Singlet structure function $$F_1$$ F1 in double-logarithmic approximation

• Main Authors: B. I. Ermolaev, S. I. Troyan
• Format: Article
• Language: English
• Published: SpringerOpen 2018-03-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-018-5675-6

Abstract The conventional ways to calculate the perturbative component of the DIS singlet structure function $$F_1$$ F1 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 $$F_1$$ F1 in the double-logarithmic approximation (DLA) and account at the same time for the running $$\alpha _s$$ αs effects. We start with a total resummation of both quark and gluon DL contributions and obtain the explicit expression for $$F_1$$ F1 in DLA. Then, applying the saddle-point method, we calculate the small-x asymptotics of $$F_1$$ F1 , which proves to be of the Regge form with the leading singularity $$\omega _0 = 1.066$$ ω0=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 $$F_1$$ F1 scales: it depends on a single variable $$Q^2/x^2$$ Q2/x2 only instead of x and $$Q^2$$ Q2 separately. Finally, we show that the small-x asymptotics reliably represent $$F_1$$ F1 at $$x \le 10^{-6}$$ x≤10-6 .