime of QCD
• Infrared regularization for spin-1 fields
• High-precision e-expansions of massive four-loop vacuum bubbles
• Hadronic Higgs Production and Decay in Supersymmetry at Next-to-Leading Order
• Supersymmetric Higgs production in gluon fusion at next-to-leading order
• ep-Finite Basis of Master Integrals for the Integration-By-Parts Method
• Towards $B\to V\gamma$ Decays at NNLO in SCET
• Heavy Quarkonium Spectrum and Production/Annihilation Rates to order ${\beta }_0^3{\alpha }_s^3$
• Higgs Decay to Gluons at NNLO
• Wilson coefficients for Higgs boson production and decoupling relations to $\mathcal{O}\left({\alpha }_s^4\right)$
• Precision Calculations in Supersymmetric Theories
• Heavy-to-light decays with a two-loop accuracy
• NNLO corrections to B --> X_u l nu in the shape-function region
• Solving Recurrence Relations for Multi-Loop Feynman Integrals
• The NNLO gluon fusion Higgs production cross-section with many heavy quarks
• Perturbative Renormalization of Neutron-Antineutron Operators
• Two-loop matching coefficients for the strong coupling in the MSSM
• The SUSY-QCD beta function to three loops
• Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals
• Matching coefficients for alpha_s and m_b to O(alpha_s^2) in the MSSM
• Gluon-fusion Higgs production at NNLO for a non-standard Higgs sector
• The Higgs boson inclusive decay channels $H\to b\bar{b}$ and $H\to gg$ up to four-loop level
• Color-octet scalar effects on Higgs boson production in gluon fusion
• Heavy-quark vacuum polarization: first two moments of the O(alphas^3 nf^2) contribution
• Towards Higgs boson production in gluon fusion to NNLO in the MSSM
• Two-loop amplitudes for Higgs plus jet production involving a modified trilinear Higgs coupling
• Higgs production at NNLO in QCD: the VBF channel
• Study of the 125 GeV Standard Model Higgs Boson Partial Widths and Branching Fractions
• Determination of the strong coupling constant from the CLEO measurement of the total hadronic cross section in $e^{+}{e}^{-}$ annihilation below 10.56 GeV
• Strong-Coupling Constant at Three Loops in Momentum Subtraction Scheme
• O(α_s^2) corrections to the running top-Yukawa coupling and the mass of the lightest Higgs boson in the MSSM
• Recent Progress in Perturbative Quantum Field Theory
• New prospects for the numerical calculation of Mellin-Barnes integrals in Minkowskian kinematics
• Two-loop matching of renormalizable operators: general considerations and applications
• Five-loop vacuum polarization in pQCD: O(m_q^2α_s^4 n_f^2) contribution
• Thermal width of the Higgs boson in hot QCD matter
• On the QCD corrections to Vainshtein's theorem for VVA correlator
• Two-Loop Vacuum Diagrams in Background Field and Heisenberg-Euler Effective Action
• On the electroweak contribution to the matching of the strong coupling constant in the SM
• Precision unification and Higgsino dark matter in GUT scale supersymmetry
• Analytic two-loop amplitudes for $tW$ production: leading color and light fermion-loop contributions
• Two-Loop Diagrammatics in a Self-Dual Background
• "Background Field Integration-by-Parts" and the Connection Between One-Loop and Two-Loop Heisenberg-Euler Effective Actions
• Sextic tensor model in rank $3$ at next-to-leading order
• Higgs Decay, Z Decay and the QCD Beta-Function
• Precise predictions for Higgs production in models with color-octet scalars
• $(Z\alpha {)}^4$ order of the polarization operator in Coulomb field at low energy
• Towards a Two-Loop Matching of Gauge Couplings in Grand Unified Theories