Twist-3 Fragmentation Research Articles

Predicting the sinϕS single-spin asymmetry of Λ production off a transversely polarized nucleon in SIDIS

We investigate the transverse target spin asymmetry $A^{\sin\phi_{S}}_{UT}$ for the unpolarized $\Lambda$ production in semi-inclusive deep inelastic scattering with the transverse momentum of the final-state lambda hyperon being integrated out. The asymmetry is contributed by the product of the transversity distribution function $h_1(x)$ of the nucleon and the collinear twist-3 fragmentation function $\tilde{H}(z)$ of the $\Lambda$ hyperon. The later one originates from the quark-gluon-quark correlation and is a naive time-reversal-odd function. We calculate $\tilde{H}$ of the $\Lambda$ hyperon by adopt a diquark spectator model. Using the numerical result of $\tilde{H}(z)$ and the available parametrization of $h_1(x)$ from SIDIS data, we predict the $\sin\phi_{S}$ asymmetry in the electroproduction of the $\Lambda$ hyperon in the kinematical region of EIC, EicC and COMPASS. In the phenomenological analysis we include the evolution effect of the distribution functions and the fragmentation functions. The results show that the asymmetries for the $\Lambda$ production SIDIS process is around 0.1 and may be accessible at EIC, EicC and COMPASS. We also find that the evolution of fragmentation function can affect the size of asymmetry.

Transverse Λ polarization in e+e− collisions

In this paper we study transverse polarization of Λ hyperons in single-inclusive leptonic annihilation. We show that when the transverse momentum of the Λ baryon is measured with respect to the thrust axis, a transverse momentum dependent (TMD) factorization formalism is required and the polarization is generated by the TMD polarizing fragmentation function (TMD PFF), D1T⊥. However, when the transverse momentum of the Λ baryon is measured with respect to the momentum of the initial leptons, a collinear twist-3 formalism is required and the polarization is generated by the intrinsic collinear twist-3 fragmentation function DT. Thus while these measurements differ from one another only by a change in the measurement axis, they probe different distribution functions. Recently, Belle measured a significant polarization in single-inclusive Λ baryon production as a function of the transverse momentum with respect to the thrust axis. However, this data can in principle be re-analyzed to measure the polarization as a function of the transverse momentum of the Λ baryon with respect to the lepton pair. This observable could be the first significant probe of the function, DT. In this paper, we first develop a TMD formalism for Λ polarization; we then present a recent twist-3 formalism that was established to describe Λ polarization. Using the TMD formalism, we demonstrate that the Λ polarization at OPAL and Belle can be described using the twist-2 TMD factorization formalism. Finally, we make a theoretical prediction for this polarization in the collinear twist-3 formalism at Belle.

On the connection between quark propagation and hadronization

We investigate the properties and structure of the recently discussed “fully inclusive jet correlator”, namely, the gauge-invariant field correlator characterizing the final state hadrons produced by a free quark as this propagates in the vacuum. Working at the operator level, we connect this object to the single-hadron fragmentation correlator of a quark, and exploit a novel gauge invariant spectral decomposition technique to derive a complete set of momentum sum rules for quark fragmentation functions up to twist-3 level; known results are recovered, and new sum rules proposed. We then show how one can explicitly connect quark hadronization and dynamical quark mass generation by studying the inclusive jet’s gauge-invariant mass term. This mass is, on the one hand, theoretically related to the integrated chiral-odd spectral function of the quark, and, on the other hand, is experimentally accessible through the E and {widetilde{E}} twist-3 fragmentation function sum rules. Thus, measurements of these fragmentation functions in deep inelastic processes provide one with an experimental gateway into the dynamical generation of mass in Quantum Chromodynamics.

Exact relations for twist-3 gluon distribution and fragmentation functions from operator identities

We perform a systematic study on the twist-3 gluon distribution and fragmentation functions which appear in the collinear twist-3 factorization for hard inclusive processes. Three types of twist-3 distribution and fragmentation functions, i.e., intrinsic, kinematical, and dynamical ones, which are necessary to describe all kinds of twist-3 cross sections, are related to each other by the operator identities based on the QCD equation of motion and the Lorentz invariance properties of the correlation functions. We derive the exact relations for all twist-3 gluonic distribution and fragmentation functions for a spin-$1/2$ hadron. Those relations allow one to express intrinsic and kinematical twist-3 gluon functions in terms of the twist-2 and dynamical twist-3 functions, which provides a basis for the renormalization of intrinsic and kinematical twist-3 functions. In addition, those model independent relations are crucial to guarantee gauge invariance and frame independence properties of the twist-3 cross sections.

