Higher Twist Effects Research Articles

Measurements of Normalized Differential Cross Sections of Inclusive η Production in e^{+}e^{-} Annihilation at Energy from 2.0000 to 3.6710GeV.

Using data samples collected with the BESIII detector operating at the BEPCII storage ring, the cross section of the inclusive process e^{+}e^{-}→η+X, normalized by the total cross section of e^{+}e^{-}→hadrons, is measured at eight center-of-mass energy points from 2.0000 to 3.6710GeV. These are the first measurements with momentum dependence in this energy region. Our measurement shows a significant discrepancy compared to the existing fragmentation functions. To address this discrepancy, a new QCD analysis is performed at the next-to-next-to-leading order with hadron mass corrections and higher twist effects, which can explain both the established high-energy data and our measurements reasonably well.

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

Nuclear Parton Distribution Functions After the First Decade of LHC Data

We present a review of the conceptual basis, current knowledge, and recent progress regarding global analysis of nuclear parton distribution functions (PDFs). After introducing the theoretical foundations and methodological approaches for the extraction of nuclear PDFs from experimental data, we discuss how different measurements in fixed-target and collider experiments provide increasingly precise constraints on various aspects of nuclear PDFs, including shadowing, antishadowing, the EMC effect, Fermi motion, flavor separation, deuteron binding, and target-mass and other higher-twist effects. Particular emphasis is given to measurements carried out in proton–lead collisions at the Large Hadron Collider, which have revolutionized the global analysis during the past decade. These measurements include electroweak boson, jet, light hadron, and heavy flavor observables. Finally, we outline the expected impact of the future Electron Ion Collider and discuss the role and interplay of nuclear PDFs with other branches of nuclear, particle, and astroparticle physics.

Twist decomposition of non-linear effects in Balitsky–Kovchegov evolution of proton structure functions

Effects of non-linear small-x evolution of the gluon distribution given by the Balitsky–Kovchegov equation are analyzed within the collinear approximation framework. We perform a twist decomposition of the proton structure functions F2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_2$$\\end{document} and FL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F_{\ extrm{L}}$$\\end{document} obtained from the Balitsky–Kovchegov equation using the Mellin representation of the scattering cross-sections at high energies. In both the structure functions we find strong corrections coming from the non-linear effects in the gluon evolution at twist 2, and strongly suppressed higher twist effects. This implies that unitarization effects of high energy scattering amplitudes are mostly the leading twist effect. Furthermore we consider the double logarithmic limit of the Balitsky–Kovchegov equation for the collinear gluon distribution, and compare the result to the Gribov–Levin–Ryskin equation. We find that these two equations differ by two powers of the hard scale logarithm for the large scales.

Lattice calculation of the intrinsic soft function and the Collins-Soper kernel

We calculate the soft function using lattice QCD in the framework of large momentum effective theory incorporating the one-loop perturbative contributions. The soft function is a crucial ingredient in the lattice determination of light cone objects using transverse-momentum-dependent (TMD) factorization. It consists of a rapidity-independent part called intrinsic soft function and a rapidity-dependent part called Collins-Soper kernel. We have adopted appropriate normalization when constructing the pseudoscalar meson form factor that is needed in the determination of the intrinsic part and applied Fierz rearrangement to suppress the higher-twist effects. In the calculation of CS kernel we consider a CLS ensemble other than the MILC ensemble used in a previous study. We have also compared the applicability of determining the CS kernel using quasi TMDWFs and quasi TMDPDFs. As an example, the determined soft function is used to obtain the physical TMD wave functions (WFs) of pion and unpolarized iso-vector TMD parton distribution functions (PDFs) of proton.

Precision calculations of Bd,s → π, K decay form factors in soft-collinear effective theory

We improve QCD calculations of the semileptonic Bd,s→ π, K decay form factors at large hadronic recoil by implementing the next-to-leading-logarithmic resummation for the obtained leading-power light-cone sum rules in the soft-collinear effective theory (SCET) framework and by computing for the first time the non-vanishing spectator-quark mass correction dictating the SU(3)-flavour symmetry breaking effects between these fundamental quantities at the one-loop accuracy. Additionally, we endeavour to investigate a variety of the subleading-power contributions to these heavy-to-light form factors at mathcal{O}left({alpha}_s^0right) with the same methodology, by including the higher-order terms in the heavy-quark expansion of the hard-collinear quark propagator, by evaluating the desired effective matrix element of the next-to-leading-order term in the SCETI representation of the weak transition current, by taking into account the off-light-cone contributions of the two-body heavy-quark effective theory (HQET) matrix elements as well as the three-particle higher-twist corrections from the subleading bottom-meson light-cone distribution amplitudes (LCDAs), and by computing the twist-five and twist-six four-body higher-twist effects with the aid of the factorization approximation. Having at our disposal the SCET sum rules for the exclusive B-meson decay form factors under discussion, we further explore in detail numerical implications of the newly computed subleading-power corrections by employing the three-parameter model for both the leading-twist and higher-twist B-meson distribution amplitudes. Taking advantage of the customary Bourrely-Caprini-Lellouch (BCL) parametrization for the complete set of the semileptonic Bd,s→ π, K form factors, we then determine the correlated numerical results for the interesting series coefficients, by carrying out the simultaneous fit of the exclusive B-meson decay form factors to both the achieved SCET sum rule predictions at small momentum transfer (q2) and the available lattice QCD results at large momentum transfer. Subsequently, we perform a comprehensive phenomenological analysis of the full angular observables, the lepton-flavour university ratios and the lepton polarization asymmetries for the flavour-changing charged- current Bto pi ell {overline{nu}}_{ell } and {B}_sto Kell {overline{nu}}_{ell } decays (with ℓ = μ, τ) together with the differential q2-distribution for the exclusive rare Bto K{nu}_{ell }{overline{nu}}_{ell } decays in the Standard Model.

Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions

The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional z2 contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional z2 contamination. Due to the non-conservation of the axial current, we elect to isolate the helicity PDFs normalized by the nucleon axial charge at the same scale μ2. The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned z2 contaminating amplitude are jointly determined by characterizing the computed pseudo-distribution in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the pseudo-distribution. Encouraging agreement is observed with recent global analyses of each non-singlet quark helicity PDF, notably a rather small non-singlet anti-quark helicity PDF for all quark momentum fractions.

Higher twists effects in DIS on nuclei at the EIC and LHeC: a phenomenological analysis

In this paper we investigate the impact of the higher - twist effects, resummed by the non - linear approaches for the QCD dynamics, on the inclusive observables that will be measured in future electron - ion colliders. We assume a phenomenological model for the dipole - nucleus scattering amplitude which takes into account the non - linear corrections and estimate the contribution of the different twists for $F_2^A(x,Q^2)$, $F_L^A(x,Q^2)$ and $\partial F_2^A /\partial ln Q^2$ considering different values of the Bjorken - $x$ variable, photon virtuality $Q^2$ and atomic number $A$. A comparison with the full predictions is performed and the impact of the distinct twists is estimated. Our results indicate that a future analysis of the logarithmic $Q^2$ slope and longitudinal structure function will allow us to probe the presence of the non - linear effects on the QCD dynamics.

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.

Lattice QCD calculation of the Collins-Soper kernel from quasi-TMDPDFs

This work presents a lattice quantum chromodynamics (QCD) calculation of the nonperturbative Collins-Soper kernel, which describes the rapidity evolution of quark transverse-momentum-dependent parton distribution functions. The kernel is extracted at transverse momentum scales in the range 400 MeV $< q_T < 1.7$ GeV in a calculation with dynamical fermions and quark masses corresponding to a larger-than-physical pion mass, $m_\pi=538(1)$ MeV. It is found that different approaches to extract the Collins-Soper kernel from the same underlying lattice QCD matrix elements yield significantly different results and uncertainty estimates, revealing that power corrections, such as those associated with higher-twist effects, and perturbative matching between quasi and light-cone beam functions, cannot be neglected.

Towards high-precision parton distributions from lattice QCD via distillation

We apply the Distillation spatial smearing program to the extraction of the unpolarized isovector valence PDF of the nucleon. The improved volume sampling and control of excited-states afforded by distillation leads to a dramatically improved determination of the requisite Ioffe-time Pseudo-distribution (pITD). The impact of higher-twist effects is subsequently explored by extending the Wilson line length present in our non-local operators to one half the spatial extent of the lattice ensemble considered. The valence PDF is extracted by analyzing both the matched Ioffe-time Distribution (ITD), as well as a direct matching of the pITD to the PDF. Through development of a novel prescription to obtain the PDF from the pITD, we establish a concerning deviation of the pITD from the expected DGLAP evolution of the pseudo-PDF. The presence of DGLAP evolution is observed once more following introduction of a discretization term into the PDF extractions. Observance and correction of this discrepancy further highlights the utility of distillation in such structure studies.

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.

Twist-2 relation and sum rule for tensor-polarized parton distribution functions of spin-1 hadrons

