Target Mass Corrections Research Articles

QCD analysis of valence structure functions using deep inelastic lepton-nucleon scattering

A new “” nonsinglet QCD analysis of the structure functions at the NNLO approximation is performed, utilizing the global fit of the data from various charged lepton scattering experiments. We extract the valence parton distribution functions (PDFs) and provide a parametrization of them, along with the correlated errors for a wide range of x and Q2. We compare valence PDFs and their uncertainties with those from different PDF sets provided by various groups. We also obtain valence PDFs and the strong coupling constant αs(MZ2), taking into account the nuclear correction concerning large x as well as the target mass correction (TMC) and higher twist (HT) effects at the NNLO. In the large x region, we extract the higher twist contributions of xF3(x,Q2), F2p(x,Q2), and F2d(x,Q2). We determine αs(MZ2) without and with considering the TMC and HT corrections and perform a comparison with the world average of αs(MZ2) and other reported results. The extracted results concerning valence PDFs with their uncertainties and αs(MZ2) value agree with available theoretical models. Published by the American Physical Society 2024

Collinear matching for next-to-leading power transverse-momentum distributions

Phenomenological studies of transverse momentum dependent (TMD) parton distributions rely on the expansion in small values of the transverse separation of fields, where TMD parton distributions match onto collinear parton distribution functions. In this work, we derive this expansion at tree-level for the genuine next-to-leading power quark-gluon-quark TMDs, taking into account all the target mass corrections. We find that only a limited number of TMD parton distributions exhibit matching to twist-three collinear distributions, leading to a significant simplification in the analysis of the structure functions of semi-inclusive deep inelastic scattering.

Kinematical higher-twist corrections in γ*→M1M2γ : Neutral meson production

We carry out the calculation of kinematical higher-twist corrections to the cross section of $\gamma^* \to M_1 M_2 \gamma$ up to twist 4, where $M_i$ is a scalar or pseudoscalar neutral meson. The three independant helicity amplitudes are presented in terms of the twist-2 generalized distribution amplitudes (GDAs), which are important non-perturbative quantities for understanding the 3D structure of hadrons. Since this process can be measured by BESIII in $e^+ e^-$ collisions, we perform the numerical estimate of the kinematical higher-twist corrections by using the kinematics of BESIII. We adopt the $\pi \pi$ GDA extracted from Belle measurements and the asymptotic $\pi \pi$ GDA to study the size of the kinematical corrections in the case of pion meson pair, and a model $\eta \eta$ GDA is used to see the impact of target mass corrections $\mathcal O(m^2/s)$ for $\gamma^* \to \eta \eta \gamma$. Our results show that the kinematical higher-twist corrections account for $\sim 20\%$ of the cross sections at BESIII on the average, and it is necessary to include them if one tries to extract GDAs from experimental measurements precisely. We also comment the case of $\pi^0 \eta$ production which is important for the search of hybrid mesons.

Next-to-leading-power kinematic corrections to DVCS: a scalar target

Using the recent results on the contributions of descendants of the leading twist operators to the operator product expansion of two electromagnetic currents we derive explicit expressions for the kinematic finite-t and target mass corrections to the DVCS helicity amplitudes to the 1/Q4 power accuracy. The cancellation of IR divergences for kinematic corrections is demonstrated to all powers in the leading order of perturbation theory. We also argue that target mass corrections in the coherent DVCS from nuclei are small and do not invalidate the factorization theorem.

