Non-singlet Structure Function Research Articles

QCD analysis of non-singlet structure functions at NNLO accuracy, based on the Laplace transform

In this work, using the Laplace transformation technique we present our results for non-singlet quark distributions as well as nucleon structure function $F_2(x,Q^2)$ in unpolarized case at next-to-next-to-leading order (NNLO) QCD accuracy. We shall particularly compare our results for the sets of valence-quark parton distribution functions with the contemporary collaborations like CT14, CT18, MMHT14, MKAM16 and NNPDF. To construct the nucleon structure function we employ the expansion of Jacobi polynomials which is a suitable transform to convert the results of non-singlet structure function from the Laplace $s$-space to Bjorken $x$-space. We shall also consider the contributions of target mass correction as well as the higher twist effects at large-$x$ region for the proton and deuteron structure functions. Our results for the unpolarized quark distribution functions and nucleon structure functions are in good agreement with recent theoretical models and available experimental data.

The non-singlet structure function of light and heavy nuclei up to next-to-leading order analysis at low x region

We compute the non-singlet structure function of some various light and heavy nuclei using the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation at leading and next-to-leading order analysis at low x and low and moderate Q2 in x≤0.05 and 1≤Q2≤12 GeV2 region. Using the bounded nuclear parton distribution functions from the HKN parametrization group, we obtain the nuclear non-singlet structure function. Its dynamical behavior as well as nuclear factor are investigated. We compare our results with the new nCTEQ15 set of nuclear parton distribution functions. Our results are in reasonably good agreement with this new global fit.

The Efficient Contour of the Inverse Mellin Transformation for the Non-Singlet Structure Functions

We estimate the accuracy of the reconstruction of the structure function xF3(x,Q2) and the non-singlet combination for the fragmentation function $$D_{u_v }^{\pi ^ + } $$ (z, Q2) used in description of the deep inelastic scattering by the Mellin inverse transformation method with the parabolic shape of contour running from the saddle point proposed by Kosower. We demonstrate the applicability of this contour calculated at some fixed value of momentum transfer squared Q20 for the evaluation of the non-singlet structure functions at any experimental Q2 values.

Analytic derivation of the next-to-leading order proton structure function F2p(x,Q2) based on the Laplace transformation

An analytical solution based on the Laplace transformation technique for the DGLAP evolution equations is presented at next-to-leading order accuracy in perturbative QCD. This technique is also applied to extract the analytical solution for the proton structure function, $F_2^p(x, Q^2)$, in the Laplace $s$-space. We present the results for the separate parton distributions for all parton species, including valence quark densities, the anti-quark and strange sea parton distribution functions (PDFs), and the gluon distribution. We successfully compare the obtained parton distribution functions and the proton structure function with the results from {\tt GJR08} and {\tt KKT12} parametrization models as well as the $x$-space results using {\tt QCDnum} code. Our calculations show a very good agreement with the available theoretical models as well as the deep inelastic scattering (DIS) experimental data throughout the small and large values of $x$. The use of our analytical solution to extract the parton densities and the proton structure function is discussed in detail to justify the analysis method considering the accuracy and speed of calculations. Overall, the accuracy we obtain from the analytical solution using the inverse Laplace transform technique is found to be better than 1 part in 10$^{4}$ to 10$^{5}$. We also present a detailed QCD analysis of non-singlet structure functions using all available DIS data to perform global QCD fits. In this regard we employ the Jacobi polynomial approach to convert the results from Laplace $s$ space to Bjorken $x$ space. The extracted valence quark densities are also presented and compared to the {\tt JR14}, {\tt MMHT14}, {\tt NNPDF} and {\tt CJ15} PDFs sets. We evaluate the numerical effects of target mass corrections (TMCs) and higher twist (HT) terms on various structure functions, and compare fits to data with and without these corrections.

QCD analysis of non-singlet structure functions

We present the results of the leading order (LO) and next-to-leading order (NLO) QCD analysis of experimental data in deep-inelastic scattering which relate to non-singlet structure functions. We use HERAFitter package to study the non-singlet xF 3 structure function. In this regards, we use the non-singlet structure function in x space and we combine CCFR experimental data with NuTeV, CDHSW and CHORUS experimental data as well. Our results at LO and NLO are compatible with the available theoretical models.

