https://doi.org/10.1140/epjc/s10052-019-7118-4
Regular Article - Theoretical Physics
A phenomenological investigation of the integral and the differential versions of the 
–
–
parton distribution functions using two different constraints and the 
1
Physics Department, Faculty of Science, Bu-Ali Sina University, Hamedan, 65178, Iran
2
Physics Department, University of Tehran, Tehran, 1439955961, Iran
* e-mail: n_olanj@basu.ac.ir
Received:
13
May
2019
Accepted:
8
July
2019
Published online:
20
July
2019
We previously investigated the compatibility of the –– (
) parton distribution functions (
) with the experimental data on the proton (longitudinal) structure functions (
(
)). Recently 
and 
(
) demonstrated that the differential version of prescription and the implementations of angular (strong) ordering (
(
)) constraints, cause the negative-discontinuous with the ordinary parton distribution functions () as the input, which leads to a sizable effect on the calculation of . In the present work, we use the new 
-
- as the input and focus on the behaviors as was raised by . The resulting and are compared with the 
-- and 
- and the 2014 data given by the 
and 
collaborations. The calculated and based on the integral prescription of the - with the and the ordinary as the input are reasonably consistent with the experimental data. Therefore, they are approximately independent to the (no need to impose cutoff on the ). At very small x regions because of the excess of gluons in the -- and --, an increase in and is achieved. Finally, according to the report the differential version by using the cutoff independent produces results far from the experimental data.
© The Author(s), 2019
