Abstract
In this paper, we present {\tt SMKA18} analysis which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton $g_1^{p}(x, Q^2)$, neutron $g_1^{n}(x, Q^2)$ and deuteron $g_1^{d}(x, Q^2)$ spin-dependent structure functions dataset including the most recent high-precision measurements from {\tt COMPASS16} experiments at CERN which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard 'Hessian error' propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering dataset and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of $x$.
Highlights
We present SMKA18 analysis, which is a first attempt to extract the set of next-to-nextleading-order (NNLO) spin-dependent parton distribution functions and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach
Before starting our detailed discussions on SMKA18 spindependent parton distribution functions (PDFs) determinations, we would like to illustrate the present status of spin-dependent PDF sets at NLO and NNLO QCD approximations and discuss some differences, briefly, which are clearly visible
The detailed study of the spin-dependent PDFs of the nucleon and the spin structure of hadron are active interdisciplinary research field lying at the crossroads of high-energy hadronic and nuclear physics, with important applications in Large Hadron Collider (LHC) phenomenology
Summary
The structure of hadrons, unpolarized parton distribution functions (PDFs) [1,2,3,4,5,6,7,8,9,10,11,12,13,14] and spin-dependent PDFs dynamics [15,16,17,18,19,20,21], is an interesting topic, which continues to attract more attention from large physics communities [22]. Using the available and up-to-date data sets, many various global QCD analyses of nucleon spin structure at next-toleading (NLO) accuracy have been completed recently These spin-dependent PDF analyses incorporate NNPDF Collaboration NNDPFpol1.1 [15], DSSV09 [36], Asymmetry Analysis Collaboration AAC09 [37], BB10 [38], LSS10 [39], DSSV14 [40], and the recent analyses from Jefferson Lab (JAM) Collaboration (JAM13 [16], JAM14 [17], JAM15 [18]), and the most recent next-to-next-leading-order (NNLO) QCD analyses from TKAA16 [19], KTA-I-17 [20], and KTA-II-17 [21]. Appendix B includes the coefficient functions of singlet distributions in the Laplace space
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