Kinematical higher-twist corrections in γ*γ→MM¯

We estimate kinematical higher-twist (up to twist 4) corrections to the ${\ensuremath{\gamma}}^{*}({q}_{1})\ensuremath{\gamma}({q}_{2})\ensuremath{\rightarrow}M({p}_{1})\overline{M}({p}_{2})$ amplitudes at large ${Q}^{2}=\ensuremath{-}{q}_{1}^{2}$ and small $s=({q}_{1}+{q}_{2}{)}^{2}$, where $M$ is a scalar or pseudoscalar meson. This process is known to factorize at leading twist into a perturbatively calculable coefficient function and generalized distribution amplitudes (GDAs). The kinematical higher-twist contributions of order $s/{Q}^{2}$ and ${m}^{2}/{Q}^{2}$ turn out to be important in the cross section, considering the kinematics accessible at Belle and Belle II. We present numerical estimates for the cross section for ${\ensuremath{\gamma}}^{*}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ with the $\ensuremath{\pi}\ensuremath{\pi}$ GDA extracted from Belle measurements and with the asymptotic $\ensuremath{\pi}\ensuremath{\pi}$ GDA as inputs to study the magnitude of the kinematical corrections. To see how the target mass corrections of order ${m}^{2}/{Q}^{2}$ affect the cross section, we also perform the calculation for ${\ensuremath{\gamma}}^{*}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\eta}$ by using a model $\ensuremath{\eta}\ensuremath{\eta}$ GDA. In the range $s>1\text{ }\text{ }{\mathrm{GeV}}^{2}$, the kinematical higher-twist corrections account for $\ensuremath{\sim}15%$ of the total cross section, an effect which is not negligible. Since $\ensuremath{\pi}\ensuremath{\pi}$ GDAs are the best way to access the pion energy-momentum tensor (EMT), our study demonstrates that an accurate evaluation of EMT form factors requires the inclusion of kinematical higher-twist contributions.

Nuclear effects in the deuteron and global QCD analyses

We report the results of a new global QCD analysis, which includes deep-inelastic $e/\mu$ scattering data off proton and deuterium, as well as Drell-Yan lepton pair production in proton-proton and proton-deuterium collisions and $W^\pm/Z$ boson production data from $pp$ and $p \bar p$ collisions at the LHC and Tevatron. Nuclear effects in the deuteron are treated in terms of a nuclear convolution approach with bound off-shell nucleons within a weak binding approximation. The off-shell correction is controlled by a universal function of the Bjorken variable $x$ describing the modification of parton distributions in bound nucleons, which is determined in our analysis along with the parton distribution functions of the proton. A number of systematic studies are performed to estimate the uncertainties arising from the use of various deuterium datasets, from the modeling of higher twist contributions to the structure functions, from the treatment of target mass corrections, as well as from the nuclear corrections in the deuteron. We obtain predictions for the ratios $F_2^n/F_2^p$, and $d/u$, focusing on the region of large $x$. We also compare our results with the ones obtained by other QCD analyses, as well as with the recent data from the MARATHON experiment.

Nucleon spin structure functions, considering target mass correction, and higher twist effects at the NNLO accuracy and their transverse momentum dependence

Using recent and updated world data on polarized structure functions ${g}_{1}$ and ${g}_{2}$ we perform an analysis based on quantum chromodynamics (QCD) as a theory of strong interactions at next-next-to-leading-order accuracy. We include also target mass corrections and higher twist effects to get more precise results in our fitting procedure. To confirm the validity of our fitting results several sum rules are examined and we do a comparison for them with results from other models. In our analysis we employ the Jacobi polynomials approach to obtain analytical solutions of the Dokshitzer-Gribov-LipatovAltarelli-Parisi evolution equations for parton distribution functions (PDFs). Using the extracted PDFs from our data analysis as input, we also compute the $x$- and ${\mathbf{p}}_{T}$-dependence of some transverse momentum dependence PDFs in polarized case, based on covariant parton model. These functions are naively even time-reversal at twist-two approximation. The results for transverse momentum dependences indicate proper and acceptable behavior with respect to what are presented in other literatures.

Deep inelastic (anti)neutrino–nucleus scattering

The present status of the field theoretical model studies of the deep inelastic scattering induced by (anti)neutrino on the nuclear targets in a wide range of Bjorken variable $x$ and four momentum transfer square $Q^2$, has been reviewed~\cite{Haider:2011qs,Haider:2012nf,Haider:2016zrk,Zaidi:2019mfd,Zaidi:2019asc,Ansari:2020xne}. The effect of the nonperturbative corrections such as target mass correction and higher twist effects, perturbative evolution of the parton densities, nuclear medium modifications in the nucleon structure functions, nuclear isoscalarity corrections on the weak nuclear structure functions have been discussed. These structure functions have been used to obtain the differential scattering cross sections. The various nuclear medium effects like the Fermi motion, binding energy, nucleon correlations, mesonic contributions, shadowing and antishadowing corrections relevant in the different regions of $x$ and $Q^2$ have been discussed. The numerical results for the structure functions and the cross sections are compared with some of the available experimental data including the recent results from MINERvA. The predictions are made in argon nuclear target which is planned to be used as a target material in DUNE at the Fermilab.

