Quark-gluon Correlation Research Articles

Single transverse-spin asymmetry for direct-photon and single-jet productions at RHIC

We study the single transverse-spin asymmetry for the inclusive direct-photon and single-jet productions in the proton–proton collision based on the twist-3 mechanism in the collinear factorization. Taking into account all the effects from the twist-3 quark–gluon correlation functions inside a transversely polarized proton, we present a prediction for the asymmetries at the typical RHIC kinematics. In both processes we find sizable asymmetries in the forward region of the polarized proton while they are almost zero in the backward region. This implies that if one finds a nonzero asymmetries in the backward region in these processes, it should be ascribed wholely to the three-gluon correlations. We also find the soft-gluon pole contribution is dominant and the soft-fermion pole contribution is negligible in the whole Feynman-x region for these asymmetries.

Single transverse spin asymmetry of prompt photon production

We study the single transverse spin asymmetry of prompt photon production in high energy proton–proton scattering. We include the contributions from both the direct and fragmentation photons. While the asymmetry for direct photon production receives only the Sivers type of contribution, the asymmetry for fragmentation photons receives both the Sivers and Collins types of contributions. We make a model calculation for quark-to-photon Collins function, which is then used to estimate the Collins asymmetry for fragmentation photons. We find that the Collins asymmetry for fragmentation photons is very small, thus the single transverse spin asymmetry of prompt photon production is mainly coming from the Sivers asymmetry in direct and fragmentation photons. We make predictions for the prompt photon spin asymmetry at RHIC energy, and emphasize the importance of such a measurement. The asymmetry of prompt photon production can provide a good measurement for the important twist-three quark–gluon correlation function, which is urgently needed in order to resolve the “sign mismatch” puzzle.

QCD evolution of naive-time-reversal-odd parton distribution functions

We reexamine the derivation of the leading order QCD evolution equations of twist-3 quark–gluon correlation functions, Tq,F(x,x) and Tq,F(σ)(x,x), which are the first transverse-momentum-moment of the naive-time-reversal-odd parton distribution functions – the Sivers and Boer–Mulders function, respectively. The evolution equations were derived by several groups with apparent differences. We identify the sources that are responsible for the differences, and are able to reconcile the results from various groups.

Imaging the Transverse (Spin) Structure of Hadrons

Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when the target and/or quark are transversely polarized. Connections between this deformation and transverse single-spin asymmetries as well as with quark-gluon correlations are discussed. The sign of transverse deformation of impact parameter dependent parton distribu- tions in a transversely polarized target can be related to the sign of the contribution from that quarkflavor to the nucleon anomalous magnetic moment. Therefore, the signs of the Sivers function for u and d quarks, as well as the signs of quark-gluon correlations embodied in the polarized structure function g2 can be understood in terms of the proton and neutron anomalous magnetic moments.

Three-gluon contribution to the single spin asymmetry in Drell-Yan and direct-photon processes

We derive the single-spin-dependent cross section for the Drell-Yan lepton-pair production and the direct-photon production in the $pp$-collision induced by the twist-3 three-gluon correlation functions in the transversely polarized nucleon in the leading order with respect to the QCD coupling constant. Combined with the contribution from the twist-3 quark-gluon correlation functions in the literature, this completes the twist-3 cross section for these processes. We also present a model calculation of the asymmetry for the direct photon production at the RHIC energy, demonstrating the sensitivity of the asymmetry to the form of the three-gluon correlation functions. In particular, we show that the asymmetry in the backward direction of the polarized nucleon is determined by the small-$x$ behavior of the correlation functions.

QCD EVOLUTION OF NAIVE-TIME-REVERSAL-ODD QUARK-GLUON CORRELATION FUNCTIONS

In this talk, we examine the existing calculations of QCD evolution kernels for the scale dependence of two sets of twist-3 quark-gluon correlation functions, Tq,F(x, x) and [Formula: see text], which are the first transverse-momentum-moment of the naive-time-reversal-odd Sivers and Boer-Mulders function, respectively. The evolution kernels at the leading order in strong coupling constant αs were derived by several groups with apparent differences. We identify the sources of discrepancies and are able to reconcile the results from various groups.

