Diquark Spectator Model Research Articles

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.

Collinear factorization at subasymptotic kinematics and validation in a diquark spectator model

We revisit the derivation of collinear factorization for Deep Inelastic Scattering at subasymptotic values of the four-momentum transfer squared, where the masses of the particles participating in the interaction cannot be neglected. By using an inclusive jet function to describe the scattered quark final state, we can restrict the needed parton kinematic approximations just to the four-momentum conservation of the hard scattering process, and explicitly expand the rest of the diagram in powers of the unobserved parton transverse momenta rather than neglecting those. This procedure provides one with more flexibility in fixing the virtuality of the scattered and recoiling partons than in the standard derivation, and naturally leads to scaling variables that more faithfully represent the partonic kinematic at subasymptotic energy than the Bjorken's ${x}_{B}$ variable. We then verify the validity of the obtained factorization formula by considering a diquark spectator model designed to reproduce the main features of electron-proton scattering at large ${x}_{B}$ in Quantum Chromodynamics. In the model, the Deep Inelastic Scattering contribution to the cross section can be explicitly isolated and analytically calculated, then compared to the factorized approximation. Limiting ourselves to the leading twist contribution, we then show that use of the new scaling variables maximizes the kinematic range of validity of collinear factorization, and highlight the intrinsic limitations of this approach due to the unavoidably approximate treatment of four-momentum conservation in factorized diagrams. Finally, we briefly discuss how these limitations may be overcome by including higher-twist corrections to the factorized calculation.

Sin(ϕΛ−ϕS) azimuthal asymmetry in transversely polarized Λ production in SIDIS within TMD factorization at the EIC

We investigate the $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ single-spin asymmetry in the transversely polarized $\mathrm{\ensuremath{\Lambda}}$ production in semi-inclusive deeply inelastic scattering process within the transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the polarizing TMD fragmentation function ${D}_{1T}^{\ensuremath{\perp}}$ of the $\mathrm{\ensuremath{\Lambda}}$ hyperon and the unpolarized TMD distribution function ${f}_{1}$ of the proton target. We adopt the spectator diquark model result and the available parametrization for ${D}_{1T}^{\ensuremath{\perp},{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{\uparrow}}/q}$ to numerically estimate the $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry at the kinematical region of the electron ion collider (EIC). To implement the TMD evolution formalism, we apply two different parametrizations on the nonperturbative Sudakov form factors associated with the distribution function of the proton and the fragmentation function of the $\mathrm{\ensuremath{\Lambda}}$. It is found that the two sets of ${D}_{1T}^{\ensuremath{\perp},{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{\uparrow}}/q}$ lead to different $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry, particularly in sign. We also discuss the impact of the assumptions and approximations applied in the calculations, which may bring large uncertainties to the results in the EIC. Future measurements on the $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry with high precision at the EIC can provide important cross checks on the available $\mathrm{\ensuremath{\Lambda}}$ polarizing fragmentation functions, as well as constrain them more stringently.

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.

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.

What can we learn about twist-2 GPDs through quasi-distributions?

Studying light-cone PDFs through Euclidean correlators is currently of high interest. In particular, quasi parton distribution functions (quasi-PDFs) have attracted a lot of attention. Quasi-PDFs converge to their respective standard distributions if the hadron momentum goes to infinity. We explore the quasi-distribution approach for twist-2 generalized parton distributions (GPDs) in the conventional diquark spectator model. Our analytical expressions of the quasi-GPDs reduce to their corresponding standard ones in the large-momentum limit, substantiating them to be practical tools to predict features of standard GPDs. We illustrate numerical results of quasi-GPDs and of quasi-PDFs. Our focus is to test how well the quasi distributions agree with their standard counterparts for finite hadron momenta. By discussing the sensitivity of our results to model parameters, we highlight robust features of the quasi-GPDs and quasi-PDFs that one may extract from this model study. We also consider moments of quasi distributions.

