Collins Fragmentation Function Research Articles

Exploring the spin structure of the nucleon at STAR

Understanding the internal spin structure of the nucleon remains a challenge in strong interaction physics. The unique capability of RHIC opened new avenues in studying the internal structure of the proton with unprecedented depth and precision. Significant progress has been made in the last few years through various measurements at STAR. The longitudinal spin measurements have contributed significantly to our understanding of the quark and gluon helicity distributions inside the proton. The longitudinal double-spin asymmetry, ALL, from STAR inclusive jet and dijet measurements provides the first evidence of a positive gluon polarization with partonic momentum fraction x > 0.05. The reconstruction of W±/Z in longitudinally polarized proton-proton collisions indicates that there is a flavor separation of the light sea quark helicity distributions. In transversely polarized proton collisions, W±/Z-bosons provide the first constraint on the sea-quark Sivers function and contributes to the tests of the predicted sign change. The tilt of the dijet opening angle provides a direct access to the first Mellin momentum of the Sivers function and avoids the spin-correlated fragmentation contributions. The novel measurements of the azimuthal distributions of identified hadrons in jets and spin-dependent dihadron correlations directly probe the collinear quark transversity in the proton, with the former coupled to the transverse momentum dependent (TMD) Collins fragmentation function and the latter to the dihadron interference fragmentation function. These measurements shed lights on Sivers function, quark transversity and spin-dependent fragmentation functions in both collinear and TMD formalism. In this proceeding, recent jet results on both the longitudinal and transverse spin structure of the proton from STAR are presented.

ECCE sensitivity studies for single hadron transverse single spin asymmetry measurements

We performed feasibility studies for various single transverse spin measurements that are related to the Sivers effect, transversity and the tensor charge, and the Collins fragmentation function. The processes studied include semi-inclusive deep inelastic scattering (SIDIS) where single hadrons (pions and kaons) were detected in addition to the scattered DIS lepton. The data were obtained in pythia6 and geant4 simulated e+p collisions at 18 GeV on 275 GeV, 18 on 100, 10 on 100, and 5 on 41 that use the ECCE detector configuration. Typical DIS kinematics were selected, most notably Q2>1GeV2, and cover the x range from 10−4 to 1. The single spin asymmetries were extracted as a function of x and Q2, as well as the semi-inclusive variables z, which corresponds to the momentum fraction the detected hadron carries relative to the struck parton, and PT, which corresponds to the transverse momentum of the detected hadron relative to the virtual photon. They are obtained in azimuthal moments in combinations of the azimuthal angles of the hadron transverse momentum and transverse spin of the nucleon relative to the lepton scattering plane. In order to extract asymmetries, the initially unpolarized MonteCarlo was re-weighted in the true kinematic variables, hadron types and parton flavors based on global fits of fixed target SIDIS experiments and e+e− annihilation data. The expected statistical precision of such measurements is extrapolated to 10 fb−1 and potential systematic uncertainties are approximated given the deviations between true and reconstructed yields. Similar neutron information is obtained by comparing the ECCE e+p pseudo-data with the same from the EIC Yellow Report and scaling the corresponding Yellow Report e+3He pseudo-data uncertainties accordingly. The impact on the knowledge of the Sivers functions, transversity and tensor charges, and the Collins function has then been evaluated in the same phenomenological extractions as in the Yellow Report. The impact is found to be comparable to that obtained with the parametrized Yellow Report detector and shows that the ECCE detector configuration can fulfill the physics goals on these quantities.

