Gauge dependence of the perturbative QCD predictions under the momentum space subtraction scheme

Abstract

The momentum space subtraction (MOM) scheme is one of the most frequently used renormalization schemes in perturbative QCD (pQCD) theory. In the paper, we make a detailed discussion on the gauge dependence of the pQCD prediction under the MOM scheme. Conventionally, there is renormalization scale ambiguity for the fixed-order pQCD predictions, which assigns an arbitrary range and an arbitrary error for the fixed-order pQCD prediction. The principle of maximum conformality (PMC) adopts the renormalization group equation to determine the magnitude of the coupling constant and hence determines an effective momentum flow of the process, which is independent to the choice of renormalization scale. There is thus no renormalization scale ambiguity in PMC predictions. To concentrate our attention on the MOM gauge dependence, we first apply the PMC to deal with the pQCD series. We adopt the Higgs boson decay width, $\Gamma (H\to gg)$, up to five-loop QCD contributions as an example to show how the gauge dependence behaves before and after applying the PMC. It is found that the Higgs decay width $\Gamma (H\to gg)$ depends very weakly on the choices of the MOM schemes, being consistent with the renormalization group invariance. It is found that the gauge dependence of $\Gamma (H\to gg)$ under the $\mathrm{MOMgg}$ scheme is less than $\pm 1\%$, which is the smallest gauge dependence among all the mentioned MOM schemes.

arXiv comment21 pages, 13 figures. References updated

References in corpus (48)

• Combined Measurement of the Higgs Boson Mass in $pp$ Collisions at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS Experiments
• The four-loop beta-function in Quantum Chromodynamics
• HIGGS BOSON PRODUCTION AT THE LHC
• The three-loop QCD $\beta$-function and anomalous dimensions
• Five-Loop Running of the QCD coupling constant
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• The five-loop beta function of Yang-Mills theory with fermions
• Higgs Decay to Order α_s^4
• The QCD Pomeron with Optimal Renormalization
• A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD
• Commensurate Scale Relations in Quantum Chromodynamics
• Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops
• The strong coupling and its running to four loops in a minimal MOM scheme
• The Renormalization Scale-Setting Problem in QCD
• Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
• Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality
• Strong-Coupling Constant with Flavor Thresholds at Five Loops in the MS-bar Scheme
• Asymptotic behaviour of the gluon propagator from lattice QCD
• QCD Corrections to Higgs Boson Production: Non- Leading Terms in the Heavy Quark Limit
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• On Higgs decays to hadrons and the R-ratio at N^4LO
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• High-Energy QCD Asymptotics of Photon-Photon Collisions
• Four-loop QCD propagators and vertices with one vanishing external momentum
• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• The Form Factors of the Gauge-Invariant Three-Gluon Vertex
• Generalization of the BLM procedure and its scales in any order of pQCD
• Two Loop QCD Vertices and Three Loop MOM $\beta$ functions
• Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta \}$-expansion and the Principle of Maximal Conformality
• Novel All-Orders Single-Scale Approach to QCD Renormalization Scale-Setting
• Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy
• Two loop QCD vertices at the symmetric point
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• A novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the $C$-scheme coupling
• Fourth-order QCD renormalization group quantities in the {\rm{V}}-scheme and the relation of the $\beta$-function to the Gell-Mann--Low function in QED
• Renormalization group functions of QCD in the minimal MOM scheme
• Implications of the Principle of Maximum Conformality for the QCD Strong Coupling
• Three-loop beta function and non-perturbative ${\alpha }_s$ in asymmetric momentum scheme
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• The Importance of Proper Renormalization Scale-Setting for Testing QCD at Colliders
• Setting the Renormalization Scale in pQCD: Comparisons of the Principle of Maximum Conformality with the Sequential Extended Brodsky-Lepage-Mackenzie Approach
• Momentum subtraction and the R-ratio
• General Properties on Applying the Principle of Minimum Sensitivity to High-order Perturbative QCD Predictions
• Reanalysis of the Higgs-boson decay $H\to gg$ up to ${\alpha }_s^6$-order level using the principle of maximum conformality
• Renormalization scheme dependence of high-Order perturbative QCD predictions

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