XF3(x,Q2) Structure Function and Gross-Llewellyn Smith Sum Rule with Nuclear Effect and Higher Twist Correction**Support from DAE-BRNS, India, as Major Research Project under Sanction No. 2012/37P/36/BRNS/2018 dated 24 Nov. 2012

We present an analysis of the xF3(x,Q2) structure function and Gross-Llewellyn Smith(GLS) sum rule taking into account the nuclear effects and higher twist correction. This analysis is based on the results presented in [N.M. Nath, et al, Indian J. Phys. 90 (2016) 117]. The corrections due to nuclear effects predicted in several earlier analysis are incorporated to our results of xF3(x,Q2) structure function and GLS sum rule for free nucleon, corrected upto next-next-to-leading order (NNLO) perturbative order and calculate the nuclear structure function as well as sum rule for nuclei. In addition, by means of a simple model we have extracted the higher twist contributions to the non-singlet structure function xF3(x,Q2) and GLS sum rule in NNLO perturbative orders and then incorporated them to our results. Our NNLO results along with nuclear effect and higher twist corrections are observed to be compatible with corresponding experimental data and other phenomenological analysis.

The nonsinglet spin-dependent structure function evolution by Laplace and characteristics methods

We evaluate the non-singlet spin-dependent structure function g1NS at leading order (LO) and next-to-leading order (NLO) by using the Laplace-transform technique and method of characteristics and also obtain its first moment at NLO. The polarized non-singlet structure function results are compared with the data from HERMES (A. Airapetian et al., Phys. Rev. D 75, 012007 (2007)) and E143 (K. Abe et al. (E143 Collab.), Phys. Rev. D 58, 112003 (1998)) at LO and NLO analyses and the first-moment the result at NLO is compared with the result of the NLO GRSV2000 fit. Considering the solution, this method is valid at low- and large-x regions.

Results on longitudinal spin physics at COMPASS

The COMPASS experiment at the CERN SPS has taken data on deep inelastic scattering of polarised muons on a polarised NH3 target in 2007 and 2011 and on a polarised LiD target in 2002–2004 and 2006. The new results on the longitudinal double spin asymmetry A 1 p and the spin-dependent structure function g 1 p obtained from the 2011 data set are presented. These results are used in a NLO QCD fit to the world data to obtain the polarised parton distributions. Also an update of the results on the Bjorken sum rule, connecting the integral of the non-singlet spin-dependent structure function with the ratio of the weak coupling constants, will be given.Direct access to the gluon polarisation is possible via the photon gluon fusion process in semi-inclusive deep inelastic scattering. This process is studied using the p T dependence of charged hadron asymmetries. The latest results indicate a positive gluon polarisation in the kinematic region of COMPASS

Non-singlet Q2-evolution by inverse Mellin transform in the analytic perturbation theory

We discuss the application of the analytic approach called the fractional Analytic Perturbation Theory (APT) to the QCD analysis of the non-singlet structure function xF3(x,Q2). The inverse Mellin transform method applyed for the fit of experimental data and for estimation of the Jacobi polynomial method accuracy in extraction of values of the scale parameter ΛQCD and the form of the xF3 structure function. Our estimates give the accuracy of the Jacobi polynomials method for the x-shape of the structure function about 10%, and accuracy for the scale parameter ΛQCD 4%.

The nonsinglet structure function evolution by Laplace method

We derive a general scheme for the evolution of the nonsinglet structure function at the leadingorder (LO) and next-to-leading-order (NLO) by using the Laplace-transform technique. Results for the nonsinglet structure function are compared with MSTW2008, GRV, and CKMT parameterizations and also EMC experimental data in the LO and NLO analysis. The results are in good agreement with the experimental data and other parameterizations in the low- and large-x regions.

The spin structure function [formula omitted] of the proton and a test of the Bjorken sum rule

New results for the double spin asymmetry A1p and the proton longitudinal spin structure function g1p are presented. They were obtained by the COMPASS Collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH3 target. The data were collected in 2011 and complement those recorded in 2007 at 160 GeV, in particular at lower values of x. They improve the statistical precision of g1p(x) by about a factor of two in the region x≲0.02. A next-to-leading order QCD fit to the g1 world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, ΔΣ, ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of g1p. The uncertainty of ΔΣ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function g1NS(x,Q2) yields as ratio of the axial and vector coupling constants |gA/gV|=1.22±0.05 (stat.)±0.10 (syst.), which validates the sum rule to an accuracy of about 9%.