The sin 2phi _h azimuthal asymmetry of pion production in SIDIS within TMD factorization

We study the sin 2phi _h azimuthal asymmetry of charged and neutral pion productions off the longitudinally polarized nucleon targets in semi-inclusive deeply inelastic scattering (SIDIS) process within the transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the TMD distribution h_{1L}^{perp } and the Collins fragmentation function H_{1}^perp . We adopt the Wandzura–Wilczek-type (WW-type) approximation for h_{1L}^{perp } and two different parametrizations on the nonperturbative Sudakov form factor for h_{1L}^{perp } and H_{1}^perp . We estimate the sin 2phi _h asymmetry at HERMES and CLAS and compare them with the corresponding experimental data. We also provide the prediction at kinematical configuration of CLAS12. It is shown that our theoretical calculation can describe the HERMES and CLAS data, except the asymmetry of the pi ^- production off proton target at HERMES and CLAS. We also find that different choices of the nonperturbative part of TMD evolution lead qualitatively similar results.

Jet-based measurements of Sivers and Collins asymmetries at the future electron-ion collider

We present predictions and projections for hadron-in-jet measurements and electron-jet azimuthal correlations at the future Electron-Ion Collider (EIC). These observables directly probe the three-dimensional (3D) structure of hadrons, in particular, the quark transversity and Sivers parton distributions and the Collins fragmentation functions. We explore the feasibility of these experimental measurements by detector simulations and discuss detector requirements. We conclude that jet observables have the potential to enhance the 3D imaging EIC program.

Azimuthal asymmetries of back-to-back π±−(π0, η, π±) pairs in e+e− annihilation

This work reports the first observation of azimuthal asymmetries around the thrust axis in $e^+e^-$ annihilation of pairs of back-to-back charged pions in one hemisphere, and $\pi^0$ and $\eta$ mesons in the opposite hemisphere. These results are complemented by a new analysis of pairs of back-to-back charged pions. The $\pi^0$ and $\eta$ asymmetries rise with the relative momentum $z$ of the detected hadrons as well as with the transverse momentum with respect to the thrust axis. These asymmetries are sensitive to the Collins fragmentation function $H_1^{\perp}$ and provide complementary information to previous measurements with charged pions and kaons in the final state. In particular, the $\eta$ final states will provide additional information on the flavor structure of $H_1^{\perp}$. This is the first measurement of the explicit transverse-momentum dependence of the Collins fragmentation function from Belle data. It uses a dataset of 980.4~fb$^{-1}$ collected by the Belle experiment at or near a center-of-mass energy of 10.58 GeV.

Role of transverse momentum dependence of unpolarized parton distribution and fragmentation functions in the analysis of azimuthal spin asymmetries

Information on the Sivers distribution and the Collins fragmentation functions and their transverse momentum dependence is mainly based on fitting single spin asymmetry data from semi-inclusive deep inelastic scattering (SIDIS). Independent information, respectively on the Sivers distribution and the Collins fragmentation, can be obtained from Drell-Yan and $e^+e^-$ annihilation processes. In the SIDIS case, the transverse momentum of the final observed hadron, which is the quantity measured, is generated both by the average transverse momentum in the distribution and in the fragmentation functions. As a consequence, these are strongly correlated and a separate extraction is made difficult. In this paper we investigate, in a simple kinematical Gaussian configuration, this correlation, its role on the transverse single spin asymmetries in SIDIS and the consequences for predictions of the Sivers asymmetry in Drell-Yan processes and for the Collins asymmetry in $e^+e^-$ annihilation. We find that, in some cases, these effects can be relevant and must be carefully taken into account.

Semi-inclusive π0 target and beam-target asymmetries from 6 GeV electron scattering with CLAS

We present precision measurements of the target and beam-target spin asymmetries from neutral pion electroproduction in deep-inelastic scattering (DIS) using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. We scattered 6-GeV, longitudinally polarized electrons off longitudinally polarized protons in a cryogenic 14NH3 target, and extracted double and single target spin asymmetries for ep→e′π0X in multidimensional bins in four-momentum transfer (1.0<Q2<3.2 GeV2), Bjorken-x (0.12<x<0.48), hadron energy fraction (0.4<z<0.7), transverse pion momentum (0<PT<1.0 GeV), and azimuthal angle ϕh between the lepton scattering and hadron production planes. We extracted asymmetries as a function of both x and PT, which provide access to transverse-momentum distributions of longitudinally polarized quarks. The double spin asymmetries depend weakly on PT. The sin⁡2ϕh moments are zero within uncertainties, which is consistent with the expected suppression of the Collins fragmentation function. The observed sin⁡ϕh moments suggest that quark gluon correlations are significant at large x.

