Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality

Abstract

A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale $\mu$ of the running coupling ${\alpha }_s({\mu }^2).$ The purpose of the running coupling in any gauge theory is to sum all terms involving the $\beta$ function; in fact, when the renormalization scale is set properly, all non-conformal $\beta \ne 0$ terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with $\beta =0$. The resulting scale-fixed predictions using the "principle of maximum conformality" (PMC) are independent of the choice of renormalization scheme -- a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale-setting in the Abelian limit. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors $n_f$ in the QCD $\beta$ function is also correctly determined. We discuss several methods for determining the PMC scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scale ambiguity and the scheme dependence using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.

13 pages,2 figures

References in corpus (9)

• Forward-backward asymmetry in top quark-antiquark production
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• 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
• Update: Accurate Determinations of alpha_s from Realistic Lattice QCD
• Application of the Principle of Maximum Conformality to the Top-Quark Forward-Backward Asymmetry at the Tevatron
• The Form Factors of the Gauge-Invariant Three-Gluon Vertex
• Dijet Production at Large Rapidity Separation in N=4 SYM
• New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models

Cited by in corpus (103)

• NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels
• The Large Hadron-Electron Collider at the HL-LHC
• A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD
• Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
• The Renormalization Scale-Setting Problem in QCD
• Evidence for high-energy resummation effects in Mueller-Navelet jets at the LHC
• The Spin Structure of the Nucleon
• The hard to soft Pomeron transition in small x DIS data using optimal renormalization
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• Description of F2 and FL at small x using a collinearly-improved BFKL resummation
• Scale Setting for Self-consistent Backgrounds
• 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
• Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders
• Puzzles in Hadronic Physics and Novel Quantum Chromodynamics Phenomenology
• 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
• Implications of the Principle of Maximum Conformality for the QCD Strong Coupling
• The Higgs boson inclusive decay channels $H\to b\bar{b}$ and $H\to gg$ up to four-loop level
• Application of the Principle of Maximum Conformality to the Top-Quark Charge Asymmetry at the LHC
• PMC${}_{\infty }$: Infinite-Order Scale-Setting using the Principle of Maximum Conformality, A Remarkably Efficient Method for Eliminating Renormalization Scale Ambiguities for Perturbative QCD
• Novel Method for the Precise Determination of the QCD Running Coupling from Event Shapes Distributions in Electron-Positron Annihilation
• On the BLM optimal renormalization scale setting for semihard processes
• 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
• Reanalysis of the Higher Order Perturbative QCD corrections to Hadronic $Z$ Decays using the Principle of Maximum Conformality
• $J/\psi +{\chi }_{cJ}$ Production at the $B$ Factories under the Principle of Maximum Conformality
• The Generalized Scheme-Independent Crewther Relation in QCD
• Information on the Pion Distribution Amplitude from the Pion-Photon Transition Form Factor with the Belle and BaBar Data
• Novel and self-consistency analysis of the QCD running coupling ${\alpha }_s(Q)$ in both the perturbative and nonperturbative domains
• Fractional Analytic QCD beyond Leading Order in timelike region
• The QCD improved electroweak parameter $\rho$
• Exclusive charmonium production from $e^{+}{e}^{-}$ annihilation round the $Z^0$ peak
• Predictions for the Top-Quark Forward-Backward Asymmetry at High Invariant Pair Mass Using the Principle of Maximum Conformality
• Ambiguities of the principle of maximum conformality procedure for hadron collider processes
• Precise perturbative predictions from fixed-order calculations
• The heavy quarkonium inclusive decays using the principle of maximum conformality
• An analysis of $H\to \gamma \gamma$ up to three-loop QCD corrections
• Renormalization-scheme variation of a QCD perturbation expansion with tamed large-order behavior
• General Properties on Applying the Principle of Minimum Sensitivity to High-order Perturbative QCD Predictions
• The $\overline{\mathrm{MS}}$-scheme ${\alpha }_s^5$ QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold $\{\beta \}$-expanded representation
• Hadronic decays of the spin-singlet heavy quarkomium under the principle of maximum conformality
• Heavy Quarkonium Production through the Semi-Exclusive $e^{+}{e}^{-}$ Annihilation Channels around the $Z^0$ Peak
• Novel Method to Reliably Determine the QCD Coupling from $R_{\mathrm{uds}}$ Measurements and its effects to Muon $g-2$ and $\alpha (M_Z^2)$ within the Tau-Charm Energy Region
• A precise determination of the top-quark pole mass
