Parton Fragmentation Functions Research Articles

Transverse momentum weighted Sivers asymmetries in SIDIS and Drell-Yan processes at COMPASS

We investigate the transverse momentum weighted Sivers asymmetries in the processes with transversely polarized proton target, including the PhTzMpsin⁡(ϕh−ϕS) weighted asymmetry in charged hadron production in semi-inclusive deeply inelastic scattering (SIDIS) and the qTMpsin⁡(ϕS) weighted asymmetry in π−p Drell-Yan process. These asymmetries can be expressed as the product of the transverse-moments of the transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FFs). Using the parametrization for the Sivers function of the proton, the unpolarized PDFs of proton and pion, and the unpolarized FF of charged hadron, we present the numerical calculation for weighted Sivers asymmetries in SIDIS and Drell-Yan processes at the kinematics of COMPASS. We find that our prediction for the SIDIS process is in agreement with the recent COMPASS measurement. Recent new high-statistics data of Sivers asymmetry measured in SIDIS process and Drell-Yan process from COMPASS favored the sign change of Sivers function. High-precision experimental data of weighted asymmetries are still needed to test the sign change property of the Sivers function between SIDIS and Drell-Yan processes and to constrain the sea quark Sivers function.

Polarized fragmenting jet functions in inclusive and exclusive jet production

In this work, we present a complete theoretical framework for analyzing the distribution of polarized hadrons within jets, with and without measuring the transverse momentum relative to the standard jet axis. Using soft-collinear effective theory (SCET), we derive the factorization and provide the theoretical calculation of both semi-inclusive and exclusive fragmenting jet functions (FJFs) under longitudinal and transverse polarization. With the polarized FJFs, one gains access to a variety of new observables that can be used for extracting both collinear and transverse momentum dependent parton distribution functions (PDFs) and fragmentation functions (FFs). As examples, we provide numerical results for the spin asymmetry ATU,TcosϕS−ϕ̂Sh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {A}_{TU,T}^{\\cos \\left({\\phi}_S-{\\hat{\\phi}}_{S_h}\\right)} $$\\end{document} from polarized semi-inclusive hadron-in-jet production in polarized pp collisions at RHIC kinematics, where a transversely polarized quark would lead to the transverse spin of the final-state hadron inside the jet and is thus sensitive to the transversity fragmentation functions. Similarly, another spin asymmetry, ATU,Lcosϕq−ϕS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {A}_{TU,L}^{\\cos \\left({\\phi}_q-{\\phi}_S\\right)} $$\\end{document} from polarized exclusive hadron-in-jet production in polarized ep collisions at EIC kinematics would allow us to access the helicity fragmentation functions. These observables demonstrate promising potential in investigating transverse momentum dependent PDFs and FFs and are worthwhile for further measurements.

A high-energy QCD portal to exotic matter: Heavy-light tetraquarks at the HL-LHC

By taking advantage of the natural stability of the high-energy resummation, recently discovered in the context of heavy-flavor studies, we investigate the inclusive hadroproduction of a neutral heavy-light, hidden-flavored tetraquark (Xcuc¯u¯ or Xbsb¯s¯ state), in association with a heavy (single c- or b-flavored) hadron or a light jet at the (HL-)LHC. We make use of the JETHAD multi-modular working package to provide predictions for rapidity, azimuthal-angle and transverse-momentum distributions calculated via the hybrid high-energy and collinear factorization, where the Balitsky–Fadin–Kuraev–Lipatov resummation of energy logarithms is supplemented by collinear parton densities and fragmentation functions. We rely upon the single-parton fragmentation mechanism, valid in the large transverse-momentum regime, to describe the tetraquark production. Our study represents a first attempt at bridging the gap between all-order calculations of high-energy QCD and the exotics.

