2,642 research outputs found

    The simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion

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    The simple method for the calculating of the anomalous dimensions of the composite operators up to 1/N^2 order is developed. We demonstrate the effectiveness of this approach by computing the critical exponents of the (Φ)s(\otimes\vec\Phi)^{s} and Φ()nΦ\vec\Phi\otimes(\otimes\vec\partial)^{n}\vec\Phi operators in the 1/N^2 order in the nonlinear sigma model. The special simplifications due to the conformal invariance of the model are discussed.Comment: 20 pages, Latex, uses Feynman.st

    Electron Mass Anomalous Dimension at O(1/N^2_f) in Quantum Electrodynamics

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    The critical exponent corresponding to the renormalization of the composite operator ψˉψ\bar{\psi}\psi is computed in quantum electrodynamics at O(1/\Nf^2) in arbitrary dimensions and covariant gauge at the non-trivial zero of the β\beta-function in the large \Nf expansion and the exponent corresponding to the anomalous dimension of the electron mass which is a gauge independent object is deduced. Expanding in powers of ϵ\epsilon == 22 - d/2d/2 we check it is consistent with the known three loop perturbative structure and determine the subsequent coefficients in the coupling constantComment: 12 pages (latex), 1 figure (available from author on request), LTH-31

    Anomalous dimension of non-singlet quark currents at O(1/Nf^2) in QCD

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    We compute the O(1/Nf^2) corrections to the flavour non-singlet quark bilinear currents in QCD in arbitrary spacetime dimensions. Hence, the anomalous dimension of the QED current ψˉσμνψ\bar{\psi} \sigma^{\mu\nu} \psi is deduced at four loops in the MSbar scheme up to one unknown parameter.Comment: 8 latex page

    Status of twist-2 operator dimensions at O(1/N_f)

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    We review the computation of the anomalous dimensions of the twist-2 unpolarized operators in the large N_f expansion. Results are discussed for the predominantly gluonic singlet operator and the O(1/N_f) part of the 3-loop splitting function is given.Comment: 4 latex pages, contribution to DIS 9

    Four loop MSbar mass anomalous dimension in the Gross-Neveu model

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    We compute the four loop term of the mass anomalous dimension in the two dimensional Gross-Neveu model in the MSbar scheme. The absence of multiplicative renormalizability which results when using dimensional regularization means that the effect of the evanescent operator, which first appears at three loops in the 4-point Green's function, has to be properly treated in the construction of the renormalization group function. We repeat the calculation of the three loop MSbar beta-function and construct the beta-function of the evanescent operator coupling which corrects earlier computations.Comment: 20 latex pages, 7 figure

    The Nambu-Jona-Lasinio Model at O(1/N^2)

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    We write down the anomalous dimensions of the fields of the Nambu--Jona-Lasinio model or chiral Gross Neveu model with a continuous global chiral symmetry for the two cases U(1)U(1) ×\times U(1)U(1) and SU(M)SU(M) ×\times SU(M)SU(M) at O(1/N2)O(1/N^2) in a 1/N1/N expansion.Comment: 9 latex pages, 4 figures (available on request from the author), LTH-308, (2 eqns corrected

    Plasma jet electrode has longer operating life

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    Water-cooled, silver-infiltrated tungsten electrode has twice the operating lifetime of the pure tungsten electrode used in plasma jet generators. This electrode reduces the erosion rate, ensures excellent heat transfer, and reduces thermal stresses

    Momentum subtraction and the R-ratio

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    We determine the R-ratio for massless quarks in several renormalization schemes to various loop orders. These are the momentum subtraction schemes of Celmaster and Gonsalves as well as the minimal momentum subtraction scheme. The dependence of the R-ratio on the schemes is analysed.Comment: 27 latex pages, 36 figures, anc directory contains txt file with electronic version of main equation
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