Small-X behaviour of the non-singlet structure function

Ermolaev, B. I.; Ryskin, M.G.; Manaenkov, S. I.

doi:10.1007/s002880050026

Cited by 47 publications

(113 citation statements)

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“…Our results (5,6) differ slightly from DGLAP also for the Q 2 -evolution, depending on x. This is shown in Fig.…”

Section: The Role Of the Regular Part In The Initial Parton Densisupporting

confidence: 43%

“…(2) to Eqs. (5,6) clearly shows the difference between DGLAP and our approach: First, our approach accounts for the double-and single-logarithmic contributions to all orders in the QCD coupling whereas in the DGLAP -expressions the coefficient functions and the anomalous dimensions are obtained up to fixed-order accuracy (two and three loops).…”

Section: Comparison Between Dglap and Our Approachmentioning

confidence: 95%

“…In order to do so, let us consider the region of x ∼ 1 where the effective values of ω in Eqs. (5,6) are large. In this region we can expand H (±) N S and C (±) N S into a series in 1/ω.…”

Section: Implementation Of Dglap With Our Higher-loop Contributionsmentioning

confidence: 96%

“…Of course, both C DGLAP and γ DGLAP contain also terms already included in Eqs. (5,6), so in order to avoid a double counting these terms should be extracted from C (±) N S , H (±) N S . In order to do so, let us consider the region of x ∼ 1 where the effective values of ω in Eqs.…”

Section: Implementation Of Dglap With Our Higher-loop Contributionsmentioning

confidence: 99%

“…ω = n, with n = 1, 2, ... and thereby obtaining the moments of the non-singlet structure functions, or alternatively by usingĈ (±) N S ,Ĥ (±) N S in Eqs. (5,6) where ω is complex. In the latter case, C DGLAP and γ DGLAP should first be continued analytically from the integer values ω = n. We have verified that the new formulae in Eq.…”

Section: Implementation Of Dglap With Our Higher-loop Contributionsmentioning

confidence: 99%

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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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“…Our results (5,6) differ slightly from DGLAP also for the Q 2 -evolution, depending on x. This is shown in Fig.…”

Section: The Role Of the Regular Part In The Initial Parton Densisupporting

confidence: 43%

Section: Comparison Between Dglap and Our Approachmentioning

confidence: 95%

Section: Implementation Of Dglap With Our Higher-loop Contributionsmentioning

confidence: 96%

Section: Implementation Of Dglap With Our Higher-loop Contributionsmentioning

confidence: 99%

Section: Implementation Of Dglap With Our Higher-loop Contributionsmentioning

confidence: 99%

See 3 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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Exact result in $$ \mathcal{N} $$ = 4 SYM theory: generalised double-logarithmic equation

Velizhanin

2022

J. High Energ. Phys.

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We present the new results for the generalised double-logarithmic equation, obtained from the analytical continuation of the seven-loop anomalous dimension of twist-2 operators in the planar $$ \mathcal{N} $$ N = 4 SYM theory. The double-logarithmic equation is related to the special asymptotic of the scattering amplitudes, when the large logarithms of the energy of scattering particles are appeared and should be summed in all order of perturbative theory. These large logarithms correspond to the poles of the analytically continued anomalous dimension. The generalised double-logarithmic equation includes the subleading logarithms. We have found, that the expansion of the generalised double-logarithmic equation can be ressumed in the form of rational functions with simple denominator. The solution of the generalised double-logarithmic equation provides a lot of information about the poles of the analytically continued anomalous dimension in all orders of perturbative theory. We have found also the generalised double-logarithmic equation for the analytically continued anomalous dimension near the value, which is related with BFKL-equation.

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High-energy operator product expansion at sub-eikonal level

Chirilli

2021

J. High Energ. Phys.

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Small-X behaviour of the non-singlet structure function

Cited by 47 publications

References 0 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

Exact result in $$ \mathcal{N} $$ = 4 SYM theory: generalised double-logarithmic equation

High-energy operator product expansion at sub-eikonal level

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