Transverse momentum dependent distribution functions in the threshold limit

We apply the joint threshold and transverse momentum dependent (TMD) factorization theorem to introduce new threshold-TMD distribution functions, including threshold-TMD parton distribution functions (PDFs) and fragmentation functions (FFs). We apply Soft-Collinear Effective Theory and renormalization group methods to carry out QCD evolution for both threshold-TMD PDFs and FFs. We show the universality of threshold-TMD functions among three standard processes, i.e. the Drell-Yan production in pp collisions, semi-inclusive deep-inelastic scattering and back-to-back two hadron production in e+e− collisions. In the end, we present the numerical predictions for different threshold-TMD functions and also transverse momentum distributions at pp, ep, and e+e− collisions.

Unpolarized QED parton distribution functions in NLO

Perturbative solutions for unpolarized QED parton distribution and fragmentation functions are presented explicitly in the next-to-leading logarithmic approximation. The scheme of iterative solution of QED evolution equations is described in detail. Terms up to are calculated analytically, where is the large logarithm which depends on the factorization energy scale μ F ≫ m e . The results are process independent and relevant for future high-precision experiments.

Resolution to the problem of consistent large transverse momentum in TMDs

Parametrizing TMD parton densities and fragmentation functions in ways that consistently match their large transverse-momentum behavior in standard collinear factorization has remained notoriously difficult. We show how the problem is solved in a recently introduced set of steps for combining perturbative and nonperturbative transverse momentum in TMD factorization. Called a ``bottom-up'' approach in a previous article, here we call it a ``hadron structure oriented'' (HSO) approach to emphasize its focus on preserving a connection to the TMD parton model interpretation. We show that the associated consistency constraints improve considerably the agreement between parametrizations of TMD functions and their large-${k}_{T}$ behavior, as calculated in collinear factorization. The procedure discussed herein will be important for guiding future extractions of TMD parton densities and fragmentation functions and for testing TMD factorization and universality. We illustrate the procedure with an application to semi-inclusive deep inelastic scattering (SIDIS) structure functions at an input scale ${Q}_{0}$, and we show that there is improved consistency between different methods of calculating at moderate transverse momentum. We end with a discussion of plans for future phenomenological applications.

The Collins Asymmetry in Λ Hyperon Produced SIDIS Process at Electron–Ion Colliders

We investigate Collins asymmetry in the Λ hyperon produced semi-inclusive deep inelastic scattering (SIDIS) process based on the kinematical region of Electron-ion collider in China (EicC) and Electron–ion collider (EIC) within the transverse momentum dependence (TMD) factorization framework at next-to-leading-logarithmic order. The asymmetry is contributed by the convolution of the target proton transversity distribution function and the Collins function of the final-state Λ hyperon. The TMD evolution effect of the corresponding parton distribution functions (PDFs) and fragmentation functions (FFs) is considered with the help of parametrization of the non-perturbative Sudakov form factors for the proton PDFs and Λ fragmentation functions. We apply the parametrization of the collinear proton transversity distribution function and the model results of Λ Collins function from the diquark spectator model as the inputs of the TMD evolution to numerically calculate Collins asymmetry in Λ produced SIDIS process at the kinematical configurations of EIC and EicC. It can be shown that the asymmetry is significant and can be measured at EIC and EicC. The flavor dependence of transversity distribution functions could be further constrained by studying the Λ hyperon produced SIDIS process in the future to improve our understanding of the spin structure within nucleons.

SIDIS-RC EvGen: A Monte-Carlo event generator of semi-inclusive deep inelastic scattering with the lowest-order QED radiative corrections

