Target Mass Corrections Research Articles

Study of spin-dependent structure functions of He3 and H3 at NNLO approximation and corresponding nuclear corrections

We determine polarized parton distribution functions (PPDFs) and structure functions from recent experimental data of polarized deep inelastic scattering (DIS) on nuleons at next-to-next-to-leading order (NNLO) approximation in perturbative quantum chromodynamic (pQCD). The nucleon polarized structure functions are computed using the Jacobi polynomial approach while target mass corrections (TMCs) are included in our fitting procedure. Having extracted the polarized spin structure functions, we extend our study to describe $^3{\mathrm He}$ and $^3{\mathrm H}$ polarized structure functions, as well as the Bjorken sum rule. We also explore the importance of the nuclear corrections on the polarized nuclear structure functions at small and large values of $x$. Our results are compared with the recent available and high precision polarized $^3{\mathrm He}$ and $^3{\mathrm H}$ experimental data.

Target mass effects in parton quasi-distributions

We study the impact of non-zero (and apparently large) value of the nucleon mass M on the shape of parton quasi-distributions Q(y,p3), in particular on its change with the change of the nucleon momentum p3. We observe that the usual target-mass corrections induced by the M-dependence of the twist-2 operators are rather small. Moreover, we show that within the framework based on parametrizations by transverse momentum dependent distribution functions (TMDs) these corrections are canceled by higher-twist contributions. We identify a novel source of kinematic target-mass dependence of TMDs and build models corrected for such dependence. We find that resulting changes may be safely neglected for p3≳2M.

Nucleon spin structure functions at NNLO in the presence of target mass corrections and higher twist effects

We extract polarized parton distribution functions (PPDFs), referred to as "KTA17," together with the highly correlated strong coupling $\alpha_s$ from recent and up-to-date $g_1$ and $g_2$ polarized structure functions world data at next-to-next-to-leading order in perturbative QCD. The stability and reliability of the results are ensured by including nonperturbative target mass corrections as well as higher-twist terms which are particularly important at the large-$x$ region at low Q$^2$. Their role in extracting the PPDFs in the nucleon is studied. Sum rules are discussed and compared with other results from the literature. This analysis is made by means of the Jacobi polynomials expansion technique to the DGLAP evolution. The uncertainties on the observables and on the PPDFs throughout this paper are computed using standard Hessian error propagation which served to provide a more realistic estimate of the PPDFs uncertainties.

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.

Problem of kinematic mass corrections for unpolarized semi-inclusive deep inelastic scattering

Miraculously, target mass corrections for inclusive deep inelastic scattering can be calculated exactly. On the contrary, there does not exist a consistent derivation of kinematic hadron mass corrections for semi-inclusive deep inelastic scattering (SIDIS). Recently this has become of topical interest, since there is a significant difference between the measured HERMES and COMPASS pion and kaon multiplicities, which cannot be explained as a consequence of evolution in $Q^2$, and it has been suggested that the difference can be understood if kinematic hadron mass corrections are taken into account. We explain why this argument is incorrect.

The complete [formula omitted] non-singlet heavy flavor corrections to the structure functions [formula omitted], [formula omitted], [formula omitted] and the associated sum rules

We calculate analytically the flavor non-singlet O(αs2) massive Wilson coefficients for the inclusive neutral current non-singlet structure functions F1,2,Lep(x,Q2) and g1,2ep(x,Q2) and charged current non-singlet structure functions F1,2,3ν(ν¯)p(x,Q2), at general virtualities Q2 in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross–Llewellyn Smith sum rule. There are no logarithmic corrections at large scales Q2 and the effects of the power corrections due to the heavy quark mass are of the size of the known O(αs4) corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region Q2≫mc,b2. We also study the target mass corrections to the above sum rules.

