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- Title
Singlet structure function F1 in double-logarithmic approximation.
- Authors
Ermolaev, B. I.; Troyan, S. I.
- Abstract
The conventional ways to calculate the perturbative component of the DIS singlet structure function F1<inline-graphic></inline-graphic> involve approaches based on BFKL which account for the single-logarithmic contributions accompanying the Born factor 1 / <italic>x</italic>. In contrast, we account for the double-logarithmic (DL) contributions unrelated to 1 / <italic>x</italic> and because of that they were disregarded as negligibly small. We calculate the singlet F1<inline-graphic></inline-graphic> in the double-logarithmic approximation (DLA) and account at the same time for the running αs<inline-graphic></inline-graphic> effects. We start with a total resummation of both quark and gluon DL contributions and obtain the explicit expression for F1<inline-graphic></inline-graphic> in DLA. Then, applying the saddle-point method, we calculate the small-<italic>x</italic> asymptotics of F1<inline-graphic></inline-graphic>, which proves to be of the Regge form with the leading singularity ω0=1.066<inline-graphic></inline-graphic>. Its large value compensates for the lack of the factor 1 / <italic>x</italic> 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-<italic>x</italic> asymptotics of F1<inline-graphic></inline-graphic> scales: it depends on a single variable Q2/x2<inline-graphic></inline-graphic> only instead of <italic>x</italic> and Q2<inline-graphic></inline-graphic> separately. Finally, we show that the small-<italic>x</italic> asymptotics reliably represent F1<inline-graphic></inline-graphic> at x≤10-6<inline-graphic></inline-graphic>.
- Subjects
POMERONS; QUANTUM chromodynamics; LOGARITHMIC functions; GLUONS; QUARKS
- Publication
European Physical Journal C -- Particles & Fields, 2018, Vol 78, Issue 3, p1
- ISSN
1434-6044
- Publication type
Article
- DOI
10.1140/epjc/s10052-018-5675-6