Collins Asymmetries Research Articles

Quark spin effects in e+e− annihilation: A Monte Carlo event generator study

Quark spin effects in e+e− annihilation to pseudoscalar and vector mesons are implemented for the first time in the Monte Carlo event generator. The spin-dependent fragmentation of the string stretched between the produced quark-antiquark pair with correlated spin states is described by the string+P30 model implemented in the string fragmentation routine of by using the package. The simulated events are used to study the model predictions for the Collins asymmetries of mesons produced back-to-back in the e+e− center of mass system by using both the thrust axis method and the hadronic plane method. The obtained asymmetries are compared to the available data from the BELLE and experiments and the underlying Collins analyzing power from the string+P30 model is compared with phenomenological extractions. Published by the American Physical Society 2024

High-Statistics Measurement of Collins and Sivers Asymmetries for Transversely Polarized Deuterons

New results are presented on a high-statistics measurement of Collins and Sivers asymmetries of charged hadrons produced in deep inelastic scattering of muons on a transversely polarized LiD6 target. The data were taken in 2022 with the COMPASS spectrometer using the 160 GeV muon beam at CERN, statistically balancing the existing data on transversely polarized proton targets. The first results from about two-thirds of the new data have total uncertainties smaller by up to a factor of three compared to the previous deuteron measurements. Using all the COMPASS proton and deuteron results, both the transversity and the Sivers distribution functions of the u and d quark, as well as the tensor charge in the measured x range are extracted. In particular, the accuracy of the d quark results is significantly improved. Published by the American Physical Society 2024

String fragmentation of a quark pair with entangled spin states: Application to e+e− annihilation

We present a recursive quantum mechanical model for the fragmentation of a string stretched between a quark and an antiquark with entangled spin states. The quarks are assumed to be produced in the e+e− annihilation process via the exchange of a virtual photon and the correlations between their spin states are described by a joint spin-density matrix. The string fragmentation process is formulated at the amplitude level by using the splitting matrices of the recent string+P30 model of polarized quark fragmentation with pseudoscalar and vector meson emissions and accounts for the systematic propagation of the spin correlations in the fragmentation chain. The model is formulated as a recursive recipe suitable for a Monte Carlo implementation. It reproduces the expected angular correlation, due to the Collins effect, between back-to-back pseudoscalar and/or vector mesons. For the latter, this correlation also involves the momenta of the decay products. We use the model for studying the sign of the Collins asymmetry for back-to-back vector and pseudoscalar mesons. Published by the American Physical Society 2024

Collins and Sivers transverse-spin asymmetries in inclusive muoproduction of ρ0 mesons

The production of vector mesons in deep inelastic scattering is an interesting yet scarcely explored channel to study the transverse spin structure of the nucleon and the spin-dependence of fragmentation. The COMPASS collaboration has performed the first measurement of the Collins and Sivers asymmetries for inclusively produced ρ0 mesons. The analysis is based on the data set collected in deep inelastic scattering in 2010 using a 160GeV/cμ+ beam impinging on a transversely polarized NH3 target. The ρ0 mesons are selected from oppositely charged hadron pairs, and the asymmetries are extracted as a function of the Bjorken-x variable, the transverse momentum of the pair and the fraction of the energy z carried by the pair. Indications for positive Collins and Sivers asymmetries are observed.

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.

Transverse spin asymmetries for inclusive $\rho^0$ production in SIDIS at COMPASS

The production of vector mesons in SIDIS is a particularly interesting channel to study the polarized fragmentation and related phenomena. Preliminary COMPASS results for the first measurement of inclusive \rho^0ρ0 Collins and Sivers transverse-spin asymmetries are presented here for the first time. The analysis is based on the data-set collected by COMPASS in 2010 using a 160 GeV/c \mu^+μ+ beam and a transversely polarized NH_3NH3 target. The asymmetries are extracted as function of Bjorken-x, of the total transverse momentum of the oppositely charged hadron pair and of the fraction of available energy z carried by the pair. Indications for positive Collins and Sivers asymmetries are obtained as expected from models.

Azimuthal single- and double-spin asymmetries in semi-inclusive deep-inelastic lepton scattering by transversely polarized protons

A comprehensive set of azimuthal single-spin and double-spin asymmetries in semi-inclusive leptoproduction of pions, charged kaons, protons, and antiprotons from transversely polarized protons is presented. These asymmetries include the previously published HERMES results on Collins and Sivers asymmetries, the analysis of which has been extended to include protons and antiprotons and also to an extraction in a three-dimensional kinematic binning and enlarged phase space. They are complemented by corresponding results for the remaining single-spin and double-spin asymmetries for transverse target-polarization orientation.