Nuclear parton distribution functions with uncertainties in a general mass variable flavor number scheme

In this article we obtain a new set of nuclear parton distribution functions (nuclear PDFs) at next-to-leading order and next-to-next-to-leading order accuracy in perturbative QCD. The common nuclear deep-inelastic scattering (DIS) data analyzed in our study are complemented by the available charged-current neutrino DIS data with nuclear targets and data from Drell-Yan cross-section measurements for several nuclear targets. In addition, the most recent DIS data from the Jefferson Lab CLAS and Hall C experiments are also added to our data sample. For these specific datasets, we consider the impact of target mass corrections and higher twist effects which are expected to be important in the region of large $x$ and intermediate-to-low $Q^2$. Our analysis is based on a publicly available open-source tool {\tt APFEL}, which has been modified to be applicable for our analysis of nuclear PDFs. Heavy quark contributions to nuclear DIS are considered within the framework of the {\tt FONLL} general-mass variable-flavor-number scheme. The most recent {\tt CT18} PDFs are used as baseline proton PDFs. The uncertainties of nuclear PDFs are determined using the standard Hessian approach. The results of our global QCD analysis are compared with existing nuclear PDF sets and with the fitted cross-sections, for which our set of nuclear PDFs provides a very good description.

Extending nuclear PDF analyses into the high- x , low- Q2 region

We use the nCTEQ analysis framework to investigate nuclear Parton Distribution Functions (nPDFs) in the region of large x and intermediate-to-low $Q$, with special attention to recent JLab Deep Inelastic Scattering data on nuclear targets. This data lies in a region which is often excluded by $W$ and $Q$ cuts in global nPDF analyses. As we relax these cuts, we enter a new kinematic region, which requires new phenomenology. In particular, we study the impact of i) target mass corrections, ii) higher twist corrections, iii) deuteron corrections, and iv) the shape of the nuclear PDF parametrization at large-$x$ close to one. Using the above tools, we produce a new nPDF set (named nCTEQ15HIX) which yields a good description of the new JLab data in this challenging kinematic region, and displays reduced uncertainties at large $x$, in particular for up and down quark flavors.

Standard model O(α) renormalization of gA and its impact on new physics searches

We present an $\mathcal{O}(\alpha)$ Standard Model calculation of the inner radiative corrections to Gamow-Teller $\beta$ decays. We find that \textit{a priori} contributions arise from the photonic vertex correction and $\gamma W$ box diagram. Upon evaluation most elastic contributions vanish due to crossing symmetry or cancellation between isoscalar and isovector photonic contributions, leaving only the polarized parity-odd contribution, i.e., the Gamow-Teller equivalent of the well-known axial $\gamma W$ box contribution for Fermi decays. We show that weak magnetism contributes significantly to the Born amplitude, and consider additional hadronic contributions at low energy using a holomorphic continuation of the polarized Bjorken sum rule constrained by experimental data. We perform the same procedure for the Fermi inner radiative correction through a combination of the running of Bjorken and Gross-Llewellyn Smith sum rules. We discuss heavy flavor, higher-twist, and target mass corrections and find a significant increase at low momentum from the latter. We find $\Delta_R^A = 0.02532(22)$ and $\Delta_R^V = 0.02473(27)$ for axial and vector inner radiative corrections, respectively, resulting in $\Delta_R^A-\Delta_R^V=0.60(5) \times 10^{-3}$, which allows us to extract $g_A^0$ for the first time to our knowledge. We discuss consequences for comparing experimental data to lattice calculations in beyond Standard Model fits. Further, we show how some traditional $\beta$ decay calculations contain part of this effect but fail to account for cancellations in the full $\mathcal{O}(\alpha)$result. Finally, we correct for a double-counting instance in the isospin $T=1/2$ mirror decay extraction of $|V_{ud}|$, the up-down matrix element of the Cabibbo-Kobayashi-Maskawa matrix, resolving a long-standing tension and leading to increased precision.