• Determination of the top-quark $\overline{\mathrm{MS}}$ running mass via its perturbative relation to the on-shell mass with the help of principle of maximum conformality
• Application of the Principle of Maximum Conformality to the Hadroproduction of the Higgs Boson at the LHC
• Gauge dependence of the perturbative QCD predictions under the momentum space subtraction scheme
• Scale-Fixed Predictions for $\gamma +{\eta }_c$ production in electron-positron collisions at NNLO in perturbative QCD
• Some recent theoretical progress in Higgs boson and top quark physics at hadron colliders
• Thrust Distribution in Electron-Positron Annihilation using the Principle of Maximum Conformality
• Properties of the decay $H\to \gamma \gamma$ using the approximate ${\alpha }_s^4$-corrections and the principle of maximum conformality
• Thrust Distribution for 3-Jet Production from $e^{+}{e}^{-}$ Annihilation within the QCD Conformal Window and in QED
• Next-to-leading order QCD corrections to the production of $B_c$ and $B_c^{\ast }$ through $W^{+}$-boson decays
• Renormalization Scale Setting for Heavy Quark Pair Production in $e^{+}{e}^{-}$ Annihilation near the Threshold Region
• Detailed Comparison of Renormalization Scale-Setting Procedures based on the Principle of Maximum Conformality
• Spontaneous mass generation and the small dimensions of the Standard Model gauge groups U(1), SU(2) and SU(3)
• Inclusive Gluon Production in Pion-Proton Collisions and the Principle Maximum Conformality Renormalization Scale
• $Z$-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
• Light-Front Holographic QCD and Color Confinement
• Top and bottom quark forward-backward asymmetries at next-to-next-to-leading order QCD in (un)polarized electron positron collisions
• Light-Front Holographic QCD and the Confinement Potential
• Light-Front Holography, Light-Front Wavefunctions, and Novel QCD Phenomena
• Color Confinement and Supersymmetric Properties of Hadron Physics from Light-Front Holography
• Revisiting the Bottom Quark Forward-Backward Asymmetry $A_{\mathrm{FB}}$ in Electron-Positron Collisions
• Reanalysis of the top-quark pair production via the $e^{+}{e}^{-}$ annihilation near the threshold region up to N${}^3$LO QCD corrections
• Achieving effective renormalization scale and scheme independence via the Principle of Observable Effective Matching
• An updated determination of the pion-photon transition form factor
• Reanalysis of the top-quark pair hadroproduction and a precise determination of the top-quark pole mass at the LHC
• Elimination of QCD Renormalization Scale and Scheme Ambiguities
• Precise determination of the top-quark on-shell mass $M_t$ via its scale-invariant perturbative relation to the top-quark $\overline{\mathrm{MS}}$ mass ${\overline{m}}_t({\overline{m}}_t)$
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• QCD on the Light-Front -- A Systematic Approach to Hadron Physics
• Revisiting the top-quark pair production at future $e^{+}{e}^{-}$ colliders
• Approximate N${}^5$LO Higgs boson decay width $\Gamma (H\to \gamma \gamma )$
• Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\mathrm{MS}}$-scheme running mass
• The $P$-wave charmonium annihilation into two photons ${\chi }_{c0,c2}\to \gamma \gamma$ with high-order QCD corrections
• A new analysis of the pQCD contributions to the electroweak parameter $\rho$ using the single-scale approach of principle of maximum conformality
• The ${\rm Y}(1S)$ leptonic decay using the principle of maximum conformality
• New determination of $|V_{\mathrm{cb}}|$ using the three-loop QCD corrections for the $B\to D^{\ast }$ semi-leptonic decays
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
• Reconsideration of the QCD corrections to the ${\eta }_c$ decays into light hadrons using the principle of maximum conformality
• High-Energy Dijets in N=4 SYM
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem
• The Higgs-Boson Decay $H\to gg$ to Order ${\alpha }_s^5$ under the mMOM-Scheme
• Scale-invariant total decay width $\Gamma (H\to b\bar{b})$ using the novel method of characteristic operator
• Updated Determination of Ellis-Jaffe Sum Rules up to ${\mathrm{N}}^3\mathrm{LO}$ QCD corrections
• QCD corrections of $e^{+}{e}^{-}\to J/\psi +c+\bar{c}$ using the principle of maximum conformality
• Light-Front Holographic Quantum Chromodynamics
• Deviation pattern approach for optimizing perturbative terms of QCD renormalization group invariant observables
• On the analytically-improved running coupling in QCD
• The Common Elements of Atomic and Hadronic Physics
• A reanalysis of event shape distributions in electron-positron annihilation
• The Forward Physics Facility at the High-Luminosity LHC
• Quark mass matrices inspired by a numerical relation
• Transition Form-Factor for ${\eta }_Q$ at NNLO in the strong coupling ${\alpha }_s$ and with all-order $v^2$ resummation
• Proceedings to the 27th Workshop "What Comes Beyond the Standard Models" Bled, July 8-17, 2024
• Do we understand the internal spaces of second quantized fermion and boson fields, with gravity included? Relation with strings theories
• Confronting BFKL dynamics with experimental studies of Mueller-Navelet jets at the LHC
• Relation between pole and running masses of heavy quarks using the principle of maximum conformality
• Novel Perspectives for Hadron Physics
• Renormalisation