Polarized Fragmentation Functions Research Articles

Transverse Λ polarization in unpolarized pp → jet Λ↑ X

In this Letter, we investigate the spontaneous transverse polarization of Λ hyperons produced in unpolarized pp collisions inside a jet, by adopting a TMD approach where transverse momentum effects are included only in the fragmentation process. We will present predictions based on the parametrizations of the Λ polarizing fragmentation function as extracted from fits to Belle e+e− data. These estimates will be compared against preliminary STAR data. We will then be able to explore the universality properties of the quark polarizing fragmentation function and, for the first time, the role of its gluon counterpart.

Transverse Λ polarization in e+e− processes within a TMD factorization approach and the polarizing fragmentation function

We perform a re-analysis of Belle data for the transverse Λ and overline{Lambda} polarization in e+e− annihilation processes within a transverse momentum dependent (TMD) factorization approach. We consider two data sets, one referring to the associated production of Λ’s with a light unpolarized hadron in an almost back-to-back configuration, and one for the inclusive Λ production, with the reconstruction of the thrust axis. We adopt the Collins-Soper-Sterman framework and employ the recent formulation on the factorization of single-inclusive hadron production. This extends a previous phenomenological study carried out in a more simplified TMD approach, leading to a new extraction of the polarizing fragmentation function (FF). While confirming several features of the previous analysis, here we include the proper QCD scale dependence of this TMD FF and carefully exploit the role of its nonperturbative component. The compatibility, within a unique TMD factorization scheme, of double and single-inclusive hadron production is discussed in detail. Moreover, we consider another data set for inclusive Λ production, at much larger energies, from the OPAL Collaboration, in order to test the consistency of the entire approach. Finally, we elaborate on some fundamental issues like the role of SU(2) isospin symmetry and the heavy quark contributions.

$\Lambda$ Polarizing Fragmentation Function from Belle $e^+ e^-$ data

Experimental data from Belle Collaboration for the transverse polarization of \LambdaΛ’s measured in e^+ e^-e+e− annihilation processes are used to extract the polarizing fragmentation function (FF) within a TMD approach. We consider both associated and inclusive \LambdaΛ production, showing a quite consistent scenario. Good separation in flavor is obtained, leading to four independent FFs. Predictions for SIDIS processes at the EIC, crucial for understanding their universality and evolution properties, are also presented.

Longitudinal and Transverse Spin Transfer of $Λ$ and $\overlineΛ$ Hyperons in Polarized $p$+$p$ Collisions at $\sqrt{s} = 200$ GeV at RHIC-STAR

Measurements of the longitudinal spin transfer, D_{LL}DLL, and the transverse spin transfer, D_{TT}DTT, of the \Lambda(\bar{\Lambda}Λ(Λ‾) hyperon in polarized pp+pp collisions are expected to be sensitive to the helicity distribution and transversity distribution of the s(\bar{s})s(s‾) quark in proton and the corresponding polarized fragmentation functions. This contribution presents the new preliminary results of the \Lambda(\bar{\Lambda}Λ(Λ‾) D_{LL}DLL and D_{TT}DTT using data collected at RHIC-STAR experiment in 2015, with twice larger statistics than previously published results.

