An improved approximate solution of Altarelli-Parisi equations

Choudhury, D. K.; Saikia, Anup

doi:10.1007/bf02845827

Cited by 15 publications

(8 citation statements)

References 7 publications

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“…We have obtained this description of gluon distribution function ignoring the quark contribution in the evolution equation given by equations (19) and (20). We compare our results of t and x-evolutions of gluon distribution function in LO given by equations (15), (17), (19) and (20) [28] for the starting distribution at Q 0 2 = 1 GeV 2 given by 10 , In figures 4 to 6 we compare our results of x-evolution of gluon distribution function from equations (17) and (20) with GRV '98 parameterization at Q 2 = 20, 40 and 80 GeV 2 respectively. 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.…”

Section: Resultsmentioning

confidence: 99%

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

Jamil

Sarma

2007

Pramana - J Phys

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Abstract. In this paper t and x-evolutions of gluon distribution function from Dokshitzer-GribovLipatov-Altarelli-Parisi (DGLAP) evolution equation in leading order (LO) at low-x, assuming the Regge behaviour of quark and gluon at this limit, are presented. We compare our results of gluon distribution function with MRST 2001, MRST 2004 and GRV '98 parameterizations and show the compatibility of Regge behaviour of quark and gluon distribution functions with perturbative quantum chromodynamics (PQCD) at low-x. We also discuss the limitations of Taylor series expansion method used earlier to solve DGLAP evolution equations, in the Regge behaviour of distribution functions.

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Section: Resultsmentioning

confidence: 99%

“…From equation (10) we can put the value of the constant V = P(x), and equation ( 12) becomes, G(x, t) = K(x)C t P(x) x -λ .…”

Section: Theorymentioning

confidence: 99%

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

Jamil

Sarma

2007

Pramana - J Phys

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“…However, simple forms of such relation are available in literature to facilitate the analytical solution of coupled DGLAP equations. In ref [17], it was assumed that Q 2 dependence of both the distributions are identical. In ref.…”

Section: Singlet Coupled Dglap Equations In Taylor Approximated Formmentioning

confidence: 99%

Comparative analysis of analytical solutions for $F_2^P$ at small $x$ in DGLAP approach

Choudhury,

Borah

2015

Preprint

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Coupled DGLAP equations involving singlet quark and gluon distributions are explored by a Taylor expansion at small x as two first order partial differential equations in two variables : Bjorken x and t (t = ln Q 2 Λ 2 ). The system of equations are then solved by the Lagrange's method and Method of Characteristics. We obtain the proton structure function F P 2 (x, t) by combining the corresponding non-singlet and singlet structure functions by both the methods. Analytical solutions for F P 2 (x, t) thus obtained are compared with the recent data published by H1 and ZEUS as well as with NNPDF3.0 parametrization and their compatibility is checked. Comparative analysis favors the analytical solution by Lagrange's method.

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“…Using Eqs. (12) and (15) in Eq. (18), we get the expression forF L (x, Q 2 ) in terms of the proton structure function only.…”

Section: Longitudinal Structure Function At Small Xmentioning

confidence: 99%

A Lower Bound on Longitudinal Structure Function at Small x from a Self-Similarity Based Model of Proton

Jahan¹,

Choudhury²

2014

Commun. Theor. Phys.

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Self-similarity based model of proton structure function at small x was reported in the literature sometime back. The phenomenological validity of the model is in the kinematical region 6.2 × 10 −7 ≤ x ≤ 10 −2 and 0.045 ≤ Q 2 ≤ 120 GeV 2 . We use momentum sum rule to pin down the corresponding self-similarity based gluon distribution function valid in the same kinematical region. The model is then used to compute bound on the longitudinal structure function F L x, Q 2 for Altarelli-Martinelli equation in QCD and is compared with the recent HERA data.

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An improved approximate solution of Altarelli-Parisi equations

Cited by 15 publications

References 7 publications

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

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

Comparative analysis of analytical solutions for $F_2^P$ at small $x$ in DGLAP approach

A Lower Bound on Longitudinal Structure Function at Small x from a Self-Similarity Based Model of Proton

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