Evolution of singlet structure functions from DGLAP equation at next-to-next-to-leading order at small-x

We observe that the DGLAP evolution equations at NNLO analysis predicts a ratio of the structure functions in region of small Bjorken variable x. The ratio FL(x, Q 2 )/F2(x, Q 2 ) is obtained and compared with the prediction of the dipole model and HERA data. In particular we show that this ratio is lower than dipole model bound at high-Q 2 values and it is higher at low-Q 2 values . Then the effect of adding a higher twist term to the description of the ratio FL(x, Q 2 )/F2(x, Q 2 ) for Q 2 < 20 GeV 2 is investigated. Also the bounds are discussed by including charm distribution on FL/F2. We discuss, furthermore, how this ratio can be determine the proton structure function with respect to the reduced cross section at high-y values.

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“…To solve Eq. (14) one needs to define an relation between the exponents and distribution functions as [20][21][22]. Thus we can rewrite Eq.…”

Section: Formalismmentioning

confidence: 99%

Ratio of the structure functions and the color dipole model bound

Boroun

Rezaei

2019

Nuclear Physics A

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“…A Taylor series expansion method to solve the evolution equations is also presented in Ref. [33] up to NNLO for the small value of Bjorken-x. Among various methods of solving the DGLAP equations, M. Hirai et al [34] employed a brute-force method [35] for the spin-independent case.…”

Section: Amentioning

confidence: 99%

QCD analysis of nucleon structure functions in deep-inelastic neutrino-nucleon scattering: Laplace transform and Jacobi polynomials approach

Nejad

Khanpour

Tehrani³

et al. 2016

Phys. Rev. C

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We present a detailed QCD analysis of nucleon structure functions xF3(x, Q 2 ), based on Laplace transforms and Jacobi polynomials approach. The analysis corresponds to the next-to-leading order and next-to-next-to-leading order approximation of perturbative QCD. The Laplace transform technique, as an exact analytical solution, is used for the solution of nonsinglet Dokshitzer-GribovLipatov-Altarelli-Parisi evolution equations at low-and large-x values. The extracted results are used as input to obtain the x and Q 2 evolution of xF3(x, Q 2 ) structure functions using the Jacobi polynomials approach. In our work, the values of the typical QCD scale Λ (n f ) MSand the strong coupling constant αs(M 2 Z ) are determined for four quark flavors (n f = 4) as well. A careful estimation of the uncertainties shall be performed using the Hessian method for the valence-quark distributions, originating from the experimental errors. We compare our valence-quark parton distribution functions sets with those of other collaborations; in particular with the BBG, CT14, MMHT14 and NNPDF sets, which are contemporary with the present analysis. The obtained results from the analysis are in good agreement with those from the literature.

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“…respectively. Where = ln elsewhere earlier [17][18][19][20][21][22][23]. we can expand the term � , � applying Taylor expansion method as…”

Section: Theorymentioning

confidence: 99%

“…Similarly by introducing more terms of Taylor expansion, we hope the same. Moreover, for the smaller values of x, the terms in the expansion containing 2 and higher powers of can be neglected [17][18][19][20][21][22][23]. Thus using the first two terms of the Taylor expansion series we can write…”

Section: Theorymentioning

confidence: 99%

“…In this paper we have obtained the 3 ( , 2 ) structure function by solving the DGLAP evolution equation analytically in leading-order (LO) and next-to-leading order (NLO) at small-x using the Taylor series expansion method which was developed in Ref. [17][18][19][20][21][22][23]. Application of Tailor series expansion method reduces the integro-differential DGLAP equation to the first-order linear differential equation, which in turn can be solved easily.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solution of DGLAP Evolution Equation for xF<sub>3</sub> Structure Function in Leading and Next-to-Leading Order at Small-x

Nath¹,

Baruah²,

Sarma³

et al. 2014

ujpa

Self Cite

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This report attempts to the phenomenological study of the charged-current neutrino deep-inelastic scattering (DIS) within the perturbative QCD framework. The study is based on the solution of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation in leading and next-to-leading order at small-x for parity-violating DIS structure function 3 ( , 2 ) by means of Taylor expansion method. The solutions are analyzed phenomenologically in comparison with the experimental data taken from CCFR, NuTeV, CHORUS and CDHSW collaborations.

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Evolution of singlet structure functions from DGLAP equation at next-to-next-to-leading order at small-x

Cited by 38 publications

References 61 publications

Ratio of the structure functions and the color dipole model bound

Ratio of the structure functions and the color dipole model bound

QCD analysis of nucleon structure functions in deep-inelastic neutrino-nucleon scattering: Laplace transform and Jacobi polynomials approach

Solution of DGLAP Evolution Equation for xF<sub>3</sub> Structure Function in Leading and Next-to-Leading Order at Small-x

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