Higher-order effects in asymptotically free gauge theories: The anomalous dimensions of Wilson operators

Floratos, E.G.; Ross, Douglas A.; Sachrajda, Christopher

doi:10.1016/0550-3213(77)90020-7

Cited by 462 publications

(352 citation statements)

References 5 publications

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“…It also means that the singular factors can be dropped from such fits when the coefficient functions account for the total resummation of the leading logarithms and therefore regular functions of x only can be chosen for the initial densities δq. 2 We remind that our estimates for the intercepts ω ± 0 were confirmed by several analyses [15] of the experimental data…”

Section: The Role Of the Singular Factor For δQ In Dglap Fitsmentioning

confidence: 81%

“…The standard DGLAP -technology of calculating f (x, Q 2 ) corresponds to first calculating Γ n (Q 2 ) and then reconstructing f (x, Q 2 ) from the moments, choosing appropriate forms for ∆q. Presently C(ω) for the non-singlet structure functions are known with two-loop [2] and three-loop [3] accuracy. In order to make the all-order resummation of the double-logarithmic contributions to f N S (x, Q 2 ) and g N S 1 (x, Q 2 ), i.e.…”

Section: Comparison Between Dglap and Our Approachmentioning

confidence: 99%

“…The standard theoretical framework is provided by DGLAP [1]. In this approach, any of f N S (x, Q 2 ), g N S 1 (x, Q 2 ) can be represented as a convolution of the coefficient functions and the evolved quark distributions calculated in LO [1], NLO [2] and NNLO [3]. Combining these results with appropriate fits for the initial quark distributions, provides a good agreement with the available experimental data (see e.q.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Non-singlet structure functions: Combining the leading logarithms resummation at small-x with DGLAP

Ermolaev

Greco²,

Troyan

2005

Physics Letters B

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The explicit expressions for the non-singlet DIS structure functions F1 and g1, obtained at small x by resumming the leading logarithmic contributions to all orders, are discussed and compared in detail with the DGLAP evolution for different values of x and Q 2 . The role played by the DGLAP inputs for the initial parton densities on the small-x behavior of the non-singlet structure functions is discussed. It is shown that the singular factors included into the fits ensure the Regge asymptotics of the non-singlet structure functions and mimic the impact of the total resummation of the leading logarithms found explicitly in our approach. Explicit expressions are presented which implement the NLO DGLAP contributions with our small -x results.

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Section: The Role Of the Singular Factor For δQ In Dglap Fitsmentioning

confidence: 81%

Section: Comparison Between Dglap and Our Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-singlet structure functions: Combining the leading logarithms resummation at small-x with DGLAP

Ermolaev

Greco²,

Troyan

2005

Physics Letters B

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“…(2.4) at the same order as the coefficient functions. This procedure is well known from deep inelastic scattering [22,24] and weak decays [25]. In this way, taking into account mixing of the operators under renormalization, all dependences on the infrared structure of the theory are absorbed into the matrix elements.…”

Section: The Coefficient Functionsmentioning

confidence: 99%

Current correlators to all orders in the quark masses

Jamin

Münz

1993

Z. Phys. C - Particles and Fields

103

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The contributions to the coefficient functions of the quark and the mixed quarkgluon condensate to mesonic correlators are calculated for the first time to all orders in the quark masses, and to lowest order in the strong coupling constant. Existing results on the coefficient functions of the unit operator and the gluon condensate are reviewed. The proper factorization of short-and long-distance contributions in the operator product expansion is discussed in detail. It is found that to accomplish this task rigorously the operator product expansion has to be performed in terms of non-normal-ordered condensates. The resulting coefficient functions are improved with the help of the renormalization group. The scale invariant combination of dimension 5 operators, including mixing with the mass operator, which is needed for the renormalization group improvement, is calculated in the leading order.

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“…This was demonstrated early on at 1-loop order [30] and at two loops [32], where a cancellation of ln 3 S terms occurs. There are solid arguments that (5.2) holds to all orders in perturbation theory [31,33].…”

Section: Semiclassical Spinning Strings Vs Highly Charged Operatorsmentioning

confidence: 96%

Gauge-String Dualities and some Applications

Benna

Klebanov

2008

String Theory and the Real World: From Particle Physics to Astrophysics

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Higher-order effects in asymptotically free gauge theories: The anomalous dimensions of Wilson operators

Cited by 462 publications

References 5 publications

Non-singlet structure functions: Combining the leading logarithms resummation at small-x with DGLAP

Non-singlet structure functions: Combining the leading logarithms resummation at small-x with DGLAP

Current correlators to all orders in the quark masses

Gauge-String Dualities and some Applications

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