Neutrino-nucleon cross sections at energies of Megaton-scale detectors

An updated set of (anti)neutrino-nucleon charged and neutral current cross sections at $3~{\rm GeV} \lesssim E_\nu \lesssim 100~{\rm GeV}$ is presented. These cross sections are of particular interest for the detector optimization and data processing and interpretation in the future Megaton-scale experiments like PINGU, ORCA, and Hyper-Kamiokande. Finite masses of charged leptons and target mass corrections in exclusive and deep inelastic $(\bar\nu)\nu N$ interactions are taken into account. A new set of QCD NNLO parton density functions, the ABMP15, is used for calculation of the DIS cross sections. The sensitivity of the cross sections to phenomenological parameters and to extrapolations of the nucleon structure functions to small $x$ and $Q^2$ is studied. An agreement within the uncertainties of our calculations with experimental data is demonstrated.

Interplay of threshold resummation and hadron mass corrections in deep inelastic processes

We discuss hadron mass corrections and threshold resummation for deep-inelastic scattering $\ell N\rightarrow\ell' X$ and semi-inclusive annihilation $e^+e^-\rightarrow h X$ processes, and provide a prescription how to consistently combine these two corrections respecting all kinematic thresholds. We find an interesting interplay between threshold resummation and target mass corrections for deep-inelastic scattering at large values of Bjorken $x_B$. In semi-inclusive annihilation, on the contrary, the two considered corrections are relevant in different kinematic regions and do not affect each other. A detailed analysis is nonetheless of interest in the light of recent high precision data from BaBar and Belle on pion and kaon production, with which we compare our calculations. For both deep inelastic scattering and single inclusive annihilation, the size of the combined corrections compared to the precision of world data is shown to be large. Therefore, we conclude that these theoretical corrections are relevant for global QCD fits in order to extract precise parton distributions at large Bjorken $x_B$, and fragmentation functions over the whole kinematic range.

Publisher’s Note: Target mass corrections and higher twist effects in polarized deep-inelastic scattering [Phys. Rev. D89, 074052 (2014)

Publisher’s Note: Target mass corrections and higher twist effects in polarized deep-inelastic scattering [Phys. Rev. D<b>89</b>, 074052 (2014)

Target mass corrections and higher twist effects in polarized deep-inelastic scattering

We perform a next-to-leading-order QCD analysis to world data on polarized structure functions $g_1$ and $g_2$ in a fixed-flavor number scheme. We include target mass corrections and higher twist effects in our fitting procedure and study their non-negligible effects on physically interesting quantities. Twist-3 contributions to both polarized structure functions are determined, and the accuracy of the extracted polarized parton distribution functions is improved. $^{3}\rm He$ and $^{3}\rm H$ polarized structure functions are described based on our fit result. Moreover, sum rules are derived and compared with available theoretical and experimental results.

Delineating parton distributions and the strong coupling

Global fits for precision determinations of parton distributions, together with the highly correlated strong coupling ${\ensuremath{\alpha}}_{s}$, are presented up to next-to-next-to-leading order (NNLO) of QCD utilizing most world data (charm and jet production data are used where theoretically possible), except Tevatron gauge boson production data and LHC data which are left for genuine predictions. This is done within the ``dynamical'' (valence-like input at ${Q}_{0}^{2}=0.8\text{ }\text{ }{\mathrm{GeV}}^{2}$) and ``standard'' (input at ${Q}_{0}^{2}=2\text{ }\text{ }{\mathrm{GeV}}^{2}$) approach. The stability and reliability of the results are ensured by including nonperturbative higher-twist terms, nuclear corrections as well as target mass corrections, and by applying various (${Q}^{2}$, ${W}^{2}$) cuts on available data. In addition, the ${Q}_{0}^{2}$ dependence of the results is studied in detail. Predictions are given, in particular for the LHC, for gauge- and Higgs-boson as well as for top-quark pair production. At NNLO the dynamical approach results in ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})=0.1136\ifmmode\pm\else\textpm\fi{}0.0004$, whereas the somewhat less constrained standard fit gives ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})=0.1162\ifmmode\pm\else\textpm\fi{}0.0006$.