Overview of recent HERMES results

The HERMES experiment has collected a wealth of data using the 27.6 GeV polarized HERA lepton beam and various polarized and unpolarized gaseous targets. This allows for a series of unique measurements of observables sensitive to the multidimensional (spin) structure of the nucleon, in particular semi-inclusive deep-inelastic scattering (SIDIS) measurements.In this contribution, transverse single-spin asymmetry, longitudinal single- and double-spin asymmetries in SIDIS will be presented. The azimuthally uniform double-spin asymmetries using longitudinally polarized nucleons constrain the flavour dependence of the quark-spin contribution to the nucleon spin. For a first time, such asymmetries are explored differential in three dimensions in Bjorken-x and the in the hadron kinematics z and Ph± (which respectively represent the energy fraction and transverse momentum of the final-state hadron) simultaneously. This approach increases the quark-flavour sensitivity and allows to probe the transverse-momentum dependence of the helicity distribution. The measurement of hadron charge-difference asymmetries allows, under certain simplifying assumptions, the direct extraction of valence quark polarisations.The azimuthal modulation of this double-spin as well as of the single-(beam)spin asymmetry probe novel quark-gluon-quark correlations through twist-3 distribution and fragmentation functions. Also here, asymmetries are explored in several dimensions. Furthermore, in case of the beam-spin asymmetry, results for electro-produced protons and antiprotons have become available. The beam-spin asymmetries for pions are compared to similar measurements for pions at CLAS and unidentified hadrons at COMPASS.

Polarized hyperon production in single-inclusive electron-positron annihilation at next-to-leading order

We study the production of polarized Λ-hyperons in electron-positron annihilation. We are particularly interested in the transverse-spin dependence of the cross section for unpolarized incident electron-positron pairs. At high energies this process may be described in the collinear twist-3 framework, where the hadronization transition of partons into a transversely polarized Λ-hyperon can be written in terms of collinear twist-3 fragmentation matrix elements. We calculate the hard partonic cross sections and interference terms in perturbative QCD to next-to-leading order accuracy. We find that the QCD equation of motion plays a crucial role in our analysis. As a byproduct, assuming the validity of QCD factorization for twist-3 observables at next-to-leading order, we derive the evolution equation for the relevant twist-3 fragmentation matrix element.

Overview of recent HERMES results

An overview of more recent and important results from the HERMES experiment is presented in this paper. HERMES collected a wealth of data using the 27.6 GeV polarized HERA lepton beam and various polarized and unpolarized gaseous targets. This allows for a series of unique measurements of observables sensitive to the multidimensional structure of the nucleon. Amongst them are the semi-inclusive deep-inelastic scattering measurements of azimuthal modulations sensitive to the leading-twist transverse momentum distributions and the distributions sensitive to convolutions of the twist-2 and twist-3 distribution and fragmentation functions. They all provide information on the three-momentum-dependent quark distributions. Knowledge about the quark distribution as a function of longitudinal momentum and transverse position in impact-parameter space can be accessed, e.g., through exclusive vector–meson leptoproduction. Particularly, the measurement of spin-density-matrix elements on an unpolarized hydrogen target and the measurement of azimuthal modulations on transversely polarized hydrogen target for the ω–meson production are described in this paper. The results of the measurement of ratios of helicity amplitudes for the ρ0 –meson leptoproduction on transversely polarized hydrogen target are also presented.

Leading order analysis of twist-3 space- and time-like cut vertices in QCD

We review the recent theoretical progress in the construction and solution of the evolution equations which govern the scale dependence for the twist-3 structure and fragmentation functions of the nucleon.

Evolution of chirality-odd twist-3 fragmentation functions

We derive the complete set of evolutions of chirality-odd twist-3 fragmentation functions at one-loop level. There are totally nine real twist-3 fragmentation functions, among which seven are independent. The renormalization-scale dependence of the nine functions has an important implication for studies of single transverse-spin asymmetries. We find that the evolutions of the three complex fragmentation functions defined by quark–gluon–quark operator are mixed with themselves. There is no mixing with the fragmentation functions defined only with bilinear quark field operators. In the large-Nc limit the evolutions of the three complex fragmentation functions are simplified and reduced to six homogeneous equations.

