Perturbative QCD Calculations of Total Cross Sections and Decay Widths in Hard Inclusive Processes

Abstract

A summary of the current understanding of methods of analytical higher order perturbative computations of total cross sections and decay widths in Quantum Chromodynamics is presented. As examples, the total cross section in electron positron annihilation, the hadronic decay rates of the tau lepton and Higgs boson up to O(α_s^2) and O(α_s^3) are considered. The evaluation of the four-loop QED β- function at an intermediate step of the calculation is briefly described. The problem of renormalization group ambiguity of perturbative results is considered and some of the existing prescriptions are discussed. The problem of estimation of theoretical uncertainty in perturbative calculations is briefly discussed.

83 pages, LaTeX, Reviews of Modern Physics style, 14 figures plus figural equations (not included). Hard copy available upon request at [email protected]. To be published in Reviews of Modern Physics

References in corpus (33)

• The renormalization of the axial anomaly in dimensional regularization
• Commensurate Scale Relations in Quantum Chromodynamics
• Renormalization group analysis of the tau-lepton decay within QCD
• Optimization of R(e+e-) and "Freezing" of the QCD Couplant at Low Energies
• Comparison of the Pade Approximation Method to Perturbative QCD Calculations
• Second Order QCD Corrections to Scalar and Pseudoscalar Higgs Decays into Massive Bottom Quarks
• Two-Loop Gluon-Condensate Contributions To Heavy-Quark Current Correlators: Exact Results And Approximations
• Pade Approximants, Borel Transforms and Renormalons: the Bjorken Sum Rule as a Case Study
• Quark Mass Effects in Fermionic Decays of the Higgs Boson in $O({\alpha }_s^2)$ Perturbative QCD
• QCD Matching Conditions at Thresholds
• QCD Perturbation Theory at Low Energies
• Analytical on-shell QED results: 3-loop vacuum polarization, 4-loop beta-function and the muon anomaly
• Large-order perturbation theory for the electromagnetic current-current correlation function
• Mass Corrections to the Tau Decay Rate
• Euclidean asymptotic expansions of Green functions of quantum fields (I) Expansions of products of singular functions
• Radiation of Heavy Quarks
• Renormalon Singularities of the QCD Vacuum Polarization Function to Leading Order in $1/N_f$
• Euclidean asymptotic expansions of Green functions of quantum fields (II) Combinatorics of the asymptotic operation
• The limit $m_q\to 0$ of perturbative QCD
• Small-Size Instanton Corrections to the $\tau$ Hadronic Width
• Renormalization Scheme Dependence and the Problem of Theoretical Uncertainties in Next-Next-to-Leading Order QCD Predictions
• Two-Loop $\mathcal{O}({\alpha }_s^2)$ Correction to the $H\to b\bar{b}$ Decay Rate Induced by the Top Quark
• Minimal Supersymmetric Higgs Boson Decay Rate in O(α_s^2) Perturbative QCD
• Status of Higher-Order Corrections in the Standard Electroweak Theory
• Alpha_s from Tau Decays
• Top Quark Contribution to Hadronic Decays of the Z-Boson at Alpha_s^2 in QCD
• Quark Mass Corrections to the Z Boson Decay Rates
• The Standard Model of Electroweak Interactions
• On the Self-Consistency of Scale-Setting Methods
• On Instanton Contributions to the tau Hadronic Width
• The Standard Model of Electroweak Interactions
• Standard Model of the Electroweak Interaction: Theoretical Developments
• Commensurate Scale Relations: Precise Tests of Quantum Chromodynamics without Scale or Scheme Ambiguity

Cited by in corpus (9)

• Resummation for QCD Hard Scattering
• Determination of the QCD Coupling ${\alpha }_s$
• Recent Progress in QCD Condensate Evaluations and Sum Rules
• Constraining the strangeness content of the nucleon by measuring the $\varphi$ meson mass shift in nuclear matter
• Phi meson spectral moments and QCD condensates in nuclear matter
• Precision Physics at LEP
• On the QCD perturbative expansion for e^+ e^- --> hadrons
• Light Gluino Contribution in Hadronic Decays of Z boson and tau lepton to O(alpha_s^3)
• Running electromagnetic coupling constant: low energy normalization and the value at M_Z