Impact of hadronic and nuclear corrections on global analysis of spin-dependent parton distributions

We present the first results of a new global next-to-leading order analysis of spin-dependent parton distribution functions from the most recent world data on inclusive polarized deep-inelastic scattering, focusing in particular on the large-x and low-Q^2 regions. By directly fitting polarization asymmetries we eliminate biases introduced by using polarized structure function data extracted under nonuniform assumptions for the unpolarized structure functions. For analysis of the large-x data we implement nuclear smearing corrections for deuterium and 3He nuclei, and systematically include target mass and higher twist corrections to the g_1 and g_2 structure functions at low Q^2. We also explore the effects of Q^2 and W^2 cuts in the data sets, and the potential impact of future data on the behavior of the spin-dependent parton distributions at intermediate and large x.

The impact of target mass correction on polarized parton distribution functions

Considering the nonzero mass effect of the target in extracting polarized parton distribution functions (PPDFs) in preasymptotic region is not negligible. We extract PPDFs from available proton structure function data and study the numerical effects of target mass corrections (TMCs). PPDFs with and without this correction are compared.

EXTRACTIONS OF POLARIZED AND UNPOLARIZED PARTON DISTRIBUTION FUNCTIONS

An overview of our ongoing extractions of parton distribution functions of the nucleon is given. First JAM results on the determination of spin-dependent parton distribution functions from world data on polarized deep-inelastic scattering are presented first, and followed by a short report on the status of the JR unpolarized parton distributions. Different aspects of PDF analysis are briefly discussed, including effects of the nuclear structure of targets, target-mass corrections and higher twist contributions to the structure functions.

Target Mass Corrections to QCD Bjorken Sum Rule for Nucleon Spin Structure Functions

We discuss the possible target mass corrections in the QCD analysis of nucleon's spin-dependent structure functions measured in the polarized deep-inelastic leptoproduction. The target mass correction for the QCD Bjorken sum rule is obtained from the Nachtmann moment and its magnitude is estimated employing positivity bound as well as the experimental data for the asymmetry parameters. We also study the uncertainty due to target mass effects in determining the QCD effective coupling constant $\alpha_s(Q^2)$ from the Bjorken sum rule. The target mass effect for the Ellis-Jaffe sum rule is also briefly discussed.

Global parton distributions with nuclear and finite-Q2corrections

We present three new sets of next-to-leading order parton distribution functions (PDFs) determined by global fits to a wide variety of data for hard scattering processes. The analysis includes target mass and higher twist corrections needed for the description of deep inelastic scattering data at large x and low Q^2, and nuclear corrections for deuterium targets. The PDF sets correspond to three different models for the nuclear effects, and provide a more realistic uncertainty range for the d quark PDF, in particular, compared with previous fits. We describe the PDF error sets for each choice of the nuclear corrections, and provide a user interface for utilizing the distributions.

Parton distributions in the presence of target mass corrections

We study the consistency of parton distribution functions in the presence of target mass corrections (TMCs) at low Q^2. We review the standard operator product expansion derivation of TMCs in both x and moment space, and present the results in closed form for all unpolarized structure functions and their moments. To avoid the unphysical region at x > 1 in the standard TMC analysis, we propose an expansion of the target mass corrected structure functions order by order in M^2/Q^2, and assess the convergence properties of the resulting forms numerically.

Erratum to: Target mass correction on the 3He polarized structure function

Erratum to: Target mass correction on the 3He polarized structure function

Erratum: Next-to-leading order analysis of target mass corrections to structure functions and asymmetries [Phys. Rev. D84, 074008 (2011)

Erratum: Next-to-leading order analysis of target mass corrections to structure functions and asymmetries [Phys. Rev. D<b>84</b>, 074008 (2011)

Finite-[formula omitted] and target mass corrections in off-forward hard reactions

We describe a systematic approach (Braun and Manashov (2011) [24]) to the calculation of kinematic corrections ∝t/Q2,m2/Q2 in hard exclusive processes which involve momentum transfer from the initial to the final hadron state. As an example, the complete expression is derived for the time-ordered product of two electromagnetic currents that includes all kinematic corrections due to the quark distribution to twist-four accuracy. The results are applicable e.g. to the studies of deeply-virtual Compton scattering.