Exploring twist-2 GPDs through quasidistributions in a diquark spectator model

Quasi parton distributions (quasi-PDFs) are currently under intense investigation. Quasi-PDFs are defined through spatial correlation functions and are thus accessible in lattice QCD. They gradually approach their corresponding standard (light-cone) PDFs as the hadron momentum increases. Recently, we investigated the concept of quasi-distributions in the case of generalized parton distributions (GPDs) by calculating the twist-2 vector GPDs in the scalar diquark spectator model. In the present work, we extend this study to the remaining six leading-twist GPDs. For large hadron momenta, all quasi-GPDs analytically reduce to the corresponding standard GPDs. We also study the numerical mismatch between quasi-GPDs and standard GPDs for finite hadron momenta. Furthermore, we present results for quasi-PDFs, and explore higher-twist effects associated with the parton momentum and the longitudinal momentum transfer to the target. We study the dependence of our results on the model parameters as well as the type of diquark. Finally, we discuss the lowest moments of quasi distributions, and elaborate on the relation between quasi-GPDs and the total angular momentum of quarks. The moment analysis suggests a preferred definition of several quasi-distributions.

Generalized quasi parton distributions in a diquark spectator model

Recently the concept of quasi parton distributions (quasi-PDFs) for hadrons has been proposed. Quasi-PDFs are defined through spatial correlation functions and as such can be computed numerically using quantum chromodynamics on a four-dimensional lattice. As the hadron momentum is increased, the quasi-PDFs converge to the corresponding standard PDFs that appear in factorization theorems for many high-energy scattering processes. Here we investigate this new concept in the case of generalized parton distributions (GPDs) by calculating the twist-2 vector GPDs in the scalar diquark spectator model. For infinite hadron momentum, the analytical results of the quasi-GPDs agree with those of the standard GPDs. Our main focus is to examine how well the quasi-GPDs agree with the standard GPDs for finite hadron momenta. We also study the sensitivity of the results on the parameters of the model. In general, our model calculation suggests that quasi-GPDs could be a viable tool for getting information about standard GPDs.

Double Collins effect in e+e−→ΛΛ¯X and e+e−→ΛπX processes in a diquark spectator model

We study the Collins function $H^\perp_{1}$ of the $\Lambda$ hyperon, which describes the fragmentation of a transversely polarized quark into an unpolarized $\Lambda$ hyperon. We calculate $H^\perp_{1}$ for light quarks of the $\Lambda$ hyperon, in the diquark spectator model with a Gaussian form factor for the hyperon-quark-diquark vertex. The model calculation includes contributions from both the scalar diquark and vector diquark spectators. Using the model result, we estimate the weighted $\cos2\phi_0$ asymmetry in the process $e^+e^- \to \Lambda\bar{\Lambda}X$ contributed by the coupling of two Collins functions. The QCD evolution effects for the first $k_T$-moment of the Collins function and the unpolarized fragmentation function $D_1(z)$ are also included. The results show that asymmetry is sizable and measurable at the kinematical configurations of Belle and BaBar experiments. We also find that the evolution effects play an important role in the phenomenological analysis.

Effect of sea quarks on single-spin asymmetries [formula omitted] in transversely polarized pp collisions at RHIC

We calculate the single-spin asymmetries ANW± of W± bosons produced in transversely polarized pp collisions with the valence part of the up (u) and down (d) quark Sivers functions treated by an available parametrization and the light-cone quark spectator–diquark model respectively, while the sea part Sivers functions of u and d quarks treated as parametrization. Comparing our results with those from experimental data at RHIC, we find that the Sivers functions of sea quarks play an important role in the determination of the shapes of ANW±. It is shown that ANW− is sensitive to u sea Sivers function, while ANW+ to d sea Sivers function intuitively. The results show that the contributions of u and d sea Sivers functions are rather sizable and of the same sign, and their signs agree with that of d valence quarks and are opposite to that of u valence quarks.