Transverse Lambda production at the future Electron-Ion Collider

We provide a comprehensive overview of transversely polarized $\Lambda$ production at the future Electron-Ion Collider (EIC). In particular, we study both spontaneous transverse $\Lambda$ polarization as well as the transverse spin transfer within the Transverse Momentum Dependent (TMD) factorization region. To describe spontaneous $\Lambda$ polarization, we consider the contribution from the TMD Polarizing Fragmentation Function (TMD PFF). Similarly, we study the contribution of the transverse spin transfer originating from the transversity TMD Fragmentation Function (TMD FF). We provide projections for the statistical uncertainties in the corresponding spin observables at the future EIC. Using these statistical uncertainties, we characterize the role that the future EIC will play in constraining these distributions. We perform an impact study in the semi-inclusive deep inelastic scattering process for spontaneous $\Lambda$ polarization with a proton beam. We find that the projected experimental data leads to a significant decrease in the uncertainties for the $u$ and sea TMD PFFs. Furthermore, to access the impact of the EIC on the transversity TMD FF, we perform the first extraction of the transversity TMD FF from the recent COMPASS data. We compare the statistical uncertainties of the future EIC with the theoretical uncertainties from our extraction and find that the EIC could have a significant role in constraining this distribution. Finally, we also provide projections for both spontaneous $\Lambda$ polarization as well as the transverse spin transfer inside the jets in back-to-back electron-jet production at the EIC.

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.

The transverse polarization of Lambda hyperons in e^+e^-rightarrow Lambda ^uparrow h X processes within TMD factorization

We investigate the transverse polarization of the Lambda hyperon in the processes e^+e^-rightarrow Lambda ^uparrow pi ^pm X and e^+e^-rightarrow Lambda ^uparrow K^pm X within the framework of the transverse momentum dependent (TMD) factorization. The transverse polarization is contributed by the convolution of the transversely polarizing fragmentation function (PFF) D_{1T}^perp of the lambda hyperon and the unpolarized fragmentation function D_1 of pion/kaon. We adopt the spectator diquark model result for D_{1T}^{perp } to numerically estimate the transverse polarization in e^+e^-rightarrow Lambda ^uparrow h X process at the kinematical region of Belle Collaboration. To implement the TMD evolution formalism of the fragmentation functions, we apply two different parametrizations on the nonperturbative Sudakov form factors associated with the fragmentation functions of the Lambda , pion and kaon. It is found that our prediction on the polarization in the Lambda pi ^+ production and {bar{Lambda }} pi ^- is consistent with the recent Belle measurement in size and sign, while the model predictions on the polarizations in Lambda pi ^- and Lambda K^pm productions show strong disagreement with the Belle data. The reason for the discrepancies is discussed and possible approaches to improve the calculation in the future are also discussed.

Isospin symmetry of fragmentation functions

We make a systematic study of the isospin symmetry of fragmentation functions by taking decay contributions into account. We assume the isospin symmetry in strong interactions and show that in the unpolarized case the isospin symmetry is held for fragmentation functions of Λ and only tiny violations are allowed for other hadrons such as nucleon and pions due to the contributions from weak decays. We present a rough estimate of the magnitudes of such violations. In the polarized case, we show that the isospin symmetry violation for Λ production should be tiny and the recent Belle data on the transverse polarization of Λ can be reproduced if the isospin symmetry is kept in the corresponding polarized fragmentation functions.

Polarizing fragmentation function and the Λ polarization in e+e− processes

The surprising polarisation of Lambdas and other hyperons measured in many unpolarised hadronic processes, p N --> Lambda X, has been a long standing challenge for QCD phenomenology. One possible explanation was suggested, related to non perturbative properties of the quark hadronisation process, and encoded in the so-called Polarising Fragmentation Function (PFF). Recent Belle data have shown a non zero Lambda polarisation also in unpolarised e+ e- processes, e+ e- --> Lambda X and e+ e- --> Lambda h X. We consider the single inclusive case and the role of the PFFs. Adopting a simplified kinematics it is shown how they can originate a polarisation P_Lambda different from 0 and give explicit expressions for it in terms of the PFFs. Although the Belle data do not allow yet, in our approach, an extraction of the PFFs, some clear predictions are given, suggesting crucial measurements, and estimates of P_Lambda are computed, in qualitative agreement with the Belle data.

Observation of Transverse Λ/Λ[over ¯] Hyperon Polarization in e^{+}e^{-} Annihilation at Belle.