SIDIS-RC EvGen is a C++ standalone Monte-Carlo event generator for studies of semi-inclusive deep inelastic scattering (SIDIS) processes at medium to high lepton beam energies. In particular, the generator contains binary and library components for generating SIDIS events and calculating cross sections for unpolarized or longitudinally polarized beam and unpolarized, longitudinally or transversely polarized target. The structure of the generator incorporates transverse momentum-dependent parton distribution and fragmentation functions, whereby we obtain multi-dimensional binned simulation results, which will facilitate the extraction of important information about the three-dimensional nucleon structure from SIDIS measurements. In order to build this software, we have used recent elaborate QED calculations of the lowest-order radiative effects, applied to the leading order Born cross section in SIDIS. In this paper, we provide details on the theoretical formalism as well as the construction and operation of SIDIS-RC EvGen, e.g., how we handle the event generation process and perform multi-dimensional integration. We also provide example programs, flowcharts, and numerical results on azimuthal transverse single-spin asymmetries. Program summaryProgram title: SIDIS-RC EvGenCPC Library link to program files:https://doi.org/10.17632/thrkn96ydd.1Licensing provisions: GNU General Public License Version 3Developer's repository link:https://github.com/duanebyer/sidisProgramming language: C++, PythonExternal packages: FOAM, ROOT, GSL, VEGAS, Cubature, Cog, WW-SIDIS, MSTWPDFNature of problem: The task is to first create a code for calculations of the leading order Born cross section as well as radiative corrections (RCs) at the next-to-leading order (NLO) of the cross section of lepton-hadron semi-inclusive deep inelastic scattering (SIDIS) at medium to high beam energies with incident unpolarized or longitudinally polarized lepton beam and unpolarized, longitudinally or transversely polarized target, enabling to compute azimuthal single-target and double-beam-target spin asymmetries. Afterwards, a Monte-Carlo event generator based upon this code is developed, where in the coding and simulation processes multi-dimensional integrals need to be calculated precisely to obtain the exact NLO RCs to the SIDIS cross section with high precision beyond ultra-relativistic limit, which means that the lepton mass is taken into account.Solution method: The project for building the SIDIS-RC EvGen software is divided into a library component called libsidis, for the purpose of calculating the inelastic tail to the SIDIS total cross section, and a binary component called sidisgen, for generating events. The Monte-Carlo event generation is performed through the usage of the FOAM library, by applying a spatial partitioning method with hyper-cubical “foam of cells”. The multi-dimensional numerical integration is carried out by the GSL, VEGAS, and Cubature packages. The SIDIS structure functions that describe the SIDIS scattering process, and which are given in terms of transverse momentum-dependent parton distribution and fragmentation functions, are calculated in Gaussian and Wandzura–Wilczek-type approximations and implemented in the generator accordingly.Additional comments including restrictions and unusual features: The restrictions depend on the complexity of problems, limited by CPU time. As a consequence, the program running time is of order of several minutes to hours. SIDIS-RC EvGen does not comprise yet the contribution coming from the radiative tail of exclusive lepton-hadron reactions, which is a separate contribution involving exclusive structure functions that are currently not well known.Developer's repository maintained by Duane Byer; Department of Physics, Duke University.

The high-energy spectrum of QCD from inclusive emissions of charmed B-mesons

We investigate the high-energy behavior of strong interactions through a study on the inclusive hadroproduction of charmed B-mesons (Bc or Bc⁎ states) accompanied by non-charmed b-hadron or light-flavored jet emissions at LHC energies and kinematic configurations. By making use of the hybrid high-energy and collinear factorization, where the standard fixed-order description based on collinear parton densities and fragmentation functions is enhanced via the Balitsky–Fadin–Kuraev–Lipatov (BFKL) resummation of energy logarithms, we perform a full next-to-leading order analysis of distributions differential in rapidities and azimuthal angles calculated by the hands of the JETHAD multi-modular working package. The large observed transverse momenta justify the use of non-relativistic QCD next-to-leading order fragmentation functions to describe the heavy-flavored meson production mechanism. We come out with the conclusion that the study of this process can be included in forthcoming analyses at the (high-luminosity) LHC as a tool to access the QCD dynamics at high energies and to explore possible common ground between different resummation approaches.

