Impact of the Double-Logarithmic contribution to Pomeron on the small-$x$ behaviour of the DIS Structure Function $F_1$

Apr 9, 2019, 9:10 AM
Cavallerizza Reale - Aula Multifunzione

Cavallerizza Reale - Aula Multifunzione

Via Verdi, 9 Turin
Parallel Session Talk WG2: Low-x and Diffraction WG2: Small-x and Diffraction


Boris Ermolaev (Ioffe Institute (RU))


Pomeron was introduced in the framework of the phenomenological Regge theory.
It governs the high-energy asymptotics of various hadronic processes and the small-$x$ behavior of $F_1$ in particular.
The best-known contribution to the QCD Pomeron comes from  the BFKL equation which
sums Leading Logarithmic (LL) contributions i.e. the
single-logarithmic (SL) contributions $\sim (\alpha_s \ln (1/x))^n$
multiplied by the overall factor $1/x$.
The high-energy asymptotics of this resummation is
known as the BFKL Pomeron.  It predicts that small-$x$ $F_1 \sim x^{- (1 + \Delta)}$, where $\Delta$ is the intercept of the BFKL Pomeron.

In contrast, we calculate $F_1$ in the Double-Logarithmic approximation (DLA),
accounting for contributions $\sim (\alpha_s \ln^2 (1/x))^n$ as well as double-logs of $Q^2$. Such terms  are not accompanied by the overall factor
$s$, so their contribution to asymptotics of $F_1$ is $\sim x^{-\Delta_{DL}}$ without the factor $x^{-1}$. It looks negligibly small compared to the
BFKL exponent $1 + \Delta$. By this reason the DL contribution to Pomeron was offhandedly ignored by the HEP
community. However, we demonstrate that the intercept $\Delta_{DL}$ proves to be so
large that its value compensates for the lack of $x^{-1}$, which
makes the DL Pomeron and BFKL Pomeron be equally important.
It means that DL Pomeron should participate in theoretical analysis
of all HEP results where the BFKL Pomeron
has been involved.

Primary author

Boris Ermolaev (Ioffe Institute (RU))

Presentation materials