Singlet structure function $$F_1$$ F 1 in double-logarithmic approximation

Abstract

The conventional ways to calculate the perturbative component of the DIS singlet structure function F 1 involve approaches based on BFKL which account for the single-logarithmic contributions accompanying the Born factor 1/x. In contrast, we account for the double-logarithmic (DL) contributions unrelated to 1/x and because of that they were disregarded as negligibly small. We calculate the singlet F 1 in the double-logarithmic approximation (DLA) and account at the same time for the running α s effects. We start with a total resummation of both quark and gluon DL contributions and obtain the explicit expression for F 1 in DLA. Then, applying the saddle-point method, we calculate the small-x asymptotics of F 1 , which proves to be of the Regge form with the leading singularity ω 0 = 1.066. Its large value compensates for the lack of the factor 1/x in the DLA contributions. Therefore, this Reggeon can be identified as a new Pomeron, which can be quite important for the description of all QCD processes involving the vacuum (Pomeron) exchanges at very high energies. We prove that the expression for the small-x asymptotics of F 1 scales: it depends on a single variable Q 2 /x 2 only instead of x and Q 2 separately. Finally, we show that the small-x asymptotics reliably represent F 1 at x ≤ 10 −6 .

Rise of the DIS structure function FL at small x caused by double-logarithmic corrections

“…However, it has recently been proved in ref. [38] that the DL contribution to Pomeron is not less important than the BFKL contribution.…”

“…We modify the approach which we used in ref. [38] to calculate F 1 in the Double-Logarithmic Approximation (DLA). This approach has nothing in common with the BFKL equation and its ensuing modifications.…”

“…Constructing IREEs in the DIS context was explained in many our papers. For instance, IREEs for the DIS structure function F 1 can be found in [38]; the overview of the technical details can be found in ref. [43].…”

“…The same form for Mellin transforms we used in ref. [38] for the structure function F 1 . It is convenient to use beyond the Born approximation the logarithmic variables ρ defined in eq.…”

“…IREEs for amplitudes A q,g were obtained in ref. [38] and IREEs for amplitudes B q,g are absolutely the same, so we do not derive them here and only briefly comment on them. IREEs for B q,g in the ω-space look as follows:…”