Transverse polarization of the Λ hyperon from unpolarized quark fragmentation in the diquark model

We investigate the spin-dependent (naive) T-odd fragmentation function $D^\perp_{1T}$, which can provide an explanation on the transverse polarization of the $\Lambda^0$ hyperon produced in an unpolarized process. We calculate $D^\perp_{1T}$ for light flavors in the spectator diquark model, with a Gaussian form factor at the hyperon-quark-diquark vertex. We include in the calculation both the scalar diquark and axial-vector diquark spectators. We determine the values of the model parameters by fitting the unpolarized fragmentation function $D^\Lambda_1$ to the DSV parametrization for $D^\Lambda_1$. In addition, we compute the longitudinal polarization fragmentation function $G^\Lambda_1$ and compare it with the known parametrization of $G^\Lambda_1$. We also estimate the transverse polarizations of $\Lambda$ production, in both semi-inclusive deep inelastic scattering and single inclusive $e^+e^-$ annihilation.

Reconstructing parton densities at large fractional momenta

Parton distribution functions (PDFs) are nonperturbative objects defined by nonlocal light-cone correlations. They cannot be computed directly from Quantum Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to compute moments of PDFs, which are matrix elements of local operators. Recently, an alternative approach has been proposed, based on the introduction of quasi-parton distribution functions (quasi-PDFs), which are matrix elements of equal-time spatial correlations and hence calculable on lattice. Quasi-PDFs approach standard PDFs in the limit of very large longitudinal proton momenta $P^z$. This limit is not attainable in lattice simulations, and quasi-PDFs fail to reproduce PDFs at high fractional longitudinal momenta. In this paper, we propose a method to improve the reconstruction of PDFs by combining information from quasi-PDFs and from the Mellin moments of regular PDFs. We test our method using the diquark spectator model for up and down valence distributions of both unpolarized and helicity PDFs. In the future, the method can be used to produce PDFs entirely based on lattice QCD results.

Predictions on the Transverse Single-Spin Asymmetries at Subleading Twist of Pion Production in Semi-Inclusive DIS

We estimate the single-spin asymmetries with [Formula: see text] and [Formula: see text] angular dependencies for electroproduction of pions in transversely polarized semi-inclusive DIS process. We consider the effect of the twist-3 transverse momentum dependent distributions which convoluted with twist-2 fragmentation functions. We calculate these distributions in a spectator-diquark model, and predict the corresponding single-spin asymmetries at the kinematics of HERMES, JLab and COMPASS. We find that the numerical estimates show that the asymmetries are sizable, and the T-odd twist-3 TMDs play an important role in these asymmetries.

Quasi-parton distribution functions: A study in the diquark spectator model

A set of quasi-parton distribution functions (quasi-PDFs) have been recently proposed by Ji. Defined as the matrix elements of equal-time spatial correlations, they can be computed on the lattice and should reduce to the standard PDFs when the proton momentum Pz is very large. Since taking the Pz→∞ limit is not feasible in lattice simulations, it is essential to provide guidance for which values of Pz the quasi-PDFs are good approximations of standard PDFs. Within the framework of the spectator diquark model, we evaluate both the up and down quarks' quasi-PDFs and standard PDFs for all leading-twist distributions (unpolarized distribution f1, helicity distribution g1, and transversity distribution h1). We find that, for intermediate parton momentum fractions x, quasi-PDFs are good approximations to standard PDFs (within 20–30%) when Pz≳1.5–2 GeV. On the other hand, for large x∼1 much larger Pz>4 GeV is necessary to obtain a satisfactory agreement between the two sets. We further test the Soffer positivity bound, and find that it does not hold in general for quasi-PDFs.