StringSpinner - adding spin to the PYTHIA string fragmentation

StringSpinner is a plugin allowing for the introduction of spin effects in the hadronization part of the PYTHIA 8 event generator. In this first version the implementation is limited to handling pesudoscalar mesons in events without parton showers. The spin effects are generated by propagating the quark polarization along the fragmentation chain according to the rules of the quantum mechanical string+P03 model. By using parametrizations for the transversity parton distribution functions, StringSpinner allows to simulate the polarized semi inclusive deep inelastic scattering process on protons and neutrons. The instructions to use StringSpinner and to modify the parametrizations of the transversity distribution functions are presented, as well as an example of the calculation of the Collins asymmetries as obtained from simulations of the transversely polarized semi inclusive deep inelastic scattering process. Program summaryProgram Title: StringSpinnerCPC Library link to program files:https://doi.org/10.17632/37jrpmyz3t.1Developer's repository link:https://gitlab.com/albikerbizi/stringspinner.gitLicensing provisions: GNU GPL v2 or laterProgramming language: C++, FortranNature of problem: To analyse and interpret the experimental data on the study of the nucleon spin structure, as well as to make predictions for future experiments simulations are needed.Solution method: Introduce spin effects in the hadronization part of a complete Monte Carlo event generator, largely used in the community of high energy particle physicists.

A new approach to semi-inclusive deep-inelastic scattering with QED and QCD factorization

We present the details of a new factorized approach to semi-inclusive deep-inelastic scattering which treats QED and QCD radiation on equal footing, and provides a systematically improvable approximation to the extraction of transverse momentum dependent parton distributions. We demonstrate how the QED contributions can be well approximated by collinear factorization, and illustrate the application of the factorized approach to QED radiation in inclusive scattering. For semi-inclusive processes, we show how radiation effects prevent a well-defined “photon-nucleon” frame, forcing one to use a two-step process to account for the radiation. We illustrate the utility of the new method by explicit application to the spin-dependent Sivers and Collins asymmetries.

Measurement of transverse single-spin asymmetries of π0 and electromagnetic jets at forward rapidity in 200 and 500 GeV transversely polarized proton-proton collisions

The STAR Collaboration reports measurements of the transverse single-spin asymmetry (TSSA) of inclusive $\pi^0$ at center-of-mass energies ($\sqrt s$) of 200 GeV and 500 GeV in transversely polarized proton-proton collisions in the pseudo-rapidity region 2.7 to 4.0. The results at the two different energies show a continuous increase of the TSSA with Feynman-$x$, and, when compared to previous measurements, no dependence on $\sqrt s$ from 19.4 GeV to 500 GeV is found. To investigate the underlying physics leading to this large TSSA, different topologies have been studied. $\pi^0$ with no nearby particles tend to have a higher TSSA than inclusive $\pi^0$. The TSSA for inclusive electromagnetic jets, sensitive to the Sivers effect in the initial state, is substantially smaller, but shows the same behavior as the inclusive $\pi^0$ asymmetry as a function of Feynman-$x$. To investigate final-state effects, the Collins asymmetry of $\pi^0$ inside electromagnetic jets has been measured. The Collins asymmetry is analyzed for its dependence on the $\pi^0$ momentum transverse to the jet thrust axis and its dependence on the fraction of jet energy carried by the $\pi^0$. The asymmetry was found to be small in each case for both center-of-mass energies. All the measurements are compared to QCD-based theoretical calculations for transverse-momentum-dependent parton distribution functions and fragmentation functions. Some discrepancies are found, which indicates new mechanisms might be involved.

Azimuthal single- and double-spin asymmetries in semi-inclusive deep-inelastic lepton scattering by transversely polarized protons

A comprehensive set of azimuthal single-spin and double-spin asymmetries in semi-inclusive leptoproduction of pions, charged kaons, protons, and antiprotons from transversely polarized protons is presented. These asymmetries include the previously published HERMES results on Collins and Sivers asymmetries, the analysis of which has been extended to include protons and antiprotons and also to an extraction in a three-dimensional kinematic binning and enlarged phase space. They are complemented by corresponding results for the remaining four single-spin and four double-spin asymmetries allowed in the one-photon-exchange approximation of the semi-inclusive deep-inelastic scattering process for target-polarization orientation perpendicular to the direction of the incoming lepton beam. Among those results, significant non-vanishing cos (ϕ−ϕS) modulations provide evidence for a sizable worm-gear (II) distribution, {g}_{1mathrm{T}}^qleft(x,{mathrm{p}}_T^2right) . Most of the other modulations are found to be consistent with zero with the notable exception of large sin (ϕS) modulations for charged pions and K+.