Azimuthal transverse single-spin asymmetries of inclusive jets and charged pions within jets from polarized-proton collisions at s=500 GeV

We report the first measurements of transverse single-spin asymmetries for inclusive jet and jet + $\pi^{\pm}$ production at midrapidity from transversely polarized proton-proton collisions at $\sqrt{s} = 500$ GeV. The data were collected in 2011 with the STAR detector sampled from 23 pb$^{-1}$ integrated luminosity with an average beam polarization of 53%. Asymmetries are reported for jets with transverse momenta $6 < p_{T, jet} < 55$ GeV/c and pseudorapidity $|\eta| < 1$. Presented are measurements of the inclusive-jet azimuthal transverse single-spin asymmetry, sensitive to twist-3 initial-state quark-gluon correlators; the Collins asymmetry, sensitive to quark transversity coupled to the polarized Collins fragmentation function; and the first measurement of the "Collins-like" asymmetry, sensitive to linearly polarized gluons. Within the present statistical precision, inclusive-jet and Collins-like asymmetries are small, with the latter allowing the first experimental constraints on gluon linear polarization in a polarized proton. At higher values of jet transverse momenta, we observe the first non-zero Collins asymmetries in polarized-proton collisions, with a statistical significance of greater than $5\sigma$. The results span a range of x similar to results from SIDIS but at much higher $Q^{2}$. The Collins results enable tests of universality and factorization-breaking in the transverse momentum-dependent formulation of perturbative quantum chromodynamics.

Collins azimuthal asymmetries of hadron production inside jets

We investigate the Collins azimuthal asymmetry of hadrons produced inside jets in transversely polarized proton–proton collisions. Recently, the quark transversity distributions and the Collins fragmentation functions have been extracted within global analyses from data of the processes semi-inclusive deep inelastic scattering and electron–positron annihilation. We calculate the Collins azimuthal asymmetry for charged pions inside jets using these extractions for RHIC kinematics at center-of-mass energies of 200 and 500 GeV. We compare our results with recent data from the STAR Collaboration at RHIC and find good agreement, which confirms the universality of the Collins fragmentation functions. In addition, we further explore the impact of transverse momentum dependent evolution effects.

Monte Carlo implementation of polarized hadronization

We study the polarized quark hadronization in a Monte Carlo (MC) framework based on the recent extension of the quark-jet framework, where a self-consistent treatment of the quark polarization transfer in a sequential hadronization picture has been presented. Here, we first adopt this approach for MC simulations of hadronization process with finite number of produced hadrons, expressing the relevant probabilities in terms of the eight leading twist quark-to-quark transverse momentum dependent (TMD) splitting functions (SFs) for elementary $q \to q'+h$ transition. We present explicit expressions for the unpolarized and Collins fragmentation functions (FFs) of unpolarized hadrons emitted at rank two. Further, we demonstrate that all the current spectator-type model calculations of the leading twist quark-to-quark TMD SFs violate the positivity constraints, and propose quark model based ansatz for these input functions that circumvents the problem. We validate our MC framework by explicitly proving the absence of unphysical azimuthal modulations of the computed polarized FFs, and by precisely reproducing the earlier derived explicit results for rank two pions. Finally, we present the full results for pion unpolarized and Collins FFs, as well as the corresponding analyzing powers from high statistics MC simulations with a large number of produced hadrons for two different model input elementary SFs. The results for both sets of input functions exhibit the same general features of opposite signed Collins function for favored and unfavored channels at large $z$, and at the same time demonstrate the flexibility of the quark-jet framework by producing significantly different dependences of the results at mid- to low-$z$ for the two model inputs.

