Spin-dependent Fragmentation Functions Research Articles

Dihadron helicity correlation in photon-nucleus collisions

The helicity correlation of two back-to-back hadrons is a powerful tool that makes it possible to probe the longitudinal spin transfer G1L in unpolarized hadronic collisions. In this work, we investigate the helicity correlation of back-to-back dihadrons produced in photon-nucleus collisions with both spacelike and quasireal photons and explore its potential in understanding the flavor dependence of spin-dependent fragmentation functions. We present helicity amplitudes of partonic scatterings with both virtual and real photons and make numerical predictions for the dihadron helicity correlations at the future Electron Ion Collider experiment and the current Relativistic Heavy Ion Collider/LHC ultraperipheral collision experiment. Future experimental measurements can also illuminate the fragmentation function of circularly polarized gluons. Published by the American Physical Society 2024

Semi-inclusive production of spin- 3/2 hadrons in deep inelastic scattering

We investigate the production of spin-3/2 hadrons in semi-inclusive deep inelastic lepton-nucleon scatterings. The complete differential cross section is derived through the kinematic analysis and expressed in terms of 288 structure functions, corresponding to all polarization configurations and azimuthal modulations. For an unpolarized lepton beam, half of the 192 structure functions have nonzero leading order contributions in the parton model, among which 42 are from rank-3 tensor polarized fragmentation functions of the hadron. For a polarized lepton beam, one third of the 96 structure functions contribute at the leading order and 14 of them are from rank-3 tensor polarized fragmentation functions. In addition to the formalism, we perform a model estimation of the spin transfer to a ShLLL polarized hadron and sizable asymmetry is expected. Therefore, these newly defined observables for the production of a spin-3/2 hadron in a deep inelastic scattering process can be explored in future experiments to understand nucleon spin structures and spin-dependent fragmentation functions. Published by the American Physical Society 2024

Correlations of dihadron polarization in central, peripheral, and ultraperipheral heavy-ion collisions

While jet quenching in relativistic heavy-ion collisions has been extensively studied over decades, the polarization of quenched hadrons has rarely been discussed. It has recently been proposed that the correlations of dihadron polarization in e+e− and pp collisions provide a novel probe of the longitudinal spin transfer from hard partons to hadrons without requiring the colliding beams to be polarized. To support realistic experimental measurement of dihadron polarization with sufficient luminosity, we extend the aforementioned study to relativistic heavy-ion collisions by convoluting the vacuum fragmentation of partons with their energy loss inside the quark-gluon plasma. We find that while the correlation functions of Λ−Λ (or Λ−Λ¯) polarization in peripheral collisions is consistent with those in pp collisions, clear enhancement can be seen in central collisions. These correlation functions appear sensitive to different assumptions in the de Florian-Stratmann-Vogelsang (DSV) of parton fragmentation functions and, therefore, could place additional constraints on the spin-dependent fragmentation functions of quarks and gluons. The correlation of dihadron polarization has also been explored in ultraperipheral heavy-ion collisions, which provides a cleaner probe of fragmentation functions of quarks produced by energetic photon-photon and photon-Pomeron interactions. Published by the American Physical Society 2024

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.

Several Topics on Transverse Momentum-Dependent Fragmentation Functions

The hadronization of a high-energy parton is described by fragmentation functions which are introduced through QCD factorizations. While the hadronization mechanism per se remains uknown, fragmentation functions can still be investigated qualitatively and quantitatively. The qualitative study mainly concentrates on extracting genuine features based on the operator definition in quantum field theory. The quantitative research focuses on describing a variety of experimental data employing the fragmentation function given by the parameterizations or model calculations. With the foundation of the transverse-momentum-dependent factorization, the QCD evolution of leading twist transverse-momentum-dependent fragmentation functions has also been established. In addition, the universality of fragmentation functions has been proven, albeit model-dependently, so that it is possible to perform a global analysis of experimental data in different high-energy reactions. The collective efforts may eventually reveal important information hidden in the shadow of nonperturbative physics. This review covers the following topics: transverse-momentum-dependent factorization and the corresponding QCD evolution, spin-dependent fragmentation functions at leading and higher twists, several experimental measurements and corresponding phenomenological studies, and some model calculations.