We report the first observation of the spontaneous polarization of Λ and Λ[over ¯] hyperons transverse to the production plane in e^{+}e^{-} annihilation, which is attributed to the effect arising from a polarizing fragmentation function. For inclusive Λ/Λ[over ¯] production, we also report results with subtracted feed-down contributions from Σ^{0} and charm. This measurement uses a dataset of 800.4 fb^{-1} collected by the Belle experiment at or near a center-of-mass energy of 10.58GeV. We observe a significant polarization that rises with the fractional energy carried by the Λ/Λ[over ¯] hyperon.

Improved measurement of the longitudinal spin transfer to Λ and Λ¯ hyperons in polarized proton-proton collisions at s=200 GeV

The longitudinal spin transfer $D_{LL}$ to $\Lambda$ and $\bar{\Lambda}$ hyperons produced in high-energy polarized proton--proton collisions is expected to be sensitive to the helicity distribution functions of strange quarks and anti-quarks of the proton, and to longitudinally polarized fragmentation functions. We report an improved measurement of $D_{LL}$ from data obtained at a center-of-mass energy of $\sqrt{s}$ = 200 GeV with the STAR detector at RHIC. The data have an approximately twelve times larger figure-of-merit than prior results and cover $|\eta|<$ 1.2 in pseudo-rapidity with transverse momenta $p_T$ up to 6 GeV/c. In the forward scattering hemisphere at largest $p_T$, the longitudinal spin transfer is found to be $D_{LL}$ = -0.036 $\pm$ 0.048 (stat) $\pm$ 0.013(sys) for $\Lambda$ hyperons and $D_{LL}$ = 0.032 $\pm$ 0.043\,(stat) $\pm$ 0.013\,(sys) for $\bar{\Lambda}$ anti-hyperons. The dependences on $\eta$ and $p_T$ are presented and compared with model evaluations.

Transverse spin transfer to Λ and Λ¯ hyperons in polarized proton-proton collisions at s=200 GeV

The transverse spin transfer from polarized protons to $\Lambda$ and $\bar{\Lambda}$ hyperons is expected to provide sensitivity to the transversity distribution of the nucleon and to the transversely polarized fragmentation functions. We report the first measurement of the transverse spin transfer to $\Lambda$ and $\bar{\Lambda}$ along the polarization direction of the fragmenting quark, $D_\mathrm{TT}$, in transversely polarized proton-proton collisions at $\sqrt{s}=200\,\mathrm{GeV}$ with the STAR detector at RHIC. The data correspond to an integrated luminosity of $18\,\mathrm{pb}^{-1}$ and cover the pseudorapidity range $\left|\eta\right| < 1.2$ and transverse momenta $p_{\mathrm{T}}$ up to $8\,\mathrm{GeV}/c$. The dependence on $p_\mathrm{T}$ and $\eta$ are presented. The $D_\mathrm{TT}$ results are found to be comparable with a model prediction, and are also consistent with zero within uncertainties.

Analytical calculation for the gluon fragmentation into spin-tripletS-wave quarkonium

Fragmentation is the dominant mechanism for hadron production with high transverse momentum. For spin-triplet S-wave heavy quarkonium production, contribution of gluon fragmenting to color-singlet channel has been numerically calculated since 1993. However, there is still no analytic expression available up to now because of its complexity. In this paper, we calculate both polarization-summed and polarized fragmentation functions of gluon fragmenting to a heavy quark-antiquark pair with quantum number $^3S_1^{[1]}$. Our calculations are performed in two different frameworks. One is the widely used nonrelativistic QCD factorization, and the other is the newly proposed soft gluon factorization. In either case, we calculate at both leading order and next-to-leading order in velocity expansion. All of our final results are presented in terms of compact analytic expressions.

