QCD analysis of nucleon structure functions in deep-inelastic neutrino-nucleon scattering: Laplace transform and Jacobi polynomials approach

Abstract

We present a detailed QCD analysis of nucleon structure functions xF3(x, Q 2 ), based on Laplace transforms and Jacobi polynomials approach. The analysis corresponds to the next-to-leading order and next-to-next-to-leading order approximation of perturbative QCD. The Laplace transform technique, as an exact analytical solution, is used for the solution of nonsinglet Dokshitzer-GribovLipatov-Altarelli-Parisi evolution equations at low-and large-x values. The extracted results are used as input to obtain the x and Q 2 evolution of xF3(x, Q 2 ) structure functions using the Jacobi polynomials approach. In our work, the values of the typical QCD scale Λ (n f ) MSand the strong coupling constant αs(M 2 Z ) are determined for four quark flavors (n f = 4) as well. A careful estimation of the uncertainties shall be performed using the Hessian method for the valence-quark distributions, originating from the experimental errors. We compare our valence-quark parton distribution functions sets with those of other collaborations; in particular with the BBG, CT14, MMHT14 and NNPDF sets, which are contemporary with the present analysis. The obtained results from the analysis are in good agreement with those from the literature.

EMC effect in the next-to-leading order approximation based on the Laplace transformation

“…But since in heavy nuclei the number of the neutrons is larger than the number of protons (N > Z), as can be seen in Eq. (20), the distribution of down valence quarks would be greater than that of up valence quarks. Following that, it can be seen, as well, that in this type of the nuclei, antiquark distributions (u A , d A , s A )…”

“…To access the PDFs and then nPDFs, it is required to get the solution of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations [6][7][8][9].DGLAP using the Laplace transform technique, some analytical solutions of these equations have been reported in recent * J.Sheibani@stu.yazd.ac.ir † A.Mirjalili@yazd.ac.ir (Corresponding Author) ‡ Atashbart@gmail.com years [10][11][12][13][14][15][16][17][18] ,which have resulted in noticeable success from the phenomenological point of view. There has also been some progress toward extracting the analytical solutions of the proton spin-independent structure function F p 2 (x, Q 2 ) [19], charged-current structure functions xF 3 (x, Q 2 ) [20], and also the spin-dependent one, i.e., xg p 1 (x, Q 2 ), at the next-to-leading order (NLO) and next-to-NLO (NNLO) approximations [21,22], using the Laplace transform technique.…”

Probing nuclear modifications of parton distribution functions through the isolated prompt photon production at energies available at the CERN Large Hadron Collider

“…In this approach, for determining the nuclear modifications one needs to fix the free-proton PDFs form an analysis already performed on the nucleon experimental data [1][2][3][4][5][6][7][8][9][10][11]. However, there is another approach in which the nPDFs are parametrised directly as a function of…”

“…In this work, we are going to perform a comprehensive study of the isolated prompt photon production in p-Pb collisions at backward rapidities to find the best kinematic regions in which the experimental measurements have most sensitivity to the nuclear modifications of parton densities.Most emphasis will be placed on the antishadowing nuclear modification. To this aim, we calculate and compare various quantities at different values of center-of-mass energy covered by the LHC and also different rapidity regions to realize which one is most useful.Besides the parton distribution functions (PDFs), whether unpolarized [1][2][3][4][5][6][7][8][9][10][11] or polarized [12][13][14][15][16][17][18], and fragmentation functions (FFs) [19][20][21][22][23], the nuclear modifications of PDFs [24][25][26][27][28][29][30][31] are also important ingredients of high energy physics calculations, in particular, for processes involving nuclei in the initial state. In fact, without having nuclear PDFs (nPDFs) which describe the structure of the colliding nuclei, the theoretical calculation of the cross sections in any nuclear collision will not be possible.…”

Study of the s−s¯ asymmetry in the proton

“…It is well known now that the factorisation theorem of Quantum Chromodynamics (QCD) [1,2] can provide a powerful tool for calculating cross sections of high energy processes, by dividing them to perturbative and nonperturbative parts. In this respect, the nonperturbative objects such as the parton distribution functions (PDFs) [3,4,5,6,7,8,9,10,11,12,13], polarized PDFs [14,15,16,17,18,19,20], nuclear PDFs [21,22,23,24,25], and fragmentation functions (FFs) [26,27,28,29] play an essential role for testing QCD, describing the experimental data, and searching New Physics. Among them, the PDFs have always been of particular importance.…”