Transverse (spin) structure of hadrons

Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when the target and/or quark are transversely polarized. Connections between this deformation and transverse single-spin asymmetries as well as with quark–gluon correlations are discussed. The sign of transverse deformation of impact parameter dependent parton distributions in a transversely polarized target can be related to the sign of the contribution from that quark flavor to the nucleon anomalous magnetic moment. Therefore, the signs of the Sivers function for u and d quarks, as well as the signs of quark–gluon correlations embodied in the polarized structure function g2 can be understood in terms of the proton and neutron anomalous magnetic moments.

Exploring the structure of the proton through polarization observables inlp→jetX

We present results for a complete set of polarization observables for jet production in lepton proton collision, where the final state lepton is not observed. The calculations are carried out in collinear factorization at the level of Born diagrams. For all the observables we also provide numerical estimates for typical kinematics of a potential future Electron Ion Collider. On the basis of this numerical study, the prospects for the transverse single target spin asymmetry are particularly promising. This observable is given by a certain quark-gluon correlation function, which has a direct relation to the transverse momentum dependent Sivers parton distribution.

Hard- and soft-fermion-pole contributions to single transverse-spin asymmetry for Drell–Yan process

We study the single transverse-spin asymmetry for the Drell–Yan lepton pair production based on the twist-3 mechanism in the collinear factorization. We calculate all the hard-pole (HP) and the soft-fermion-pole (SFP) contributions to the single-spin-dependent cross section originating from the quark–gluon correlation functions in the transversely polarized nucleon in the leading order with respect to the QCD coupling constant. Combined with the soft-gluon-pole (SGP) contribution, this completes the corresponding twist-3 cross section. In the real photon limit, where all the HP contributions are transformed into the SFP contribution, we find that the SFP partonic hard cross section for the two independent quark–gluon correlation functions coincides in each scattering channel, as in the case of the inclusive light-hadron production. Our result enables one to extract the quark–gluon correlation functions from the forthcoming experiments at several facilities such as RHIC and J-PARC.

A phenomenological study of single transverse-spin asymmetry for inclusive light-hadron productions at RHIC

We study the single transverse-spin asymmetry for inclusive light-hadron productions in the proton-proton collision, $\pphx$ ($h=\pi,K,\eta$), for the RHIC kinematics based on the twist-3 mechanism in the collinear factorization. The analysis includes all the contributions from the soft-gluon pole and the soft-fermion pole for the twist-3 quark-gluon correlation functions in the transversely polarized proton. After discussing the flavor decomposition and the $P_T$-dependence of the asymmetry obtained in the previous analysis at the center-of-mass energy $\sqrt{S}=62.4$ and 200 GeV, we will give a prediction for the asymmetry at $\sqrt{S}=500$ GeV and also for the $\eta$-meson production. We found slightly smaller asymmetry at $\sqrt{S}=500$ GeV for $\pi^{\pm,0}$ and $K^+$ compared with those at the lower energies. The asymmetry for the $\eta$-meson turned out to be significantly larger than that for $\pi^0$.

Master formula for the three-gluon contribution to single spin asymmetry in semi-inclusive deep inelastic scattering

We derive a ``master formula'' for the contribution of the three-gluon correlation function in the nucleon to the twist-3 single-spin-dependent cross section for semi-inclusive deep-inelastic scattering, $e{p}^{\ensuremath{\uparrow}}\ensuremath{\rightarrow}eDX$. This is an extension of the similar formula known for the so-called soft-gluon-pole contribution induced by the quark-gluon correlation function in a variety of processes. Our master formula reduces the relevant interfering partonic subprocess with the participation of the three gluons to the Born cross sections for the ${\ensuremath{\gamma}}^{*}g\ensuremath{\rightarrow}c\overline{c}$ scattering, which reveals the new structure behind the twist-3 single spin asymmetry and simplifies the actual calculation greatly. A possible extension to higher order corrections is also discussed.

