$O(\alpha {\alpha }_s^2)$ correction to the electroweak $\rho$ parameter

Abstract

The three-loop QCD contributions to the vacuum polarization functions of the $Z$ and $W$ bosons at zero momentum are calculated. The top quark is considered to be massive and the other quarks massless. Using these results, we calculate the correction to the electroweak $\rho$ parameter. All computations are done in the framework of dimensional regularization as well as regularization by dimensional reduction. We use recurrence relations obtained by the method of integration by parts to reduce all integrals to a small set of master integrals. A comparison of the two-loop and three-loop QCD corrections to the $\rho$ parameter is performed.

9 pages, LaTeX. This is the corrected version with $\zeta (4)$ coefficient fixed

References in corpus (3)

• The three-loop QCD $\beta$-function and anomalous dimensions
• The renormalization of the axial anomaly in dimensional regularization
• Radiative Correction Effects of a Very Heavy Top

Cited by in corpus (153)

• Precision Corrections in the Minimal Supersymmetric Standard Model
• SuSpect: a Fortran Code for the Supersymmetric and Higgs Particle Spectrum in the MSSM
• The global electroweak fit at NNLO and prospects for the LHC and ILC
• Connection between Feynman integrals having different values of the space-time dimension
• Update of the global electroweak fit and constraints on two-Higgs-doublet models
• Precise Prediction for the W-Boson Mass in the Standard Model
• The relation between the $\overline{\mathrm{MS}}$ and the on-shell quark mass at order ${\alpha }_s^3$
• Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
• Electroweak Radiative Corrections to Neutral-Current Drell-Yan Processes at Hadron Colliders
• Electroweak Precision Observables in the Minimal Supersymmetric Standard Model
• ZFITTER v.6.21 - A Semi-Analytical Program for Fermion Pair Production in e+e- Annihilation
• Hadronic vacuum polarization: $(g-2{)}_{\mu }$ versus global electroweak fits
• QCD Corrections to the $e^{+}{e}^{-}$ Cross Section and the $Z$ Boson Decay Rate
• MATAD: a program package for the computation of MAssive TADpoles
• Mellin Moments of the {$O({\alpha }_s^3$)} Heavy Flavor Contributions to unpolarized Deep-Inelastic Scattering at $Q^2\gg m^2$ and Anomalous Dimensions
• Explicit solutions of the 3--loop vacuum integral recurrence relations
• Precise Prediction for M_W in the MSSM
• Physics at the e+ e- Linear Collider
• ZFITTER: a semi-analytical program for fermion pair production in e+e- annihilation, from version 6.21 to version 6.42
• Mass Bounds on a Very Light Neutralino
• Corrections of order ${\cal O}(G_F M_t^2 \as^2)$ to the $\rho$ parameter
• Delta r and the W-boson mass in the Singlet Extension of the Standard Model
• Precise calculation of MW, sin^2 theta_MSbar, and sin^2 theta_eff
• Electroweak two-loop corrections to the MW-MZ mass correlation in the Standard Model
• Electroweak two-loop corrections to the effective weak mixing angle
• QCD Corrections from Top Quark to Relations between Electroweak Parameters to Order ${\alpha }_s^2$
• Complete fermionic two-loop results for the M_W-M_Z interdependence
• Three Loop Top Quark Contributions to the rho Parameter
• The Weak Charge of the Proton and New Physics
• Global Fit to Modified Neutrino Couplings and the Cabibbo-Angle Anomaly
• $\text{HEPfit}$: a Code for the Combination of Indirect and Direct Constraints on High Energy Physics Models
• Four-Loop Singlet Contribution to the $\rho$ Parameter
• Single Scale Tadpoles and O(GF mt^2 as^3) Corrections to the rho Parameter
• Higher-order electroweak corrections to the partial widths and branching ratios of the Z boson
• Supersymmetric contributions to electroweak precision observables: QCD corrections
• Four-Loop QCD Corrections to the Rho Parameter
• Results and Techniques of Multi-Loop Calculations
• Leading QCD Corrections to Scalar Quark Contributions to Electroweak Precision Observables
• Complete Two Loop Electroweak Contributions to the Muon Lifetime in the Standard Model