Twist-3 fragmentation contribution to polarized hyperon production in unpolarized hadronic collisions

It has been known for a long time that hyperons produced in hadronic collisions are polarized perpendicular to the production plane of the reaction. This effect cannot be described by using twist-2 collinear parton correlators only. Here we compute the contribution of twist-3 fragmentation functions to the production of transversely polarized hyperons in unpolarized proton-proton collisions in the framework of collinear factorization. By taking into account the relations among the relevant twist-3 fragmentation functions which follow from the QCD equation of motion and the Lorentz invariance property of the correlators, we present the leading-order cross section for this term.

Double-spin asymmetryALTcosϕSin semi-inclusive DIS at CLAS12 and EIC within the collinear framework

We study the longitudinal-transverse double-spin asymmetry with a $\cos\phi_S$ modulation in semi-inclusive deep inelastic scattering for charged and neutral pions production. We consider the particular case in which the transverse momentum of the final state hadron is integrated out. The corresponding asymmetry may be contributed by two parts: one is the convolution of the twist-3 distribution function $g_{T}(x)$ and the unpolarized fragmentation function $D_1(z)$, the other is related to the coupling of the transversity distribution function $h_1(x)$ and the collinear twist-3 fragmentation function $\tilde{E}(z)$. We take into account both contributions to predict the $\cos\phi_S$ asymmetry at the kinematics of CLAS12 and a future Electron Ion Collider. We find that the asymmetry of pion production at CLAS12 is sizable, and $\tilde{E}(z)$ can play an important role in the asymmetry in the large-$z$ region.

Operator constraints for twist-3 functions and Lorentz invariance properties of twist-3 observables

We investigate the behavior under Lorentz tranformations of perturbative coefficient functions in a collinear twist-3 formalism relevant for high-energy observables including transverse polarization of hadrons. We argue that those perturbative coefficient functions can, {\it a priori}, acquire quite different yet Lorentz-invariant forms in various frames. This somewhat surprising difference can be traced back to a general dependence of the perturbative coefficient functions on lightcone vectors which are introduced by the twist-3 factorization formulae and which are frame-dependent. One can remove this spurious frame dependence by invoking so-called Lorentz invariance relations (LIRs) between twist-3 parton correlation functions. Some of those relations for twist-3 distribution functions were discussed in the literature before. In this paper we derive the corresponding LIRs for twist-3 fragmentation functions. We explicitly demonstrate that these LIRs remove the lightcone vector dependence by considering transverse spin observables in the single-inclusive production of hadrons in lepton-nucleon collisions, $\ell N\to hX$. With the LIRs in hand, we also show that twist-3 observables in general can be written solely in terms of three-parton correlation functions.

Twist-3 contributions in semi-inclusive DIS with transversely polarized target

Abstract We study semi-inclusive DIS with a transversely polarized target in the approach of collinear factorization. The effects related to the transverse polarization are at twist-3. We derive the complete result of twist-3 contributions to the relevant hadronic tensor at leading order of α s , and construct correspondingly experimental observables. Measuring these observables will help to extract the twist-2 transversity distribution, twist-3 distributions and twist-3 fragmentation functions of the produced unpolarized hadron. A detailed comparison with the approach of transverse-momentum-dependent factorization is made.

Transverse Single Spin Asymmetries of Forward π0 and Jet-like Events in s = 500 GeV Polarized Proton Collisions at STAR

The large transverse single spin asymmetries (SSA) of high [Formula: see text] inclusive hadrons produced in polarized proton collisions are usually explained by means of collinear twist-3 multi-parton correlations. In this picture these asymmetries can originate from initial-state twist-3 parton distributions in the polarized proton and/or through the coupling between proton transversity and twist-3 fragmentation functions. The measurement of SSA for forward inclusive hadrons produced in [Formula: see text] collisions out to high transverse momentum helps to examine the validity and interplay of these initial- and final-state models. These models can be further explored by investigating the dependence of the SSA on event topologies. We present our latest status on the measurement of SSA for forward inclusive [Formula: see text] detected within [Formula: see text] in [Formula: see text] = 500 GeV [Formula: see text] collisions as well as its dependence on event topologies. We will also present our analysis of Sivers and Collins asymmetries for forward jet-like events consisting of multi-photon final states. The measurements are based on the data taken in 2011 with integrated luminosity [Formula: see text] 22 [Formula: see text].