Regge-like initial input and evolution of non-singlet structure functions from DGLAP equation up to next-next-to-leading order at low x and low Q 2

This is an attempt to study how the features of Regge theory, along with QCD predictions, lead towards the understanding of unpolarized non-singlet structure functions \(F_{2}^{\text {NS}} (x,Q^{2} )\) and xF3(x,Q2) at low x and low Q2. Combining the features of perturbative quantum chromodynamics (pQCD) and Regge theory, an ansatz for \(F_{2}^{\text {NS}} (x,Q^{2})\) and xF3(x,Q2) structure functions at small x was obtained, which when used as the initial input to Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) equation, gives the Q2 evolution of the non-singlet structure functions. The non-singlet structure functions, evolved in accordance with DGLAP evolution equations up to next-next-to-leading order are studied phenomenologically in comparison with the available experimental and parametrization results taken from NMC, CCFR, NuTeV, CORUS, CDHSW, NNPDF and MSTW Collaborations and a very good agreement is observed in this regard.

The Nonsinglet Structure Function Evolution by Laplace Method

The Nonsinglet Structure Function Evolution by Laplace Method

Non-singlet structure function FNS2 (x,t) in DGLAP approach

In this work the non-singlet structure function FNS2(x, t) have been obtained by solving DGLAP evolution equation in leading order (LO) at the small x limit. Here we have used a Taylor series expansion and then the method of characteristics and Lagrange's method to solve the evolution equations. We make a detailed comparison of the predictions of the two methods with two different levels of approximations with experimental data as well as with numerical solutions.

An improved analysis of the x distribution of a non-singlet structure function

Using Lagrange’s auxiliary method, we find the most general solution of the non-singlet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation at low x in the leading order and find analytical expressions for xF 3. Comparisons with Chicago-Columbia-Fermilab-Rochester (CCFR) neutrino data and with exact results are also made.

Non-singlet spin structure function $g_{1}^{\rm NS}(x,t)$ in the DGLAP approach

An analytical solution of the non-singlet polarized parton distribution Δq NS(x,Q 2) = (Δu(x,Q 2) − Δd(x,Q 2)) is obtained by solving the DGLAP (Gribov and Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972); Lipatov, ibid, 20, 94 (1975); Dokshitzer, Sov. Phys. JETP 46, 641 (1997); Altarelli and Parisi, Nucl. Phys. B126, 298 (1977)) equation by the method of characteristics. We then evaluate the non-singlet spin-dependent structure function $g_1^{\rm NS}$ . The result is compared with the data from HERMES (Airapetian et al, Phys. Rev. D75, 012007 (2007)).

Solution of singlet and non-singlet unpolarized DGLAP evolution equations in next-to-next-to-leading order (NNLO) by method of characteristics

In this paper, the singlet and non-singlet structure functions have been obtained by solving Dokshitzer, Gribov, Lipatov, Altarelli, Parisi evolution equations in next-to- next-to-leading order at the small x limit. Here we have used Taylor Series expansion and then the method of characteristics to solve the evolution equation. We have also calculated t and x-evolutions of deuteron structure function as well as non singlet structure function and the results have been compared with the New Muon Collaboration, E665 experimental data, CLAS Collaboration and NNPDF Collaboration data.

An analysis of non-singlet structure function in next-to-next-to-leading order at small-x

A more general form of non-singlet structure function in Next-to-Next-to-leading order (NNLO) by solving Dokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP) equation at small-x is obtained. Results are compared with Fermi Lab Experiment E665 data.

DGLAP evolution equation in NNLO at small-x and method of characteristics: non-singlet case

The non-singlet structure functions have been obtained by solving Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations in next-next-to-leading order (NNLO) at the small-x limit. Here a Taylor series expansion has been used and then applied the method of characteristics to solve the evolution equations. Results are compared with the Fermi Lab experiment E665 data and New Muon Collaboration (NMC) data.

Nonsinglet spin-dependent structure functions

We investigate the nonsinglet spin-dependent structure function for polarized deep inelastic scattering (DIS) of leptons on nucleons in the next-to-leading-order (NLO) approximation. We perform a fit to extract the polarized parton distribution functions (PPDFs) and the nonsinglet spin structure function using the most recent proton and neutron DIS data. We demonstrate that our results yield good agreement with available observables.