• Electroweak Precision Fit and New Physics in light of $W$ Boson Mass
• Indirect Sensitivities to the Scale of Supersymmetry
• Complete electroweak two-loop corrections to Z boson production and decay
• Pole masses of quarks in dimensional reduction
• Impact of the recent measurements of the top-quark and W-boson masses on electroweak precision fits
• Indirect probes of the trilinear Higgs coupling: $gg\to h$ and $h\to \gamma \gamma$
• MS vs. Pole Masses of Gauge Bosons: Electroweak Bosonic Two-Loop Corrections
• Three-Loop Leading Top Mass Contributions to the rho Parameter
• Explicit results for all orders of the epsilon-expansion of certain massive and massless diagrams
• The two-loop electroweak bosonic corrections to ${\sin }^2{\theta }_{\mathrm{eff}}^{\mathrm{b}}$
• A magic connection between massive and massless diagrams
• Global analysis of electroweak data in the Standard Model
• Automatic Computation of Feynman Diagrams
• On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order
• Two-loop heavy top corrections to the Z boson partial widths
• Recurrence Relations for Three-Loop Prototypes of Bubble Diagrams with a Mass
• Three-Loop O(alpha_s^2 G_F M_t^2) Corrections to Hadronic Higgs Decays
• Z Pole Observables in the MSSM
• Electroweak Precision Tests of the Standard Model after the Discovery of the Higgs Boson
• Radiative Corrections in Precision Electroweak Physics: a Historical Perspective
• Leading Electroweak Two-Loop Corrections to Precision Observables in the MSSM
• Implications of LHC search results on the W boson mass prediction in the MSSM
• Single mass scale diagrams: construction of a basis for the $\epsilon$-expansion
• Constraints on the quartic Higgs self-coupling from double-Higgs production at future hadron colliders
• Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses
• Evaluation of the general 3-loop vacuum Feynman integral
• Virtual Top-Quark Effects on the H->bb-bar Decay at Next-to-Leading Order in QCD
• Precision Calculations in Supersymmetric Theories
• Estimations of Order alpha_s^3 and alpha_s^4 Corrections to Mass-Dependent Observables
• Excesses in the low-mass Higgs-boson search and the W-boson mass measurement
• Phenomenological Indications of the Scale of Supersymmetry
• α_S from $F_{\pi }$ and Renormalization Group Optimized Perturbation
• Four-Loop Tadpoles: Applications in QCD
• Effective potential at three loops
• Electroweak pseudo-observables and Z-boson form factors at two-loop accuracy
• $SU(2{)}_L$ triplet scalar as the origin of the 95 GeV excess?
• Some remarks on the epsilon-expansion of dimensionally regulated Feynman diagrams
• Electroweak Precision Observables: Two-Loop Yukawa Corrections of Supersymmetric Particles
• Hadronic Uncertainties versus New Physics for the $W$ boson Mass and Muon $g-2$ Anomalies
• On the effective theory of neutrino-electron and neutrino-quark interactions
• Two-loop electroweak fermionic corrections to sin^2 theta_{eff}^{b anti-b}
• Moments of heavy quark correlators with two masses: exact mass dependence to three loops
• Precision Physics at LEP
• Three-Loop O(alpha_s^2 G_F M_t^2) Corrections to Higgs Production and Decay at e^+e^- Colliders
• Violation of custodial symmetry from W-boson mass measurements
• Precise calculation of the W boson pole mass beyond the Standard Model with FlexibleSUSY
• Two-loop fermionic electroweak corrections to the Z-boson width and production rate
• TOPAZ0 2.0 - A Program for Computing De-Convoluted and Realistic Observables Around the $Z^0$ Peak
• Lambda^{QCD}_{MS} from Renormalization Group Optimized Perturbation
• Theory of Z boson decays
• Standard Model parameters in the tadpole-free pure $\overline{\mathrm{MS}}$ scheme
• Virtual Top Effects on Low-Mass Higgs Interactions at Next-to-Leading Order in QCD
• Chiral Symmetry Breaking in QCD: A Variational Approach
• The Two-mass Contribution to the Three-Loop Gluonic Operator Matrix Element $A_{gg,Q}^{(3)}$
• Pole mass of the W boson at two-loop order in the pure MS-bar scheme
• Pole- versus MS-mass definitions in the electroweak theory
• Compact analytical form for non-zeta terms in critical exponents at order 1/N^3