Transverse-momentum-dependent fragmentation functions in e+e- annihilation

Fragmentation functions are non-perturbative functions used to describe the formation of colorless, observable hadrons starting from a colored, partonic initial state. The knowledge of these functions are based on the experimental data, and a good parameterization of the fragmentation processes can shed light on the confining aspect of QCD, and are also a key ingredient in accessing nucleon parton distribution functions in semi-inclusive deep inelastic scattering and proton-proton collisions. In the last decade, a strong interest has risen about the transverse-momentum-dependent (TMD) fragmentation functions, which can be used as tools to probe the 3D-structure of nucleons, and to investigate the Q2 evolution of TMD objects. In this review we will summarize the existing light-quarks fragmentation related measurements from the BaBar, Belle, and BESIII e + e - experiments; in particular, we will focus on the polarized TMD Collins fragmentation functions, emerging from correlations between the transverse polarization of the fragmenting parton and the direction of the resulting hadrons.

Measurement of Azimuthal Asymmetries in Inclusive Charged Dipion Production in e^{+}e^{-} Annihilations at sqrt[s]=3.65 GeV.

We present a measurement of the azimuthal asymmetries of two charged pions in the inclusive process e^{+}e^{-}→ππX, based on a data set of 62 pb^{-1} at the center-of-mass energy of 3.65GeV collected with the BESIII detector. These asymmetries can be attributed to the Collins fragmentation function. We observe a nonzero asymmetry, which increases with increasing pion momentum. As our energy scale is close to that of the existing semi-inclusive deep inelastic scattering experimental data, the measured asymmetries are important inputs for the global analysis of extracting the quark transversity distribution inside the nucleon and are valuable to explore the energy evolution of the spin-dependent fragmentation function.

Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution

We study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in $e^+e^-$ annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins-Soper-Sterman (CSS) formalism, we extract transversity distributions for $u$ and $d$ quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back di-hadron productions in $e^+e^-$ annihilations measured by BELLE and BABAR Collaborations and SIDIS data from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results, and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. We make detailed predictions for future experiments and discuss their impact.

Azimuthal Single-Spin Asymmetries of Charged Pions in Jets in s = 200 GeV p↑p Collisions at STAR

Single spin asymmetry measurements ([Formula: see text]) of the azimuthal distribution of charged pions inside jets produced in transversely polarized proton collisions are sensitive to the transversity distribution and the Collins fragmentation function. The STAR Detector at the Relativistic Heavy Ion Collider is well suited for these types of measurements as it is capable of full jet reconstruction and charged pion identification in the mid-rapidity region ([Formula: see text][Formula: see text][Formula: see text][Formula: see text]). We report here the first observation of Collins [Formula: see text] asymmetries in [Formula: see text] GeV [Formula: see text] collisions.

Measurement of Collins asymmetry at BESIII

In this talk, I present the recent measurement of the Collins fragmentation function based on a set of 62 pb-1 e+e- annihilation data at √s = 3.65 GeV collected with the BESIII detector at the BEPCII storage rings. In this work, the azimuthal asymmetries of two charged pions in the inclusive process e+e- → ππX are explored. These asymmetries can be attributed to the Collins fragmentation function, which describes the behavior of a hadron produced from a transversely polarized quark. The corresponding four-momentum transfer of the virtual photon, Q2, is close to the energy scale of the existing semi-inclusive DIS experimental data. We observe a nonzero asymmetry, which increases with increasing pion momentum and also indicates a larger spin-dependent Collins effect than at higher energy scale. The dependence of the asymmetry on the transverse momentum of hadrons to the reference axis is also investigated. The measured asymmetries are important inputs for the global analysis of extracting the quark transversity distribution inside the nucleon, and are valuable to explore the energy evolution of the spin-dependent fragmentation function.

