Pis’ma v ZhETF, vol. 109, iss. 5, pp. 291 - 291

March 10

Longitudinal structure function F_L at small x extracted from the

Berger-Block-Tan parametrization of F₂

L.P.Kaptari^+∗, A.V.Kotikov^+∗1), N.Yu.Chernikova^×, P.Zhang^◦

⁺Institute of Modern Physics, 730000 Lanzhou, China

^∗Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia

^×Sunday school, 141980 Dubna, Russia

^◦University of Chinese Academy of Sciences, 100049 Beijing, China

Submitted 4 December 2018

Resubmitted 4 December 2018

Accepted 27 December 2018

DOI: 10.1134/S0370274X19050011

The longitudinal structure function F_L(x, Q²) is ex-

tracted at low values of the Bjorken variable x from

the Berger-Block-Tan (BBT) parametrization [1-4] of

F₂(x, Q²), which describes fairly well the available ex-

perimental data on the reduced cross sections and, at

asymptotically low x, provides a behaviour of the cross

sections ∼ ln² 1/x, in accordance with the Froissart pre-

dictions [5]. In order to maintain the correct asymp-

totical behaviour of the longitudinal structure function

F_L(x, Q²), it is sought in the same form as the BBT

parametrization of F₂(x, Q²). To facilitate our calcula-

tions, the corresponding parametrizations of F₂(x, Q²)

and F_L(x, Q²) are considered in space of Mellin mo-

menta. This allows to find the parameters of F_L(x, Q²)

in an explicit analytical form. The extracted longitudi-

Fig. 1. (Color online) Q² dependence of the extracted lon-

nal structure function is in a reasonable good agreement

gitudinal SF F^BBTL(x, Q²) at fixed value of the invariant

with the available experimental data.

mass W = 230 GeV, solid curve. The shaded area corre-

In Figure 1 we present an example of the extracted

sponds to uncertainties of the BBT parameters in [4]. Ex-

SF F^BBTL(x, Q²) at a fixed value of the invariant mass

perimental data by the H1 Collaboration are taken from [6]

W² = (p + q)² in comparison with the available exper-

imental data of the H1-collaboration [6]. The shaded

area represents the uncertainties in the BBT parame-

1. E. L. Berger, M. M. Block, and C. I. Tan, Phys. Rev.

ters obtained in [4]. It can be seen that the suggested

Lett. 98, 242001 (2007).

extraction procedure describes fairly well the data, es-

2. M. M. Block, E. L. Berger, and C. I. Tan, Phys. Rev.

pecially in the interval Q² > 5 GeV². At lower values

Lett. 97, 252003 (2006).

of the momentum transfer Q² < 5 GeV² the next-to-

3. M. M. Block, L. Durand, P. Ha, and D. W. McKay, Phys.

leading (NLO) corrections and their resummation (see,

Rev. D 84, 094010 (2011).

e.g. [7]) become rather important. An analogous analy-

4. M. M. Block, L. Durand, and P. Ha, Phys. Rev. D 89(9),

sis of the F^BBTL(x, Q²) at low x and Q² with NLO taken

094027 (2014).

into account will be presented elsewhere.

5. M. Froissart, Phys. Rev. 123, 1053 (1961).

Full text of the paper is published in JETP Letters

6. V. Andreev, A. Baghdasaryan, S. Baghdasaryan et al.

journal. DOI: 10.1134/S0021364019050023

(H1 Collaboration), Eur. Phys. J. C 74(4), 2814 (2014).

7. A. V. Kotikov, Phys. Lett. B 338, 349 (1994) [JETP

Lett. 59, 1 (1995)].

¹⁾e-mail: kotikov@theor.jinr.ru

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