A solution of the DGLAP equation for gluon at low x

Abstract

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate ∂ F 2´x Q 2 µ ∂ ln Q 2 using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.

An Analysis of Momentum Fractions of Quarks and Gluons in a Model of Proton

“…Q 2 s = 5.58 × 10 23 GeV 2 (for a = 1) and Q 2 s = 5.43 × 10 6 GeV 2 (for a = 3.1418), the quarks with momentum fractions 6.2 × 10 −7 ≤ x ≤ 10 −2 would populate the entire proton and the model will fall short of accounting momentum sum rule beyond it. The momentum sum rule inequality (Eq (4)) can similarly be applied to nucleon models [15] based on approximate solution of DGLAP equation [16] valid at small x. The correspondence between the results of the present model and QCD asymptotics has also been highlighted.…”

Regge behaviour of distribution functions and t and x-evolutions of gluon distribution function at low-x

“…We compare our results in the range 10 −5 ≤x≤10 −1 and we get a very good fit of our result to the GRV '98 parameterization. In some recent papers [41] Choudhury and Saharia, presented a form of gluon distribution function at low-x obtained from a unique solution with one single initial condition through the application of the method of characteristics [42]. They have overcome the limitations of non-uniqueness of some of the earlier approaches [15].…”

An Analytical Study of the Nonsinglet Spin Structure Functiong1NS(x,t)Up to NLO in the DGLAP Approach at SmallBorah1, Choudhury2 2014Advances in High Energy Physics

“…The spin-dependent DGLAP [1][2][3][4] evolution equations provide us the basic framework to study the polarized quark and gluon structure functions which finally give us polarized proton and neutron structure functions. Apart from the discussions about the numerical solutions [5][6][7][8][9][10][11][12][13][14][15][16][17] of DGLAP equations, analytical approaches towards these evolution equations at small are also available in literature [18][19][20][21][22][23] with reasonable phenomenological success.…”