https://doi.org/10.1140/epjc/s10052-020-7814-0
Regular Article - Experimental Physics
Analytic derivation of the photon structure function 
at the leading order and the next-to-leading order approximations based on the Laplace transform method
Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran
* e-mail: zarrin@phys.usb.ac.ir
Received:
10
July
2019
Accepted:
6
March
2020
Published online:
13
April
2020
In this paper, we present the analytical solutions, based on the Laplace transform method, for the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi evolution equations of the photon at the leading order (LO) and next-to-leading order (NLO) approximations in perturbative QCD. Using these solutions, we derive the singlet, non-singlet, gluon, and photon distribution functions of the photon and also the photon structure function at the LO and NLO approximations. We show that the resulting distribution functions are in agreement with the results of the parameterization model formulated by Gluck, Reya, and Vogt (GRV) (Phys Rev D 46(5):1973, 1992). Moreover, our numerical results of are comparable with the results achieved by Aurenche, Fontannaz, and Guillet (AFG) (Eur Phys J C Part Fields 44(3):395–409, 2005) and also with the experimental data released by the L3, DELPHI, OPAL, ALEPH and PLUTO collaborations.
© The Author(s), 2020
