Renormalization-group calculation of the color-Coulomb potential

Attilio Cucchieri, Daniel Zwanziger

    Research output: Contribution to journalArticle

    Abstract

    We report here on the application of the perturbative renormalization-group to the Coulomb gauge in QCD. We use it to determine the high-momentum asymptotic form of the instantaneous color-Coulomb potential V(k→) and of the vacuum polarization P(k→,k 4). These quantities are renormalization-group invariants in the sense that they are independent of the renormalization scheme. A scheme-independent definition of the running coupling constant is provided by k→ 2V(k→)=x 0g 2(k→/Λ Coul), and of α s≡ g 2(k→/Λ Coul)/4π, where x 0= 12N/(11N -2N f), and Λ Coul is a finite QCD mass scale. We also show how to calculate the coefficients in the expansion of the invariant β function β(g)≡\k→\(∂g/∂\k→\)=- (b 0g 3 + b 1g 5 + b 2g 7+ ...), where all coefficients are scheme independent.

    Original languageEnglish (US)
    Article number014002
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume65
    Issue number1
    DOIs
    StatePublished - 2002

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    Coulomb potential
    quantum chromodynamics
    color
    coefficients
    momentum
    vacuum
    expansion
    polarization

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

    Cite this

    Renormalization-group calculation of the color-Coulomb potential. / Cucchieri, Attilio; Zwanziger, Daniel.

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 65, No. 1, 014002, 2002.

    Research output: Contribution to journalArticle

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    N2 - We report here on the application of the perturbative renormalization-group to the Coulomb gauge in QCD. We use it to determine the high-momentum asymptotic form of the instantaneous color-Coulomb potential V(k→) and of the vacuum polarization P(k→,k 4). These quantities are renormalization-group invariants in the sense that they are independent of the renormalization scheme. A scheme-independent definition of the running coupling constant is provided by k→ 2V(k→)=x 0g 2(k→/Λ Coul), and of α s≡ g 2(k→/Λ Coul)/4π, where x 0= 12N/(11N -2N f), and Λ Coul is a finite QCD mass scale. We also show how to calculate the coefficients in the expansion of the invariant β function β(g)≡\k→\(∂g/∂\k→\)=- (b 0g 3 + b 1g 5 + b 2g 7+ ...), where all coefficients are scheme independent.

    AB - We report here on the application of the perturbative renormalization-group to the Coulomb gauge in QCD. We use it to determine the high-momentum asymptotic form of the instantaneous color-Coulomb potential V(k→) and of the vacuum polarization P(k→,k 4). These quantities are renormalization-group invariants in the sense that they are independent of the renormalization scheme. A scheme-independent definition of the running coupling constant is provided by k→ 2V(k→)=x 0g 2(k→/Λ Coul), and of α s≡ g 2(k→/Λ Coul)/4π, where x 0= 12N/(11N -2N f), and Λ Coul is a finite QCD mass scale. We also show how to calculate the coefficients in the expansion of the invariant β function β(g)≡\k→\(∂g/∂\k→\)=- (b 0g 3 + b 1g 5 + b 2g 7+ ...), where all coefficients are scheme independent.

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