Sum rules for structure functions and their twist-2 relations have important roles in constraining their magnitudes and x dependencies and in studying higher-twist effects. The Wandzura-Wilczek (WW) relation and the Burkhardt-Cottingham (BC) sum rule are such examples for the polarized structure functions g1 and g2. Recently, new twist-3 and twist-4 parton distribution functions were proposed for spin-1 hadrons, so that it became possible to investigate spin-1 structure functions including higher-twist ones. We show in this work that an analogous twist-2 relation and a sum rule exist for the tensor-polarized parton distribution functions f1LL and fLT, where f1LL is a twist-2 function and fLT is a twist-3 one. Namely, the twist-2 part of fLT is expressed by an integral of f1LL (or b1) and the integral of the function f2LT = (2/3)fLT− f1LL over x vanishes. If the parton-model sum rule for f1LL (b1) is applied by assuming vanishing tensor-polarized antiquark distributions, another sum rule also exists for fLT itself. These relations should be valuable for studying tensor-polarized distribution functions of spin-1 hadrons and for separating twist-2 components from higher-twist terms, as the WW relation and BC sum rule have been used for investigating x dependence and higher-twist effects in g2. In deriving these relations, we indicate that four twist-3 multiparton distribution functions FLT, GLT, {H}_{LL}^{perp } , and HTT exist for tensor-polarized spin-1 hadrons. These multiparton distribution functions are also interesting to probe multiparton correlations in spin-1 hadrons. In the near future, we expect that physics of spin-1 hadrons will become a popular topic, since there are experimental projects to investigate spin structure of the spin-1 deuteron at the Jefferson Laboratory, the Fermilab, the nuclotron-based ion collider facility, the electron-ion colliders in US and China in 2020’s and 2030’s.

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.

Double deeply virtual Compton scattering with positron beams at SoLID

Double Deeply Virtual Compton Scattering (DDVCS) is the only experimental channel for the determination of the dependence of the Generalized Parton Distributions (GPDs) on both the average and the transferred momentum independently. The physics observables of the electron induced di-muon production reaction $\vv{e}^{\pm}p \to e^{\pm}p\mu^+\mu^-$ off unpolarized hydrogen are discussed. Their measurement with the high luminosity and large acceptance SoLID spectrometer at the Thomas Jefferson National Accelerator Facility, using polarized and unpolarized positron and electron beams at 11 GeV is investigated. This experimental configuration is shown to provide unprecedented access to the GPDs with the determination of the real and imaginary parts of the Compton Form Factor ${\mathcal H}$ in an unexplored phase space, and to enable an exploratory investigation of higher twist effects.

An evaluation of the proton structure functions F2 and FL at small x

We describe the determination of the DIS structure functions F2 and FL by using the singlet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Altarelli-Martinelli equations at small values of x. The determination of the longitudinal structure function is presented as a parameterization of F2(x,Q2) and its derivative. Analytical expressions for σr(x,Q2) in terms of the effective parameters of the parameterization of F2(x,Q2) and FL(x,Q2) are presented. This analysis is enriched by including the higher-twist effects in calculation of the reduced cross sections which is important at low-x and low-Q2 regions. Numerical calculations and comparison with H1 data demonstrate that the suggested method provides reliable FL(x,Q2) and σr(x,Q2) at low x in a wide range of the low absolute four-momentum transfers squared (1.5 GeV2<Q2<120 GeV2) at moderate and high inelasticity. Expanding the method to low and ultra low values of x can be considered in the process analysis of new colliders. We compare the obtained longitudinal structure function with respect to the LHeC simulated uncertainties (Agostini et al. (2020) [4]) with the results from CT18 (Hou et al. (2021) [54]) parametrization model.

Higher-Twist Effect in Pion Parton DistributionSupported by the National Natural Science Foundation of China (Grant No. 11851303).

A higher-twist modified parton evolution equation is used to evolve the initial valence quark distributions in pions, which are derived based on light-front quantization via BLFQ collaboration. The results are consistent with the valence quark distributions of the E615 experiment, and the pion structure function of the H1 experiment. The structure function data highlight the necessity for a higher-twist modification in the small x region. Comparisons with some other models are also given.

Gluon distributions and their applications to Ioffe-time distributions

We investigate unpolarized and polarized gluon distributions and their applications to the Ioffe-time distributions, which are related to lattice QCD calculations of parton distribution functions. Guided by the counting rules based on the perturbative QCD at large momentum fraction $x$ and the color coherence of gluon couplings at small $x$, we parametrize gluon distributions in the helicity basis. By fitting the unpolarized gluon distribution, the inferred polarized gluon distribution from our parametrization agrees with the one from global analysis. A simultaneous fit to both unpolarized and polarized gluon distributions is also performed to explore the model uncertainty. The agreement with the global analysis supports the $(1-x)$ power suppression of the helicity-antialigned distribution relative to the helicity-aligned distribution. The corresponding Ioffe-time distributions and their asymptotic expansions are calculated from the gluon distributions. Our results of the Ioffe-time distributions can provide guidance to the extrapolation of lattice QCD data to the region lacking precise gluonic matrix elements. Therefore, they can help regulate the ill-posed inverse problem associated with extracting the gluon distributions from discrete data from first-principle calculations, which are available in a limited range of the nucleon momentum and the spatial separation between the gluonic currents. Given various limitations in obtaining lattice QCD data at large Ioffe time, phenomenological approaches can provide important complementary information to extract the gluon distributions in the entire $x$ region. The possibility of investigating higher-twist effects and other systematic uncertainties in the contemporary first-principle calculations of parton distributions from phenomenologically well-determined Ioffe-time distributions in the large Ioffe-time region is also discussed.

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.