Measurement of Transverse Spin Dependent Azimuthal Correlations of Charged Pion(s) in $p^{\uparrow} p$ Collisions at $\sqrt s = 200$ GeV at STAR

At the leading twist, the transversity distribution function, h^{q}_{1}(x)h1q(x), where xx is the longitudinal momentum fraction of the proton carried by quark qq, encodes the transverse spin structure of the nucleon. Extraction of it is difficult because of its chiral-odd nature. In transversely polarized proton-proton collisions (p^\uparrow pp↑p), h_{1}^{q}(x)h1q(x) can be coupled with another chiral-odd partner, a spin-dependent fragmentation function (FF). The resulting asymmetries in hadron(s) azimuthal correlations directly probe h_{1}^{q}(x)h1q(x). We report the measurement of correlation asymmetries for charged pion(s) in p^\uparrow pp↑p, through the Collins and the Interference FF channel.

Polarized jet fragmentation functions

We develop the theoretical framework needed to study the distribution of hadrons with general polarization inside jets, with and without transverse momentum measured with respect to the standard jet axis. The key development in this paper, referred to as “polarized jet fragmentation functions”, opens up new opportunities to study both collinear and transverse momentum dependent (TMD) fragmentation functions. As two examples of the developed framework, we study longitudinally polarized collinear Λ and transversely polarized TMD Λ production inside jets in both pp and ep collisions. We find that both observables have high potential in constraining spin-dependent fragmentation functions with sizeable asymmetries predicted, in particular, at the future Electron-Ion Collider.

Spin alignment of vector mesons in high energy pp collisions

The spin alignment of vector meson produced in high energy reactions is determined by the spin-dependent fragmentation function $D_{1LL} (z,\mu_f)$ that is shown to be independent of the polarization of the fragmenting quark. In this paper, we extract the spin-dependent fragmentation function $D_{1LL} (z,\mu_f)$ from data on the spin alignment of $K^{*0}$ in $e^+e^-$ annihilation at LEP in two different scenarios and apply them to make predictions in $pp$ collisions. We make detailed analysis of contributions from different sub-processes and show that the spin alignment should be quite significant also in high energy $pp$ collisions.

Polarized heavy baryon production in quark-diquark model considering two different scenarios

At sufficiently large transverse momentum, the dominant production mechanism for heavy baryons is actually the fragmentation. In this work, we first study the direct fragmentation of a heavy quark into the unpolarized triply heavy baryons in the leading order of perturbative QCD. In a completely different approach, we also analyze the two-stage fragmentation of a heavy quark into a scalar diquark followed by the fragmentation of such a scalar diquark into a triply heavy baryon: quark-diquark model of baryons. The results of this model are in acceptable agreement with those obtained through a full perturbative regime. Relying on the quark-diquark model and considering two different scenarios we determine the spin-dependent fragmentation functions of polarized heavy baryons in such a way that a vector or a pseudoscalar heavy diquark is an intermediate particle between the initial heavy quark and the final state baryon.

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.

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.

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.

Spin-dependent fragmentation functions of gluon splitting into heavy quarkonia considering three different scenarios

Heavy quarkonium production is a powerful implement to study the strong interaction dynamics and QCD theory. Fragmentation is the dominant production mechanism for heavy quarkonia with large transverse momentum. With the large heavy quark mass, the relative motion of the heavy quark pair inside a heavy quarkonium is effectively nonrelativistic and it is also well known that their fragmentation functions can be calculated in the perturbative QCD framework. Here, we analytically calculate the process-independent fragmentation functions for a gluon to split into the spin-singlet and spin-triplet [Formula: see text]-wave heavy quarkonia using three different scenarios. We will show that the fragmentation probability of the gluon into the spin-triplet bound-state is the biggest one.

Fragmentation functions at Belle

Fragmentation functions (FFs) describe the formation of final state hadrons from final state quarks or gluons. Precise knowledge of these functions is a key ingredient in extracting spin-dependent parton distribution functions from spin asymmetries observed in polarized Semi-Inclusive Deep Inelastic Scattering (SIDIS) and in inclusive hadron production in polarized proton-proton collisions. However, fragmentation functions can not be determined from first principles Quantum Chromodynamics (QCD) and have to be extracted from experimental data. The Belle experiment at KEK in Japan has acquired large data samples from hadron production in e+e− annihilation. Precision measurements of identified hadron yields from Belle can be used to improve the precision of the presently available hadron fragmentation data. In this talk Belle results on spin-dependent fragmentation functions will be summarized and the status of the spin-averaged hadron yield analysis will be presented.

