Abstract
The coupled Altarelli-Parisi (AP) equations for polarized singlet quark distribution and polarized gluon distribution, when considered in the small x limit of the next to leading order (NLO) splitting functions, reduce to a system of two first order linear nonhomogeneous integrodifferential equations. We have applied the method of successive approximations to obtain the solutions of these equations. We have applied the same method to obtain the approximate analytic expressions for spin-dependent quark distribution functions with individual flavour and polarized structure functions for nucleon.
Highlights
The study of the evolution of the quark and gluon contributions at small x Bjorken variable towards the spin of the proton through Altarelli-Parisi equations AP 1–3 is an important area of DIS
To obtain the analytical forms of the fourth approximate solutions, we parametrize the results of the third iteration in the range 10−5 x 1 the range of x where LSS’05 numerical results for parton distributions are available by the following effective functional forms: ΔΣ3 x, t LΣ x 1 τ − τ0 τ − τ0 2 2 exp N1 τ − τ0 exp N2 τ − τ0, 3.47
DSSV MS −0.114 we have given a formalism based on the method of successive approximations, for obtaining analytical solutions in the next to leading order NLO, valid in small x region
Summary
The study of the evolution of the quark and gluon contributions at small x Bjorken variable towards the spin of the proton through Altarelli-Parisi equations AP 1–3 is an important area of DIS. There are theoretical arguments that polarized gluon distribution ΔG x and the unpolarized gluon distribution G x are connected through the relation ΔG x ≈ xG x at small x, but they cannot be verified due to lack of data. Precise measurement of the polarized structure function g1 x, Q2 and its logarithmic scale dependence can determine ΔG x at small x and it can reduce the extrapolation uncertainties of ΔG x in the integral ΔG x, Q2. Down to a very small value of 10−4 and it will eventually give the gluon contribution to the spin of the proton over all x to about. The same set of measurements will provide a significantly better determination of the total quark contribution ΔΣ 5 .
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