Nonperturbative and higher order perturbative effects in deep inelastic ντ/ν¯τ -nucleon scattering

The effect of nonperturbative and higher order perturbative corrections to all the free nucleon structure functions ($F_{iN}(x,Q^2); i=1-5$) in the DIS of $\nu_\tau/{\bar\nu}_\tau$ on nucleon is studied. The target mass correction (TMC) and higher twist (HT) effects are incorporated following the works of Kretzer et al. and Dasgupta et al., respectively. The evaluation of the nucleon structure functions has been performed by using the MMHT 2014 parameterization of the parton distribution functions (PDFs). The calculations have been performed at the next-to-leading(NLO) order. These nucleon structure functions (SF) are used to calculate the DIS cross section by further including the kinematical corrections due to $\tau$-lepton mass. Due to the inclusion of lepton mass two additional structure functions $F_{4N}(x,Q^2)$ and $F_{5N}(x,Q^2)$ become non-negligible. The results for the nucleon structure functions, differential and total scattering cross sections are presented. The various effects considered in this work are effective in the different regions of $x$ and $Q^2$, and quite important in the energy region of $E_{\nu_\tau/{\bar\nu}_\tau} < 15$ GeV. A comparative study of our results with the existing results in the literature for the cross sections is made in the energy region of interest for the DUNE, SHiP, DsTau and HyperK experiments proposed to be done in the near future.

Lattice QCD evaluation of the Compton amplitude employing the Feynman-Hellmann theorem

The forward Compton amplitude describes the process of virtual photon scattering from a hadron and provides an essential ingredient for the understanding of hadron structure. As a physical amplitude, the Compton tensor naturally includes all target mass corrections and higher twist effects at a fixed virtuality, $Q^2$. By making use of the second-order Feynman-Hellmann theorem, the nucleon Compton tensor is calculated in lattice QCD at an unphysical quark mass across a range of photon momenta $3 \lesssim Q^2 \lesssim 7$ GeV$^2$. This allows for the $Q^2$ dependence of the low moments of the nucleon structure functions to be studied in a lattice calculation for the first time. The results demonstrate that a systematic investigation of power corrections and the approach to parton asymptotics is now within reach.

Calculation of transverse momentum dependent distributions beyond the leading power

We compute the contribution of twist-2 and twist-3 parton distribution functions to the small-b expansion for transverse momentum dependent (TMD) distributions at all powers of b. The computation is done by the twist-decomposition method based on the spinor formalism for all eight quark TMD distributions. The newly computed terms are accompanied by the prefactor (M2b2)n and represent the target-mass corrections to the resummed cross-section. For the first time, a non-trivial expression for the pretzelosity distribution is derived.

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.

Implementation of target mass corrections and higher-twist effects in the xFitter framework

Knowledge of parton distribution functions (PDFs) at large momentum fraction $ x $ is not only important to study the flavor and spin dynamics of quarks in the nucleon, but also to search for signals of new physics at collider experiments. It is well known now that the nonperturbative QCD effects generally play a more significant role at such kinematic regions. In this work, we present an open-source QCD analysis of PDFs considering target mass corrections (TMCs) and higher-twist (HT) effects which are necessary when the analysis includes also data points from deep inelastic scattering (DIS) with larger values of $ x $ and smaller values of photon virtuality $ Q^2 $. To this aim, we use the xFitter package, as a comprehensive and powerful tool for studying PDFs. We report and discuss our recent activities on the implementation of TMCs and HT effects in the xFitter framework in a user-friendly way, so that the user can switch on or off them, and also choose between different options. We check the validity of the modifications by performing sample analyses of PDFs considering TMCs and HT effects and using a wide range of DIS data.