PROBING POLARIZED GLUON DISTRIBUTIONS THROUGH CHARMED HADRON PRODUCTION IN POLARIZED pp COLLISIONS AT BNL-RHIC ENERGY

In order to extract information about behavior of polarized gluons in the nucleon, charmed hadron productions, i.e. D*+ meson and [Formula: see text] baryon productions, are studied in polarized pp reactions at BNL-RHIC energy. For these processes, the spin correlation asymmetry DLL between the target proton and the produced charmed hadron, and its statistical sensitivity δDLL are calculated. From analyses on these processes, we found that the pseudorapidity distribution of DLL in the limited transverse momentum region is quite effective for distinguishing the model of polarized gluons as well as the model of spin-dependent fragmentation functions.

Excited state contributions to the heavy baryon fragmentation functions in a quark-diquark model

Spin dependent fragmentation functions for heavy flavor quarks to fragment into heavy baryons are calculated in a quark-diquark model. The production of intermediate spin 1/2 and 3/2 excited states is explicitly included. The resulting ${\ensuremath{\Lambda}}_{b}$ production rate and polarization at CERN LEP energies are in agreement with experiment. The ${\ensuremath{\Lambda}}_{c}$ and ${\ensuremath{\Xi}}_{c}$ functions are also obtained. The spin independent ${f}_{1}(z)$ is compared to data. The integrated values for production rates agree with the data.

Spin dependent fragmentation functions for heavy flavor baryons and single heavy hyperon polarization

Spin dependent fragmentation functions for heavy flavor quarks to fragment into heavy baryons are carculated in a quark-diquark model. The production of intermediate spin 1/2 and 3/2 excited states is explicity included. Λ b , Λc and Ξ c production rate and polarization at LEP energies are calculated and, where possible, compared with experiment. A different approach, also relying on a heavy quark-diquark model, is proposed for the small momentum transfer inclusive production of polarized heavy flavor hyperons. The predicted Λc polarization is roughly in agreement with experiment.

How could the proton transversity be measured

The perspectives of two new nonstandard methods of transversal quark polarization measurement are considered: the jet handedness and the so-called "Collins effect" due to spin dependent T-odd fragmentation function responsible for the left-right asymmetry in fragmenting of transversally polarized quarks. Recent experimental indications in favor of these effects are observed: 1.The correlation of the T-odd one-particle fragmentation functions found by DELPHI in $Z\to 2$-jet decay. Integrated over the fraction of longitudinal and transversal momenta, this correlation is of 1.6% order, which means order of 13% for the analyzing power. 2.A rather large ($\approx10%$) handedness transversal to the production plane observed in the diffractive production of ($\pi^-\pi^+\pi^-$) triples from nuclei by the $40 {\rm GeV/c}$ $\pi^-$--beam. It shows a clear dynamic origin and resembles the single spin asymmetry behavior. All this makes us hope to use these effects in polarized DIS experiments for transversity measurement. The first estimation of transversity was done by using the azimuthal asymmetry in semi-inclusive DIS recently measured by HERMES and SMC.

Single transverse spin asymmetries in inclusive hadron production

A consistent phenomenological approach to the computation of transverse single spin asymmetries in inclusive hadron production is presented, based on the assumed generalization of the QCD factorization theorem to the case in which quark intrinsic motion is taken into account. New k ⊥ and spin dependent quark distribution and fragmentation functions are considered: some of them are fixed by fitting data on p ↑ p → πX and predictions are given for single spin asymmetries in ℓp ↑ → πX and γ ∗p ↑ → πX processes.

Quark Flavor Separation inΛ-Baryon Fragmentation

It is shown that unpolarized and polarized $\ensuremath{\Lambda}$ and $\overline{\ensuremath{\Lambda}}$ production in neutrino and antineutrino deep inelastic scattering, can provide a clean separation of unpolarized and polarized fragmentation functions of a quark into a $\ensuremath{\Lambda}$, for both light-flavor quarks and antiquarks and also for strange quarks. Combining with $\ensuremath{\Lambda}$ and $\overline{\ensuremath{\Lambda}}$ production in polarized electron deep inelastic scattering, one can systematically measure or check the various flavor and spin dependent fragmentation functions. Such measurements can provide crucial tests of different predictions concerning the spin structure of hadrons and the quark-antiquark asymmetry of the nucleon sea.