Unpolarized transverse momentum distributions from a global fit of Drell-Yan and semi-inclusive deep-inelastic scattering data

We present an extraction of unpolarized transverse-momentum-dependent parton distribution and fragmentation functions based on more than two thousand data points from several experiments for two different processes: semi-inclusive deep-inelastic scattering and Drell-Yan production. The baseline analysis is performed using the Monte Carlo replica method and resumming large logarithms at N3LL accuracy. The resulting description of the data is very good (χ2/Ndat = 1.06). For semi-inclusive deep-inelastic scattering, predictions for multiplicities are normalized by factors that cure the discrepancy with data introduced by higher-order perturbative corrections.

Extracting the jet transport coefficient from hadron suppressions by confronting current NLO parton fragmentation functions

Nuclear modification factors of single hadrons and dihadrons at large transverse momentum ( $$p_{\mathrm{T}}$$ ) in high-energy heavy-ion collisions are studied in a next-to-leading-order (NLO) perturbative QCD parton model. Parton fragmentation functions (FFs) in $$A+A$$ collisions are modified due to jet energy loss which is proportional to the jet transport coefficient $$\hat{q}$$ characterizing the interaction between the parton jet and the produced medium. By confronting 6 current sets of NLO parton FFs for large $$p_{\mathrm{T}}$$ hadron productions, we extract $$\hat{q}$$ quantitatively via a global fit to data for both single hadron and dihadron suppressions and obtain $$\hat{q}/T^3 = 4.74 - 6.72$$ at $$T = 370$$ MeV in central $$Au+Au$$ collisions at $$\sqrt{s_{\mathrm{NN}}}=200$$ GeV, and $$\hat{q}/T^3 = 3.07 - 3.98$$ at $$T = 480$$ MeV in central $$Pb+Pb$$ collisions at $$\sqrt{s_{\mathrm{NN}}}=2.76$$ TeV. The numerical results show that the uncertainties for $$\hat{q}$$ extraction are brought by the different contributions of gluon-to-hadron in the six sets of FFs due to gluon energy loss being 9/4 times of quark energy loss.

Combining nonperturbative transverse momentum dependence with TMD evolution

Central to understanding the nonperturbative, intrinsic partonic nature of hadron structure are the concepts of transverse momentum dependent (TMD) parton distribution and fragmentation functions. A TMD factorization approach to the phenomenology of semi-inclusive processes that includes evolution, higher orders, and matching to larger transverse momentum is ultimately necessary for reliably connecting with phenomenologically extracted nonperturbative structures, especially when widely different scales are involved. In this paper, we will address some of the difficulties that arise when phenomenological techniques that were originally designed for very high energy applications are extended to studies of hadron structures, and we will solidify the connection between standard high energy TMD implementations and the more intuitive, parton model based approaches to phenomenology that emphasize nonperturbative hadron structure. In the process, we will elaborate on differences between forward and backward TMD evolution, which in the context of this paper, we call ``bottom-up'' and ``top-down'' approaches, and we will explain the advantages of a bottom-up strategy. We will also emphasize and clarify the role of the integral relations that connect TMD and collinear correlation functions. We will show explicitly how they constrain the nonperturbative ``$g$-functions'' of standard Collins-Soper-Sterman implementations of TMD factorization. This paper is especially targeted toward phenomenologists and model builders who are interested in merging specific nonperturbative models and calculations (including lattice QCD) with TMD factorization at large $Q$. Our main result is a recipe for incorporating nonperturbative models into TMD factorization and for constraining their parameters in a way that matches perturbative QCD and evolution.

High-energy emissions of light mesons plus heavy flavor at the LHC and the Forward Physics Facility