Longitudinal spin transfer to Λ and $$\bar \Lambda$$ in polarized proton-proton collisions at √s = 200 GeV at STAR

The longitudinal spin transfer DLL of Λ and \(\bar \Lambda\) hyperons is expected to be sensitive to the helicity distribution function of strange (anti-)quarks, and to the polarized fragmentation functions. We report new results on DLL, extracted from √s = 200 GeV polarized pp collisions recorded at the STAR detector during the 2009 RHIC run. These new results cover mid-rapidity |η| < 1.2, with extended pT up to 6 GeV/c.

QCD evolution of naive-time-reversal-odd fragmentation functions

We study QCD evolution equations of the first transverse-momentum moment of the naive-time-reversal-odd fragmentation functions---the Collins function and the polarizing fragmentation function. We find for the Collins function case that the evolution kernel has a diagonal piece the same as that for the transversity fragmentation function, while for the polarizing fragmentation function case this piece is the same as that for the unpolarized fragmentation function. Our results might have important implications in the current global analysis of spin asymmetries.

Longitudinal polarization of hyperons in the forward region in polarizedppcollisions

We study the longitudinal polarization of hyperons and anti-hyperons at forward pseudorapidity, $2.5<\eta<4$, in singly polarized $pp$ collisions at RHIC energies by using different parameterizations of the polarized parton densities and different models for the polarized fragmentation functions. The results show that the $\Sigma^+$ polarization is able to distinguish different pictures on spin transfer in high energy fragmentation processes; and the polarization of $\Lambda$ and $\bar\Lambda$ hyperons can provide sensitivity to the helicity distribution of strange sea quarks. The influence from beam remnant to hyperon polarization in the forward region is also discussed.

Formula omitted] timelike Wilson coefficients for parton–fragmentation functions in Mellin space

We calculate the Mellin moments of the O ( α s 2 ) coefficient functions for the unpolarized and polarized fragmentation functions. They can be expressed in terms of multiple finite harmonic sums of maximal weight w = 4 . Using algebraic and structural relations between harmonic sums one finds that besides the single harmonic sums only three basic sums and their derivatives w.r.t. the summation index contribute. The Mellin moments are analytically continued to complex values of the Mellin variable. This representation significantly reduces the large complexity being present in x-space calculations and allows very compact and fast numerical implementations.

DIS charged current [formula omitted] production as a probe of Δs and Δg

To probe polarized s-quark and gluon densities in the proton, we propose a semi-inclusive Λ c + production in charged current deep inelastic scattering; l + + p → v + Λ c + + X, which could be observed clearly at a future high energy ep collider. We focus on the transverse momentum distribution of the spin correlation asymmetry between the initial proton and the final Λ c +. Numerical calculations show that this process is quite effective for testing not only the model of polarized s-quark and gluon densities but also the model of polarized fragmentation functions of the c-quark decaying into Λ c +.

OVERVIEW OF LAMBDA AND HYPERON PHYSICS

Some aspects of hyperon polarization phenomena in inclusive production in several high energy collision processes are reviewed. We concentrate on ways to achieve an accurate determination of the unpolarized and polarized fragmentation functions of a quark into a [Formula: see text]. A possible extension to the production of the other hyperons (Σ±,0, Ξ-,0), will be also briefly discussed.

Polarized hyperons from pA scattering in the gluon saturation regime

We study the production of transversely polarized Λ hyperons in high-energy collisions of protons with large nuclei. The large gluon density of the target at saturation provides an intrinsic semi-hard scale which should naturally allow for a weak-coupling QCD description of the process in terms of a convolution of the quark distribution of the proton with the elementary quark–nucleus scattering cross section (resummed to all twists) and a fragmentation function. In this case of transversely polarized Λ production we employ a so-called polarizing fragmentation function, which is an odd function of the transverse momentum of the Λ relative to the fragmenting quark. Due to this kt-odd nature, the resulting Λ polarization is essentially proportional to the derivative of the quark–nucleus cross section with respect to transverse momentum, which peaks near the saturation momentum scale. Such processes might therefore provide generic signatures for high parton density effects and for the approach to the “black-body” (unitarity) limit of hadronic scattering.