Refined analysis on the parton distribution functions of the proton

We explore the application of a two-component model of proton structure functions in the analysis of deep-inelastic scattering (DIS) data at low Q2 and small x. This model incorporates both vector meson dominance and the correct photo-production limit. The CJ15 parameterization is applied to the QCD component, in order to take into account effects of order 1/Q2 effects, such as target mass corrections and higher twist (HT) contributions. The parameters of the leading twist parton distribution functions (PDFs) and HT coefficient functions are determined by fitting DIS data. The second moments of the PDFs are extracted and compared with other global fits and lattice determinations.

Charged-current deep-inelastic scattering of muon neutrinos ( νμ ) off Fe56

In this paper, we study charged current deep inelastic scattering of muon neutrinos off ^{56}Fe nuclei using Hirai, Kumano and Saito model. The LHA Parton Distribution Functions (PDFs) - CT10 are used to describe the partonic content of hadrons. Modification of PDFs inside the nuclei is done using EPPS16 parameterization at next-to-leading order. Target mass correction has also been incorporated in the calculations. We calculate the structure functions (F_{2}(x,Q^{2}) and xF_{3}(x,Q^{2})), the ratios (R_{2}(x,Q^{2}) = \frac{F^{^{56}Fe}_{2}}{F^{Nucleon}_{2}} and R_{3}(x,Q^{2}) = \frac{F^{^{56}Fe}_{3}}{F^{Nucleon}_{3}}) and the differential cross sections of muon neutrino deep inelastic scattering off a nucleon and ^{56}Fe nuclei. We compare the obtained results with measured experimental data. The present theoretical approach gives a good description of data.

Light-Cone Parton Distribution Functions from Lattice QCD.

We extract parton distribution functions (PDFs) of the nucleon from lattice QCD using an ensemble of gauge field configurations simulated with light quark masses fixed to their physical values. Theoretical and algorithmic improvements that allow such a calculation include momentum smearing to reach large nucleon boosts with reduced statistical errors, nonperturbative renormalization, target mass corrections, and a novel modified matching of lattice QCD results to connect to what is extracted from experimental measurements. We give results on the unpolarized and helicity PDFs in the modified minimal subtraction scheme at a scale of 2GeV and reproduce the main features of the experimentally determined quantities, showing an overlap for a range of Bjorken-x values. This first direct nonperturbative evaluation opens a most promising path to compute PDFs in an abinitio way on the lattice and provides a framework for investigating also a wider class of similar quantities, which require the evaluation of hadronic matrix elements of nonlocal operators.

Improved determination ofd¯(x)−u¯(x)flavor asymmetry in the proton by data from the BONuS experiment at JLAB and using an approach by Brodsky, Hoyer, Peterson, and Sakai

The experimental data taken from both Drell-Yan and deep-inelastic scattering (DIS) experiments suggest a sign-change in $\bar d(x) - \bar u(x)$ flavor asymmetry in the proton at large values of momentum fraction $x$. In this work, we present a phenomenological study of $\bar d(x) - \bar u(x)$ flavor asymmetry. First, we extract the $\bar d(x)-\bar u(x)$ distribution using the more recent data from the BONuS experiment at Jefferson Lab on the ratio of neutron to proton structure functions, $F_2^n/F_2^p$, and show that it undergoes a sing-change and becomes negative at large values of momentum fraction $x$, as expected. The stability and reliability of our obtained results have been examined by including target mass corrections (TMCs) as well as higher twist (HT) terms which are particularly important at the large-$x$ region at low Q$^2$. Then, we calculate the $\bar d(x) - \bar u(x)$ distribution using the Brodsky, Hoyer, Peterson, and Sakai (BHPS) model and show that if one chooses a mass for the down quark smaller than the one for the up quark it leads to a better description for the Fermilab E866 data. In order to prove this claim, we determine the masses of down and up sea quarks by fitting to the available and up-to-date experimental data for the $\bar d(x)-\bar u(x)$ distribution. In this respect, unlike the previous performed theoretical studies, we have shown that this distribution has a sign-change at $x>0.3$ after evolution to the scale of available experimental data.