Pis’ma v ZhETF, vol. 111, iss. 2, pp. 59 - 60
© 2020
January 25
Gluon evolution for the Berger-Block-Tan form of the structure
function F2
A. V. Kotikov1)
II Institut fur Theoretische Physik, Universitat Hamburg, 22761 Hamburg, Germany
Theoretical Physics of the Joint Institute for Nuclear Research, 141980 Dubna, Russia
Submitted 25 November 2019
Resubmitted 10 December 2019
Accepted 10
December 2019
DOI: 10.31857/S0370274X20020010
In the snall-x regime, nonperturbative effects were
Full text of the paper is published in JETP Letters
expected to play an important role. However, as it has
journal. DOI: 10.1134/S0021364020020022
been observed up to very low Q2 ∼ 1 GeV2 values,
considered processes are described reasonably well by
1.
A. M. Cooper-Sarkar, R. C. E. Devenish, and
perturbative OCD (pQCD) methods (see, for example,
A. De Roeck, Int. J. Mod. Phys. A 13, 3385 (1998).
[1, 2]). It should be noted, nonetheless, that at extremely
2.
A. V. Kotikov, Phys. Part. Nucl. 38, 1 (2007).
low x, x → 0, the pQCD evolution provides a rather
3.
A. V. Kotikov and G. Parente, Nucl. Phys. B 549, 242
singular behavior of the parton distribution functions
(1999).
(PDFs) (see, e.g., [3-8] and references therein), which
4.
A. Y. Illarionov, A.V. Kotikov, and G. Parente
strongly violates the Froissard boundary [9].
Bermudez, Phys. Part. Nucl. 39, 307 (2008).
In
[10,
11] a new form of the deep inelastic
5.
G. Cvetic, A. Y. Illarionov, B. A. Kniehl, and
lepton-hadron scattering (DIS) structure function (SF)
A. V. Kotikov, Phys. Lett. B 679, 350 (2009).
F2(x, Q2) was proposed. It will be called below as the
6.
A. V. Kotikov and B. G. Shaikhatdenov, Phys. Part.
Berger-Block-Tan (BBT) structure function. The SF
Nucl. 44, 543 (2013).
FBBT2(x, Q2) leads to the low x asymptotics of the (re-
7.
A. V. Kotikov and B. G. Shaikhatdenov, Phys. Atom.
ducted) DIS cross-sections ∼ ln2 1/x, which is in turn
Nucl. 78(4), 525 (2015).
in an agreement with the Froissard predictions [9]. This
8.
A. V. Kotikov and B. G. Shaikhatdenov, Phys. Part.
Nucl. 48(5), 829 (2017).
parametrization is relevant in investigations of ultra-
9.
M. Froissart, Phys. Rev. 123, 1053 (1961).
high energy processes, such as scattering of cosmic neu-
10.
E. L. Berger, M. M. Block, and C. I. Tan, Phys. Rev.
trino off hadrons (see [12-16]).
Lett. 98, 242001 (2007).
Following to our previous studies in [17, 18] and [19-
11.
M. M. Block, E. L. Berger, and C. I. Tan, Phys. Rev.
21], recently the gluon density fg(x, Q2) and the longi-
Lett. 97, 252003 (2006).
tudinal DIS SF FL(x, Q2) in the BBT form have been
12.
R. Fiore, L. L. Jenkovszky, A.V. Kotikov, F. Paccanoni,
obtained in [22, 23] and [24, 25] at small values of x,
A. Papa, and E. Predazzi, Phys. Rev. D 71, 033002
using the SF FBBT2(x, Q2). To do it, we proposed a vio-
(2005).
lation of twist-two evolution of gluon density by a non-
13.
R. Fiore, L. L. Jenkovszky, A. Kotikov, F. Paccanoni,
linear term. The purpose of the present Letter to show
A. Papa, and E. Predazzi, Phys. Rev. D 68, 093010
the exact form of the violation. All the results will be
(2003).
done at the leading order (LO) of perturbation theory.
14.
R. Fiore, L. L. Jenkovszky, A.V. Kotikov, F. Paccanoni,
We show that the nonlinear term is negative at low
and A. Papa, Phys. Rev. D 73, 053012 (2006).
x values and is suppressed as 1/ ln2(1/x), that is in a
15.
A. Y. Illarionov, B. A. Kniehl, and A. V. Kotikov, Phys.
Rev. Lett. 106, 231802 (2011).
full agreement with earlier studies in [26]. However, the
16.
M. M. Block, L. Durand, and P. Ha, Phys. Rev. D 89(9),
Q2-dependence is different: at large Q2 values our non-
094027 (2014).
linear term ∼ 1/ln(Q2) but the corresponding one in
17.
A. V. Kotikov, JETP Lett. 59, 667 (1994).
[26] ∼ 1/Q2.
18.
A. V. Kotikov and G. Parente, Phys. Lett. B 379, 195
(1996).
1)e-mail: kotikov@theor.jinr.ru
19.
A. V. Kotikov, JETP 80, 979 (1995).
Письма в ЖЭТФ том 111 вып. 1 - 2
2020
59