Measurement of Collins Asymmetries in Inclusive Production of Charged Pion Pairs at BESIII

We present the preliminary results of the measurement of the azimuthal asymmetries of two charged pions in the inclusive process [Formula: see text] in the BESIII experiment. These asymmetries are attributed to the so-called Collins fragmentation function, which depict the behavior of a hadron produced from a transversely polarized quark. This spin-dependent function is an important input for the global analysis of extracting the transversity inside the nucleon. In addition, by comparison with the measured asymmetries at Belle, this measurement provides the first data to explore the [Formula: see text] evolution of the spin-dependent fragmentation function. This work is performed based on about 62[Formula: see text][Formula: see text] data collected with the BESIII detector at BEPCII at [Formula: see text]=3.65[Formula: see text]GeV.

Nucleon tensor charge from Collins azimuthal asymmetry measurements

We investigate the nucleon tensor charge from current experiments by a combined analysis of the Collins asymmetries in two hadron production in $e^+e^-$ annihilations and semi-inclusive hadron production in deep inelastic scattering processes. The transverse momentum dependent evolution is taken into account, for the first time, in the global fit of the Collins fragmentation functions and the quark transversity distributions at the approximate next-to-leading logarithmic order. We obtain the nucleon tensor charge contribution from up and down quarks as $\delta u=+0.30^{+0.12}_{-0.08}$ and $\delta d=-0.20_{-0.11}^{+0.28}$ at 90\% confidence level for momentum fraction $0.0065 \le x_B \le 0.35$ and $Q^2=$ 10 GeV$^2$.

Measurement of Collins asymmetry in inclusive production of pion pairs at BaBar

We present a measurement of the azimuthal asymmetries induced by the Collins effect in inclusive production of pion pairs in the e + e − → ππX annihilation process, where two charged pion pairs are produced in opposite hemispheres. The data collected by the BABAR detector at the SLAC Linear Accelerator Laboratory allows the determination of the Collins fragmentation function as a function of the pion fractional energies and transverse momenta, as well as the determination of its behavior in a 4-dimensional space. These results can be combined with semi-inclusive deep inelastic scattering data to extract the transversity parton distribution function, which is the least known leading-twist component of the QCD description of the nucleon.

Measurement of “pretzelosity” asymmetry of charged pion production in semi-inclusive deep inelastic scattering on a polarizedHe3target

An experiment to measure single-spin asymmetries in semi-inclusive production of charged pions in deep-inelastic scattering on a transversely polarized $^3$He target was performed at Jefferson Lab in the kinematic region of $0.16<x<0.35$ and $1.4<Q^2<2.7$ ${\rm GeV^2}$. The pretzelosity asymmetries on $^3$He, which can be expressed as the convolution of the $h^\perp_{1T}$ transverse momentum dependent distribution functions and the Collins fragmentation functions in the leading order, were measured for the first time. Using the effective polarization approximation, we extracted the corresponding neutron asymmetries from the measured $^3$He asymmetries and cross-section ratios between the proton and $^3$He. Our results show that for both $\pi^{\pm}$ on $^3$He and on the neutron the pretzelosity asymmetries are consistent with zero within experimental uncertainties.

Collins and sivers effects in p↑p → jet πX: Universality and process dependence

In this paper we briefly review the transverse momentum dependent generalized parton model and its application to the study of azimuthal asymmetries in the distribution of leading hadrons (mainly pions) inside large transverse momentum jets inclusively produced in polarized proton-proton collisions. We put particular emphasis on the phenomenological interest of these observables, in combination with similar asymmetries measured in semi-inclusive deeply inelastic scattering, Drell-Yan processes and e+e- collisions, for the study of the universality properties of the transverse momentum dependent parton distribution and fragmentation functions. We present results for RHIC kinematics at center-of-mass energies sqrt{s} = 200 and 500 GeV, for central and mainly forward jet rapidities, in particular for the Sivers distribution and the Collins fragmentation function, that are believed to be responsible of many of the largest asymmetries measured in the last years. We also briefly discuss the case of inclusive jet production and recent phenomenological applications of other theoretical approaches, like the colour gauge invariant generalized parton model and the collinear twist-three approach, aiming at clarifying the issues of the universality and process dependence of transverse momentum dependent functions.