The study of the dynamics of strong interactions in the high-energy regime is a core line of frontier researches at the LHC as well as at new-generation colliding facilities. Here, the enhancement of energy logarithms due to diffractive semihard final states spoils the convergence of the perturbative series in the QCD running coupling, thus calling for an improvement of the pure collinear factorization that accounts for an all-order resummation of these large logarithmic contributions. Motivated by the recent discovery that inclusive emissions of heavy-flavored particles allow for clear signals of a stabilization of high-energy resummed differential distributions under higher-order corrections and scale variations, we provide novel predictions of rapidity and azimuthal-angle observables for the inclusive hadroproduction of a light meson ($\ensuremath{\eta}$ or ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$) in association with a heavy-flavored hadron (${\mathrm{\ensuremath{\Lambda}}}_{c}$ or $b$-flavored hadron). We calculate our observables in a hybrid high-energy and collinear factorization framework, where next-to-leading Balitsky-Fadin-Kuraev-Lipatov-resummed partonic cross sections are convoluted with collinear parton distributions and fragmentation functions. We consider kinematic ranges typically covered by acceptances of LHC detectors, and new ones coming from the combined tag of an ultra-forward particle at the future Forward Physics Facility and of a central one at ATLAS via a tight timing-coincidence setup. By performing a detailed study on uncertainties associated to collinear inputs via a replica-driven analysis, as well as on ones intrinsically coming from the high-energy resummation, we highlight the challenges and the steps required to gauge the feasibility of precision studies of our processes.

Parton distribution effects in the direct photon production at hadron collisions

Parton distribution functions are crucial to understand the internal kinematics of hadrons. There are currently a large number of distribution functions on the market, and thanks to today's technology, performing computational analysis of the differential cross-sections has become more accessible. Despite technological advances, accurately accessing to the internal structure of hadrons remains a difficult task from a theoretical point of view. In this work, we analyze the impact on the differential cross-sections when updating the sets of parton distribution and fragmentation functions, for the production of one hadron plus a direct photon at the energy scale of RHIC and LHC experiments.

Polarized vector meson production in semi-inclusive DIS

We make a systematic calculation for polarized vector meson production in semi-inclusive lepton-nucleon deep inelastic scattering ${e}^{\ensuremath{-}}N\ensuremath{\rightarrow}{e}^{\ensuremath{-}}VX$. We consider the general case of neutral current electroweak interactions at high energies which give rise to parity-violating effects. We present a general kinematic analysis for the process and show that the cross sections are expressed by 81 structure functions. We further give a parton model calculation for the process and show the results for the structure functions in terms of the transverse momentum dependent parton distribution functions and fragmentation functions at the leading order and leading twist of perturbative quantum chromodynamics. The results show that there are 27 nonzero structure functions at this order, among which 15 are related to the tensor polarization of the vector meson. Thirteen structure functions are generated by parity-violating effects. We also present the result and a rough numerical estimate for the spin alignment of the vector meson.

Longitudinal and transverse polarizations of Λ hyperon in unpolarized SIDIS and e+e− annihilation

We make a systematic study of $\mathrm{\ensuremath{\Lambda}}$ hyperon polarizations in unpolarized lepton induced semi-inclusive reactions such as ${e}^{\ensuremath{-}}N\ensuremath{\rightarrow}{e}^{\ensuremath{-}}\mathrm{\ensuremath{\Lambda}}X$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}hX$. We present the general form of cross sections in terms of structure functions obtained from a general kinematic analysis. This already shows that the produced hyperons can be polarized in three orthogonal directions, i.e., the longitudinal direction along the hyperon momentum, the normal direction of the production plane, and the transverse direction in the production plane. We present the parton model results at the leading twist and leading order in perturbative QCD using transverse momentum dependent factorization and provide the expressions for these structure functions and polarizations in terms of three-dimensional parton distribution functions and fragmentation functions. We emphasize in particular that by studying the longitudinal polarization and the transverse polarization in the production plane, we can extract the corresponding chiral-odd fragmentation functions ${H}_{1Lq}^{\ensuremath{\perp}\mathrm{\ensuremath{\Lambda}}}$, ${H}_{1Tq}^{\mathrm{\ensuremath{\Lambda}}}$, and ${H}_{1Tq}^{\ensuremath{\perp}\mathrm{\ensuremath{\Lambda}}}$. We also present numerical results of rough estimates utilizing available parametrizations of fragmentation functions and approximations. We discuss how to measure these polarizations and point out in particular that they can be carried out in future EIC and/or ${e}^{+}{e}^{\ensuremath{-}}$ annihilation experiments such as Belle.