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.

The Collins asymmetry in electroproduction of Kaon at the electron ion colliders within TMD factorization

We apply the transverse momentum dependent factorization formalism to investigate the transverse single spin dependent Collins asymmetry with a sin (phi _h+phi _s) modulation in the semi-inclusive production of Kaon meson in deep inelastic scattering process. The asymmetry is contributed by the convolutions of the transversity distribution function h_1(x) of the target proton and the Collins function of the Kaon in the final state. We adopt the available parametrization of h_1(x) as well as the recent extracted result for the Kaon Collins function. To perform the transverse momentum dependent evolution, the parametrization of the nonperturbative Sudakov form factor of the proton and final state Kaon are utilized. We numerically predict the Collins asymmetry for charged Kaon production at the electron ion colliders within the accuracy of next-to-leading-logarithmic order. It is found that the asymmetry is sizable and could be measured. We emphasize the importance of planned electron ion colliders in the aspect of constraining sea quark distribution functions as well as accessing the information of the nucleon spin structure and the hadronization mechanism.

Transversity distributions from difference asymmetries in semi-inclusive DIS

In recent years information on the transversity distribution $h_1$ has been obtained combining the Collins asymmetry results from semi-inclusive deep inelastic scattering (SIDIS) data on transversely polarized nucleon targets with the information on the fragmentation function of a transversely polarized quark from the asymmetries measured in $e^+e^-$ annihilation into hadrons. An alternative method was proposed long time ago, which does not require the $e^+e^-$ data, but allows one to get ratios of the $u$ and $d$ quark transversity distributions from the SIDIS data alone. The method utilizes the ratio of the difference of the Collins asymmetries of positively and negatively charged hadrons produced on transversely polarized proton and deuteron targets. We have applied this method to the COMPASS proton and deuteron data, and extracted the ratio $h_1^d/h_1^u$. The results are compared to those obtained in a previous point--by--point extraction based both on SIDIS and $e^+e^-$ data.

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.

First Monte Carlo Global Analysis of Nucleon Transversity with Lattice QCD Constraints

We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new MonteCarlo method based on nested sampling and constraints on the isovector tensor charge g_{T} from lattice QCD. A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with g_{T} values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses, which found significantly smaller g_{T} values. The contributions to the nucleon tensor charge from u and d quarks are found to be δu=0.3(2) and δd=-0.7(2) at a scale Q^{2}=2 GeV^{2}.

Azimuthal Spin Asymmetries in SIDIS

We have presented the results for the single and double spin asymmetries in semi-inclusive deep inelastic scatterings for proton in a light front quark–diquark model. The asymmetries are found to satisfy certain inequalities. The model wavefunctions are modified to generate complex phase which is essential to produce asymmetries with Sivers and Boer-Mulders functions. The model predictions for Collins, Sivers and Boer-Mulders asymmetries are found to be consistent with data.

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.

Model predictions for azimuthal spin asymmetries for HERMES and COMPASS kinematics

We have presented the results for the single and double spin asymmetries in semi-inclusive deep inelastic scatterings for proton in a light front quark-diquark model. The asymmetries generated by the T-even TMDs are discussed here. The model predictions are found to agree with the available data. We also present our model predictions for the Collins asymmetry for the future electron-ion collider experiments.

A Monte Carlo code for the fragmentation of polarized quarks

We describe a Monte Carlo code for the fragmentation of polarized quarks into pseudoscalar mesons. The quark jet is generated by iteration of the splitting q → h + q′ where q and q′ indicate quarks and h a hadron. The splitting function describing the energy sharing between q′ and h is calculated on the basis of the Symmetric Lund Model where the quark spin is introduced through spin matrices as foreseen in the 3P0 mechanism. A complex mass parameter is introduced for the parametrisation of the Collins effect. The results for the Collins analysing power and the comparison with the Collins asymmetries measured by the COMPASS collaboration are presented. For the first time preliminary results on the simulated azimuthal asymmetry due to the Boer-Mulders function are also given.