Transverse single-spin asymmetries of pion production in semi-inclusive DIS at subleading twist

We study the single-spin asymmetries with the $\sin\phi_S$ and $\sin(2\phi_h -\phi_S)$ angular dependences for charged and neutral pions produced in semi-inclusive deep inelastic scattering on the transversely polarized proton target. The theoretical interpretations of the two asymmetries are presented in terms of the convolution of the twist-3 quark transverse momentum dependent distributions and twist-2 fragmentation functions. Specifically, we investigate the role of the distributions $f_T$, $h_T$ and $h_T^\perp$ in the $\sin\phi_S$ asymmetry, as well as the role of the distributions $f_T^\perp$, $h_T$ and $h_T^\perp$ in the $\sin(2\phi_h -\phi_S)$ asymmetry. We calculate these distributions in a spectator-diquark model and predict the corresponding asymmetries for the first time, considering the kinematics at HERMES, JLab and COMPASS. The numerical estimates show that the asymmetries are sizable, and the dominant contribution to the $\sin\phi_S$ asymmetry comes from the T-odd distribution $f_T$, while $f_T^\perp$ gives the main contribution to the $\sin(2\phi_h -\phi_S)$ asymmetry. The future measurements on these asymmetries can shed light on the information of twist-3 transverse momentum dependent distributions.

Generalized form factors of the nucleon in a light-cone spectator-diquark model

We investigate the generalized form factors of the nucleon in a light-cone spectator-diquark model. Compared to the form factors, the generalized form factors contain some more information of the structure of the nucleon. In our calculation, both the scalar and the axial-vector spectator diquark are taken into account. As a relation between the spin in the instant form and that in the light-cone form, the Melosh--Wigner rotation effect is included for both the quark and the axial-vector diquark. We also provide numerical results from our model calculations, and the results are comparable with those from lattice QCD.

SINGLE-SPIN ASYMMETRIES IN SEMI-INCLUSIVE DEEP INELASTIC SCATTERING AND DRELL-YAN PROCESSES

In this brief article, we summarize our recent work1 regarding the origin of the nucleon Sivers functions within the diquark spectator model in semi-inclusive deep inelastic scattering (SIDIS) and the Drell-Yan process (DY). We demonstrate that the C, P, T symmetry properties of transverse spinors always couple the spin-dependent part of the numerator algebra to the imaginary part of the denominator in the cross section. This complex phase, and its sign change under time reversal, is believed to be responsible for the predicted sign change of the Sivers functions in SIDIS and DY. We study the complex phase generated in both processes by the "color-lensing" mechanism and find that, although the phases appear to be different in structure between SIDIS and DY, they do give rise to the expected sign flip relation at leading twist.

Quark to Λ-hyperon spin transfers in the current-fragmentation region

We perform a study on the struck quark to the Λ-hyperon fragmentation processes by taking into account the anti-quark fragmentations and intermediate decays from other hyperons. We concentrate on how the longitudinally polarized quark fragments to the longitudinally polarized Λ, how unpolarized quark and anti-quark fragment to the unpolarized Λ, and how quark and anti-quark fragment to the Λ through the intermediate decay processes. We calculate the effective fragmentation functions in the light-cone SU(6) quark–spectator–diquark model via the Gribov–Lipatov relation, with the Melosh–Wigner rotation effect also included. The calculated results are in reasonable agreement with the HERMES semi-inclusive ep experimental data and the OPAL and ALEPH e+e− annihilation experimental data.

T-odd quark–gluon–quark correlation function in the diquark model

We study the transverse momentum dependent quark–gluon–quark correlation function. Using a spectator diquark model, we calculate the eight time-reversal-odd interaction-dependent twist-3 quark distributions appearing in the decomposition of the transverse momentum dependent quark–gluon–quark correlator. In order to obtain finite results, we assume a dipole form factor for the nucleon–quark–diquark coupling, instead of a point-like coupling. The results are compared with the time-reversal-odd interaction-independent twist-3 TMDs calculated in the same model.

Weighted azimuthal asymmetries in a diquark spectator model

We analytically calculate weighted azimuthal asymmetries in semi-inclusive lepton-nucleon deep-inelastic scattering and Drell-Yan processes, using transverse-momentum-dependent partonic densities obtained in a diquark spectator model. We compare the asymmetries with available preliminary experimental data, in particular for the Collins and the Sivers effect. We make predictions for other cases of interest in running and planned experiments.