• Numerical multi-loop integrals and applications
• Three-loop massive tadpoles and polylogarithms through weight six
• Top-quark pole mass in the tadpole-free MS-bar scheme
• Z boson pole mass at two-loop order in the pure MS-bar scheme
• Three-loop vacuum integrals with arbitrary masses
• Three-loop contributions to the $\rho$ parameter and iterated integrals of modular forms
• Two-loop amplitudes for Higgs plus jet production involving a modified trilinear Higgs coupling
• Delta r in the Two-Higgs-Doublet Model at full one loop level -- and beyond
• Interdependence of the new "MUON G-2" Result and the $W$-Boson Mass
• Tripling down on the $W$ boson mass
• Variational Quark Mass Expansion and the Order Parameters of Chiral Symmetry Breaking
• Theoretical Aspects of Standard-Model Higgs-Boson Physics at a Future e^+ e^- Linear Collider
• Higgs Decay into Gluons up to O(α_s^3 G_F m_t^2)
• Improved prediction for the mass of the W boson in the NMSSM
• Calculation of fermionic two-loop contributions to muon decay
• Leading fermionic three-loop corrections to electroweak precision observables
• W mass and Leptonic Z-decays in the NMSSM
• Two-loop Fermionic Electroweak Corrections to the Effective Leptonic Weak Mixing Angle in the Standard Model
• Low-mass Higgs decays to four leptons at one loop and beyond
• Precise prediction for the W boson mass in the MRSSM
• Two-loop improved predictions for $M_W$ and ${\sin }^2{\theta }_{eff}$ in Two-Higgs-Doublet Models
• Orthopositronium lifetime at O(alpha) and O(alpha^3 ln(alpha)) in closed form
• LEADING VACUUM-POLARIZATION CONTRIBUTIONS TO THE RELATION BETWEEN POLE AND RUNNING MASSES
• Transcendental numbers and the topology of three-loop bubbles
• The QCD improved electroweak parameter $\rho$
• Three-loop vacuum integrals in FORM and REDUCE
• The Standard Model at 200 GeV
• Matching relations for decoupling in the Standard Model at two loops and beyond
• GRIFFIN: A C++ library for electroweak radiative corrections in fermion scattering and decay processes
• Minimal model for the $W$-boson mass, $(g-2{)}_{\mu }$, $h\to {\mu }^{+}{\mu }^{-}$ and quark-mixing-matrix unitarity
• Searching for Anomalous Weak Couplings of Heavy Flavors at the SLC and LEP
• Renormalon contributions to δρ
• Three-loop QCD corrections to the electroweak boson masses
• CP violating supersymmetric contributions to the electroweak $\rho$ parameter
• The Effective Weak Mixing Angle in the MSSM
• An effective field theory approach to the QCD corrections to the large-$m_t$ $Zb\bar{b}$ vertex
• On electroweak corrections to neutral current Drell-Yan with the POWHEG BOX
• How reliably can the Higgs-Boson Mass be predicted from Electroweak Precision Data?
• $Z$-boson hadronic decay width up to $\mathcal{O}({\alpha }_s^4)$-order QCD corrections using the single-scale approach of the principle of maximum conformality
• Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
• Two-Loop Results for M_W in the Standard Model and the MSSM
• Observations Concerning the Magnitude of t \bar{t} Threshold Effects on Electroweak Parameters
• Analysis of a model with a common source of CP violation
• Computer package DIZET v. 6.45
• A new analysis of the pQCD contributions to the electroweak parameter $\rho$ using the single-scale approach of principle of maximum conformality
• Evaluation of three-loop self-energy master integrals with four or five propagators
• Non-trivial Test of Electroweak Quantum Effects
• Predictions for Fermion Pair Production at e+e- Colliders
• Theoretical uncertainties for measurements of alpha_s from electroweak observables
• Dynamical Chiral Symmetry Breaking from Variationally Improved Perturbative Expansion
• Dependence of Electroweak Parameters on the Definition of the Top-Quark Mass
• Electroweak Theory Without Higgs Bosons
• Monte Carlo Event Generators for Future Lepton Colliders
• Electroweak interactions: a theoretical overview
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals
• New physics effects on the $W$-boson mass from a doublet extension of the SM Higgs sector