Nuclear modification factor of light neutral-meson spectra up to high transverse momentum in p–Pb collisions at [formula omitted] TeV

Neutral pion (π0) and η meson production cross sections were measured up to unprecedentedly high transverse momenta (pT) in p–Pb collisions at sNN=8.16TeV. The mesons were reconstructed via their two-photon decay channel in the rapidity interval −1.3<y<0.3 in the ranges of 0.4<pT<200 GeV/c and 1.0<pT<50 GeV/c, respectively. The respective nuclear modification factor (RpPb) is presented for pT up to of 200 and 30 GeV/c, where the former was achieved by extending the π0 measurement in pp collisions at s=8TeV using the merged cluster technique. The values of RpPb are below unity for pT<10 GeV/c, while they are consistent with unity for pT>10 GeV/c, leaving essentially no room for final state energy loss. The new data provide strong constraints for nuclear parton distribution and fragmentation functions over a broad kinematic range and are compared to model predictions as well as previous results at sNN=5.02TeV.

The high-energy limit of perturbative QCD: Theory and phenomenology

After a brief introduction of formal and phenomenological progresses in the study of the high-energy limit of perturbative QCD, we present arguments supporting the statement that the inclusive emission of Higgs bosons or heavy-flavored hadrons acts as fair stabilizer of high-energy resummed differential distributions. We come out with the message that the hybrid high-energy and collinear factorization, built in term of the next-to-leading logarithmic resummation à la BFKL and supplemented by collinear parton distributions and fragmentation functions, is a valid and powerful tool to gauge the feasibility of precision analyses of QCD in its high-energy limit.

Applying different angular ordering constraints and kt -factorization approaches to the single inclusive hadron production in the e+e− annihilation processes

We study the differential cross section of the single inclusive ${e}^{+}{e}^{\ensuremath{-}}$ annihilation to the hadrons via $\ensuremath{\gamma}$-production, in the different ${k}_{t}$-factorization frameworks. In order to take into account the transverse momenta of the incoming partons, for the first time, we apply the Kimber et al. (KMR) method to calculate the unintegrated parton fragmentation functions (UFFs) from the ordinary integrated one, i.e., the parton fragmentation functions (FFs), which satisfy the similar Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations, such as those of parton distribution functions (PDFs). Also, by utilizing the different angular ordering constraints the results corresponding to the Martin et al. (MRW) in the leading order (LO) and the next-to-leading-order (NLO) are obtained. The LO sets of DSS library for the input FFs is used. The numerical results are compared with the experimental data in the different energies which are reported by the different collaborations, such as TASSO, AMY, MARK II, CELLO, DELPHI, SLD, ALEPH and Belle with the other $\mathrm{QCD}+\mathrm{fragmentation}$ models such as pythia6.4 and 8.2 parton showers. The behaviors of the normalized differential cross sections and the multiplicity versus the ``transverse momentum'' (${p}_{\ensuremath{\perp}}$) are discussed. The final results demonstrate that the KMR and MRW UFFs give a good description of data and there is not much significant difference between the above three schemes. On the other hand, our results become closer to the data for the lower values of ${p}_{\ensuremath{\perp}}$ and the higher values of center of mass energies.

Matching of fracture functions for SIDIS in target fragmentation region

In the target fragmentation region of Semi-Inclusive Deep Inelastic Scattering, the diffractively produced hadron has small transverse momentum. If it is at order of ΛQCD, it prevents to make predictions with the standard collinear factorization. However, in this case, differential cross-sections can be predicted by the factorization with fracture functions, diffractive parton distributions. If the transverse momentum is much larger than ΛQCD but much smaller than Q which is the virtuality of the virtual photon, both factorizations apply. In this case, fracture functions can be factorized with collinear parton distributions and fragmentation functions. We study the factorization up to twist-3 level and obtain gauge invariant results. They will be helpful for modeling fracture functions and useful for resummation of large logarithm of the transverse momentum appearing in collinear factorization.