scholarly journals RUNNING COUPLING CONSTANTS OF FERMIONS WITH MASSES IN QUANTUM ELECTRODYNAMICS AND QUANTUM CHROMODYNAMICS

2001 ◽  
Vol 16 (16) ◽  
pp. 2873-2894 ◽  
Author(s):  
GUANG-JIONG NI ◽  
GUO-HONG YANG ◽  
RONG-TANG FU ◽  
HAIBIN WANG
Keyword(s):  
Renormalization Group ◽  
Quantum Chromodynamics ◽  
Momentum Transfer ◽  
Quantum Electrodynamics ◽  
Renormalization Group Equation ◽  
Energy Scale ◽  
Coupling Constants ◽  
Group Equation ◽  
Running Coupling ◽  
Renormalization Method

Based on a simple but effective regularization-renormalization method (RRM), the running coupling constants (RCC) of fermions with masses in quantum electrodynamics (QED) and quantum chromodynamics (QCD) are calculated by renormalization group equation (RGE). Starting at Q=0 (Q being the momentum transfer), the RCC in QED increases with the increase of Q whereas the RCCs for different flavors of quarks with masses in QCD are different and they increase with the decrease of Q to reach a maximum at low Q for each flavor of quark and then decreases to zero at Q→0. Thus a constraint on the mass of light quarks, the hadronization energy scale of quark–antiquark pairs are derived.

scholarly journals THE EFFECTIVE POTENTIAL IN THE MASSIVE $\phi_4^4$ MODEL

2007 ◽  
Vol 22 (01) ◽  
pp. 1-9 ◽  
Author(s):  
F. BRANDT ◽  
F. CHISHTIE ◽  
D. G. C. MCKEON
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Effective Potential ◽  
Quantum Electrodynamics ◽  
Renormalization Group Equation ◽  
Massless Scalar ◽  
Group Equation ◽  
Scalar Quantum ◽  
Text Model

By applying the renormalization group equation, it has been shown that the effective potential V in the massless [Formula: see text] model and in massless scalar quantum electrodynamics is independent of the scalar field. This analysis is extended here to the massive [Formula: see text] model, showing that the effective potential is independent of ϕ here as well.

scholarly journals RENORMALIZATION GROUP EQUATION OF QUARK–LEPTON MASS MATRICES IN THE SO(10) MODEL WITH TWO-HIGGS SCALARS

2003 ◽  
Vol 18 (10) ◽  
pp. 719-731 ◽  
Author(s):  
TAKESHI FUKUYAMA ◽  
TATSURU KIKUCHI
Keyword(s):  
Renormalization Group ◽  
Symmetry Breaking ◽  
Yukawa Coupling ◽  
Intermediate Energy ◽  
Renormalization Group Equation ◽  
Coupling Constants ◽  
Group Equation ◽  
Mass Matrices ◽  
Renormalization Group Equations ◽  
Charged Leptons

The renormalization group equations (RGEs) of the mass matrices of quarks and leptons in an SO(10) model with two-Higgs scalars in the Yukawa coupling are studied. This model is the minimal model of SUSY and non-SUSY SO(10) GUT which can reproduce all the experimental data. Non-SUSY SO(10) GUT model has the intermediate energy phase, Pati–Salam phase, and passes through the symmetry breaking pattern, SO (10) → SU (2)L × SU (2)R × SU (4)C → SU (2)L × U (1)Y × SU (3)C. Though minimal, it has, after the Pati–Salam phase, four Higgs doublets in Yukawa interactions. We consider the RGEs of the Yukawa coupling constants of quarks and charged leptons and of the coupling constants of the dimension-five operators of neutrinos corresponding to the above symmetry breaking pattern. The scalar quartic interactions are also incorporated.

scholarly journals INVESTIGATION OF A NEW ANALYTIC RUNNING COUPLING IN QCD

2000 ◽  
Vol 15 (40) ◽  
pp. 2401-2411 ◽  
Author(s):  
A. V. NESTERENKO
Keyword(s):  
Asymptotic Behavior ◽  
Renormalization Group ◽  
Inverse Function ◽  
Renormalization Group Equation ◽  
Lambert W Function ◽  
Group Equation ◽  
Consistent Estimation ◽  
Mathematical Properties ◽  
Running Coupling ◽  
Β Function

The mathematical properties of the new analytic running coupling (NARC) in QCD are investigated. This running coupling naturally arises under "analytization" of the renormalization group equation. One of the crucial points in our consideration is the relation established between the NARC and its inverse function. The latter is expressed in terms of the so-called Lambert W function. This relation enables one to present explicitly the NARC in the renorminvariant form and to derive the corresponding β function. The asymptotic behavior of this β function is examined. The consistent estimation of the parameter Λ QCD is given.

scholarly journals Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation

2009 ◽  
Vol 324 (2) ◽  
pp. 414-469 ◽  
Author(s):  
Alessandro Codello ◽  
Roberto Percacci ◽  
Christoph Rahmede
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation

RENORMALIZATION GROUP EQUATION AND EFFECTIVE ACTION IN STRING THEORY

1989 ◽  
Vol 04 (10) ◽  
pp. 941-951 ◽  
Author(s):  
J. GAITE
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Generating Functional ◽  
S Matrix

The connection between the renormalization group for the σ-model effective action for the Polyakov string and the S-matrix generating functional for dual amplitudes is studied. A more general approach to the renormalization group equation for string theory is proposed.

scholarly journals The KAM theorem and renormalization group

2009 ◽  
Vol 29 (2) ◽  
pp. 419-431 ◽  
Author(s):  
E. DE SIMONE ◽  
A. KUPIAINEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Elementary Proof ◽  
Renormalization Group Equation ◽  
Quadratic Nonlinearity ◽  
Picard Iteration ◽  
Group Equation ◽  
Quantum Field ◽  
Kam Theorem

AbstractWe give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a certain PDE with quadratic nonlinearity, the so-called Polchinski renormalization group equation studied in quantum field theory.

scholarly journals The renormalization group equations revisited

2018 ◽  
Vol 33 (26) ◽  
pp. 1830024 ◽  
Author(s):  
Jean-François Mathiot
Keyword(s):  
Renormalization Group ◽  
Dimensional Regularization ◽  
Direct Consequence ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Coupling Constant ◽  
Loop Order ◽  
Subtraction Scheme ◽  
Minimal Subtraction Scheme ◽  
Renormalization Group Equations

Starting from a well-defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare parameters, respectively. We apply our formalism to the minimal subtraction scheme using dimensional regularization. We first argue that the relevant regularization scale in this case should be dimensionless. By relating bare and renormalized parameters to physical observables, we calculate the coefficients of the renormalization group equation up to two-loop order in the [Formula: see text] theory. We show that the usual assumption, considering the bare parameters to be independent of the regularization scale, is not a direct consequence of any physical argument. The coefficients that we find in our two-loop calculation are identical to the standard practice. We finally comment on the decoupling properties of the renormalized coupling constant.

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