A Prediction for the 4-Loop βFunction

Abstract

We predict that the four-loop contribution β_3 to the QCD βfunction in the MS-bar prescription is given by β_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where N_f is the number of flavours and the coefficient of N_f^3 is an exact result from large-N_f expansion. In the phenomenologically-interesting case N_f=3, we estimate β_3 = (7.6 \pm 0.1) x 10^3. We discuss our estimates of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) Φ^4 theory, and on variations in the details of our estimation method, which goes beyond conventional Pade approximants by estimating and correcting for subasymptotic deviations from exact results.

11 pages, LaTeX, including 2 figures in 3 ps files; requires epsfig.sty; added comparison with recent exact results

References in corpus (1)

• Renormalization-Scheme Dependence of Pade Summation in QCD

Cited by in corpus (41)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions
• Higher twists and ${\alpha }_s(M_Z)$ extractions from the NNLO QCD analysis of the CCFR data for $x{F}_3$ structure function
• The connection between the DRED and NSVZ renormalisation schemes
• Asymptotic Pade Approximant Predictions: up to Five Loops in QCD and SQCD
• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• Relations between Observables and the Infrared Fixed-Point in QCD
• Bilocal expansion of the Borel amplitude and the hadronic tau decay width
• Pade-Improvement of QCD Running Coupling Constants, Running Masses, Higgs Decay Rates, and Scalar Channel Sum Rules
• QCD vacuum condensates from tau-lepton decay data
• RG/Pade Estimate of the Three-Loop Contribution to the QCD Static Potential Function
• Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by Č\'ıžek, Zamastil, and Skála. I. Algebraic Theory
• Prediction Properties of Aitken's Iterated Delta^2 Process, of Wynn's Epsilon Algorithm, and of Brezinski's Iterated Theta Algorithm
• Asymptotic Pade-Approximant Methods and QCD Current Correlation Functions
• Extending the Predictive Power of Perturbative QCD
• Is there evidence for dimension-two corrections in QCD two-point functions?
• Quark mass anomalous dimension at O(1/N_f^2) in QCD
• Is Radiative Electroweak Symmetry Breaking Consistent with a 125 GeV Higgs Mass?
• Asymptotic Improvement of Resummation and Perturbative Predictions in Quantum Field Theory
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• HHH Whitepaper
• Pade-Improved Extraction of ${\alpha }_s(M_{\tau })$ from $R_{\tau }$
• Scale- and scheme-independent extension of Pade approximants; Bjorken polarized sum rule as an example
• Asymptotic Pade-Approximant Predictions for Renormalization-Group Functions of Massive ${\varphi }^4$ Scalar Field Theory
• Estimate of the Three-Loop Perturbative Contribution to Inclusive Semileptonic b to u Decays
• Pade-Improved Estimates of Hadronic Higgs Decay Rates
• $\beta$-functions in large-$N_f$ supersymmetric gauge theories
• New high order relations between physical observables in perturbative QCD
• The QCD Static Energy using Optimal Renormalization and Asymptotic Padé-approximant Methods
• Ratio of strange to non-strange quark condensates in QCD
• The heavy quarkonium inclusive decays using the principle of maximum conformality
• Nonperturbative Contributions in an Analytic Running Coupling of QCD
• Renormalization-Scale Invariance, Minimal Sensitivity, and the Inclusive Hadronic Decays of a 115 GeV Higgs Particle
• Pade Estimate of QCD's Infrared Boundary
• Estimate of the Three-Loop MS bar Contribution to sigma(W_L^+ W_L^- --> Z_L Z_L)
• Three Loop Estimate of the Inclusive Semileptonic $b\to c$ Decay Rate
• Renormalization-group improved Higgs to two gluons decay rate
• Constraints on Higher-Order Perturbative Corrections in $b\to u$ Semileptonic Decays from Residual Renormalization-Scale Dependence
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• Pade-Improved Estimate of Perturbative Contributions to Inclusive Semileptonic $b\to u$ Decays
• Spiral Multi-component Structure in Pade - Approximant QCD