Twist-3 fragmentation effects for ALT in light hadron production from proton–proton collisions

We compute the contribution from the twist-3 fragmentation function for light hadron production in collisions between transversely and longitudinally polarized protons, i.e., p↑p→→hX, which can cause a double-spin asymmetry (DSA) ALT. This is a naïve T-even twist-3 observable that we analyze in collinear factorization using both Feynman gauge and lightcone gauge as well as give a general proof of color gauge invariance. So far only twist-3 effects in the transversely polarized proton have been studied for ALT in p↑p→→hX. However, there are indications that the naïve T-odd transverse single-spin asymmetry (SSA) AN in p↑p→hX is dominated not by such distribution effects but rather by a fragmentation mechanism. Therefore, one may expect similarly that the fragmentation contribution is important for ALT. Given possible plans at RHIC to measure this observable, it is timely to provide a calculation of this term.

Twist-3 fragmentation functions in a spectator model with gluon rescattering

We study the twist-3 fragmentation functions H and H˜, by applying a spectator model. In the calculation we consider the effect of the gluon rescattering at one loop level. We find that in this case the hard-vertex diagram, which gives zero contribution to the Collins function, does contribute to the fragmentation function H. The calculation shows that the twist-3 T-odd fragmentation functions are free of light-cone divergences. The parameters of the model are fitted from the known parametrization of the unpolarized fragmentation D1 and the Collins function H1⊥. We find that our result for the favored fragmentation function is consistent with the recent extraction on H and H˜ from pp data. We also check numerically the equation of motion relation for H, H˜ and find that relation holds fairly well in the spectator model.

Transverse Single-Spin Asymmetries in Proton-Proton Collisions Within Collinear Factorization

We provide a new analysis within collinear factorization of transverse single-spin asymmetries (TSSAs) in high transverse momentum charged and neutral pion production in pp collisions at the Relativistic Heavy Ion Collider (RHIC). This study incorporates the so-called twist-3 fragmentation term and shows that one can describe RHIC data through this mechanism. Moreover, by fixing other non-perturbative inputs through extractions of transverse momentum dependent functions in e+e- → h1h2X and semi-inclusive deep-inelastic scattering (SIDIS), we provide for the first time a consistency between certain spin/azimuthal asymmetries in all three reactions (i.e., pp, e+e-, and SIDIS).

ANin proton-proton collisions and the role of twist-3 fragmentation

We review and give an update on the current status of what causes transverse single-spin asymme- tries (TSSAs) in semi-inclusive processes where a single hadron is detected in the final state, especially those involving proton-proton (pp) collisions. In particular, we provide a new analysis within collinear factorization of TSSAs in high transverse momentum charged and neutral pion production in ppcollisions at the Relativistic Heavy Ion Collider (RHIC). This study incorporates the so-called twist-3 fragmentation term and shows that one can describe RHIC data through this mechanism. Moreover, by fixing other non-perturbative inputs through extractions of transverse momentum dependent functions in e + e − → h1h2X and semi-inclusive deep-inelastic scattering (SIDIS), we provide for the first time a consistency between certain spin/azimuthal asymmetries in all three reactions (i.e., pp, e + e − , and SIDIS).

New Collinear Twist-3 Analysis of Transverse SSA: Toward a Solution for the Sign-Mismatch Problem

We present a new collinear twist-3 analysis of the transverse SSA A N at RHIC. We use the TMD Sivers/Collins function to fix some of the relevant collinear twist-3 functions and perform a fit of the RHIC data with other parameterized twist-3 functions. This allows us to keep the consistency among descriptions in pp collision, SIDIS, and e + e − annihilation and thus could provide a unified description of the spin asymmetries in the low- and high-P T processes. By taking into account the twist-3 fragmentation contribution, we show for the first time this contribution could be the main source of A N in \({pp^{\uparrow} \rightarrow hX}\) and its inclusion could provide a solution for the sign-mismatch problem.

Contribution of the twist-3 fragmentation function to the single transverse-spin asymmetry in semi-inclusive deep inelastic scattering

We study the contribution of the twist-3 fragmentation function to the single-transverse spin asymmetry in semi-inclusive deep inelastic scattering within the framework of the collinear factorization. Making use of the Ward-Takahashi identity in QCD, we establish the formalism in the Feynman gauge to calculate the non-pole contribution of the twist-3 fragmentation function to the asymmetry and derive the complete cross-section formula in the leading order QCD perturbation theory. The obtained twist-3 hadronic tensor is shown to satisfy the electromagnetic gauge-invariance. The behavior in the small transverse- momentum region for the five structure functions is also given.