Solutions of Coupled DGLAP Evolution Equations for Singlet and Gluon Structure Functions in leading order at low-x

In this paper, we solved the coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for singlet and gluon structure functions in leading order (LO) at low-x assuming the Regge behaviour of quark and gluon structure functions at this limit, and t and x-evolutions of singlet and gluon structure functions are presented. We have compared our results of gluon structure function with global MRST 2004 and GRV 1998 gluon parameterizations and the results of deuteron structure function with New Muon Collaboration (NMC) data. We have shown that the solutions of coupled equations give accurate results for the structure functions and also the compatibility of Regge behaviour of quark and gluon structure functions with perturbative quantum chromodynamics (PQCD) at low-x.Comment: 14 pages, 4 figure

The NNLO QCD analysis of gluon distribution function at small-x

A next-to-next-to-leading order (NNLO) QCD calculation of gluon distribution function at small-x is presented. The gluon distribution function is explored analytically in the DGLAP approach by a Taylor expansion at small x as two first order partial differential equations in two variables : Bjorken x and t (t = ln(Q2/{\Lambda}2) ). We have solved the system of equations at LO, NLO and NNLO respectively by the La- granges method. The resulting analytical expressions are compared with the available global PDF sets as well as with the results of the BDM model. We have further performed a \c{hi}2 test to check the com- patibility of our predictions and observed that our results can be consistently described in the context of perturbative QCD. A comparative analysis of the obtained results at LO, NLO and NNLO reveals that the NNLO approximation has a significant contribution to the gluon distribution function particularly in the small-x region.Comment: 32 pages, 23 figure

Solution of non-singlet DGLAP evolution equation in leading order and next-to-leading order at small-x by method of characteristics

The non-singlet structure functions have been obtained by solving Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations in leading order (LO) and next-to-leading order (NLO) at the small-x limit. Here a Taylor series expansion has been used and then the method of characteristics has been applied to solve the evolution equations. Results are comopared with the Fermilab experiment E665 data and New Muon Collaboration (NMC) data.Comment: 11 pages including 5 figure

Complete solution of Altarelli-Parisi evolution equation in next-to-leading order and non-singlet structure function at low-x

We present complete solution of Altarelli-Parisi (AP) evolution equation in next-to-leading order (NLO) and obtain t-evolution of non-singlet structure function at low-x. Results are compared with HERA low-x and low-Q^2 data and also with those of complete solution in leading order (LO) of AP evolution equation.Comment: 8 pages, 4 figure

Particular and unique solutions of DGLAP evolution equation in leading order and gluon structure function at small-x

We present particular and unique solutions of Dokshitzer- Gribov- Lipatov- Altarelli-Parisi (DGLAP) evolution equation for gluon structure function in leading order (LO) and obtain t and x-evolutions of gluon structure function at small-x. The results are compared with a recent global parameterization.Comment: 16 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:hep-ph/060504

Particular and unique solutions of DGLAP evolution equations and light sea and valence quark structure functions at low-x

We present particular and unique solutions of Dokshitzer-Gribov-Lipatov- Altarelli-Parisi (DGLAP) evolution equations for light sea and valence quark structure functions in leading order (LO). We obtain t evolutions of sea and valence quark structure functions and x- evolutions of light sea quark structure functions from DGLAP evolution equations. The results are compared with a recent global parameterization.Comment: 17 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:hep-ph/0605040, arXiv:1002.1589, arXiv:1002.0623, arXiv:1002.3243, arXiv:1209.422

Gluon distribution at moderately low-x from NMC deuteron structure function data

We present some simple methods to find gluon distribution from analysis of deuteron F_{2} structure function data at moderately low-x. Here we use the leading order(LO) Altarelli -Parisi(AP) evolution equation and New Muon Collaboration (NMC) deuteron F_{2} structure function data to extract gluon distribution. We also compare our results with those of other authors.Comment: 13 pages, 5 figure

Polarized Dokshitzer-Gribov-Lipatov- Altarelli-Parisi equations and t-evolution of structure functions in next-to-leading order at small-x

In this paper the spin-dependent singlet and non-singlet structure functions have been obtained by solving Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations in next-to-leading order in the small x limit. Here we have used Taylor series expansion and then the particular and unique solution to solve the evolution equations. We have also calculated t evolutions of deuteron, proton and neutron structure functions and the results are compared with the SLAC E-143 Collaboration data.Comment: 19 pages, 3 figure

On phenomenological study of the solution of nonlinear GLR-MQ evolution equation beyond leading order

We present a phenomenological study of the small-x behaviour of gluon distribution function $G(x,Q^2)$ at next-to-leading order (NLO) and next-to-next-to-leading order(NNLO) in light of the nonlinear Gribov-Ryskin-Levin-Mueller-Qiu (GLR-MQ)evolution equation by keeping the transverse size of the gluons ($\sim 1/Q$) fixed. We consider the NLO and NNLO corrections, of the gluon-gluon spitting function $P_{gg} (z)$ and strong coupling constant $\alpha_s (Q^2)$. We have suggested semi-analytical solutions based on Regge like ansatz of gluon density $G(x,Q^2)$, which are supposed to be valid in the moderate range of photon virtuality$(Q^2)$ and at small Bjorken variable$(x)$. The study of the effects of nonlinearities that arise due to gluon recombination effects at small-x is very interesting, which eventually tames down the unusual growth of gluon densities towards small-x as predicted by the linear DGLAP evolution equation.Comment: 20 pages, 10 figures, new references adde

Charge density of the electron at higher velocity

Depending on the recent experiments and some new way of explaining electron we have developed here equations for velocities of different mode with the charge density. This includes as well how the charge-density can be distributed in the equatorial region with different velocities and observer-angles.Comment: 7 pages, 6 figure