Observation concerning the process dependence of the Sivers functions

The $k_\perp$-moment of a quark's Sivers function is known to be related to the corresponding twist-three quark-gluon correlation function $T_{q,F}(x, x)$. The two functions have been extracted from data for single-spin asymmetries in semi-inclusive deep inelastic scattering and in single-inclusive hadron production in $pp$ collisions, respectively. Performing a consistent comparison of the extracted functions, we find that they show a "sign mismatch": while the magnitude of the functions is roughly consistent, the $k_\perp$-moment of the Sivers function has opposite sign from that of $T_{q,F}(x, x)$, both for up and for down quarks. Barring any inconsistencies in our theoretical understanding of the Sivers functions and their process dependence, the implication of this mismatch is that either, the Sivers effect is not dominantly responsible for the observed single-spin asymmetries in $pp$ collisions or, the current semi-inclusive lepton scattering data do not sufficiently constrain the $k_\perp$-moment of the quark Sivers functions. Both possibilities strengthen the case for further experimental investigations of single-spin asymmetries in high-energy $pp$ and $ep$ scattering.

A new twist-3 analysis of the single transverse-spin asymmetry for pion and kaon production at RHIC

We present a new analysis for the single-transverse spin asymmetry (SSA) for the inclusive pion and kaon productions in the proton-proton collisions measured at RHIC. The framework we use is the collinear factorization in which SSA appears as a twist-3 observable resulting from the multiparton correlations in the hadrons. As a relevant multiparton correlation, we include all the contributions associated with the quark-gluon correlation functions in the transversely polarized proton, i.e., those from the soft-gluon-pole (SGP) and the soft-fermion-pole (SFP). We have found that the SGP contribution alone is insufficient to describe the observed RHIC AN data and the inclusion of the SFP contribution plays an important role for the improved description of the data. In particular, PT-dependence of AN and AN for K− have been well described in our new analysis.

SCALE DEPENDENCE OF TWIST-3 CORRELATION FUNCTIONS

In this talk, we introduce two sets of twist-3 quark-gluon correlation functions that are relevant to transverse single spin asymmetries, and present corresponding evolution equations at the leading order in strong coupling constant, αs. The similarities and differences between the evolution of the leading power parton distributions and that of the twist-3 multiparton correlation functions are also discussed.

Transverse (Spin) Structure of Hadrons

Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when the target and/or quark are transversely polarized. Connections between this deformation and transverse single-spin asymmetries as well as with quark-gluon correlations are discussed. The sign of transverse deformation of impact parameter dependent parton distributions in a transversely polarized target can be related to the sign of the contribution from that quark flavor to the nucleon anomalous magnetic moment. Therefore, the signs of the Sivers function for $u$ and $d$ quarks, as well as the signs of quark-gluon correlations embodied in the polarized structure function $g_2$ can be understood in terms of the proton and neutron anomalous magnetic moments.

New analysis of the single transverse-spin asymmetry for hadron production at RHIC

We analyze the single transverse-spin asymmetry (SSAs) for inclusive hadron production in the $pp$ collision at RHIC based on the twist-3 mechanism in QCD. As an origin of SSAs, we take into account of all kinds of pole contributions associated with the twist-3 quark-gluon correlation functions in the polarized proton. By the inclusion of the soft-fermion-pole contribution in addition to the soft-gluon-pole contribution, we find SSAs observed at RHIC are better described for all kinds of mesons. $P_T$-dependence of the asymmetry and the comparison with the FNAL data are also presented.

Quark-gluon correlation functions relevant to single transverse spin asymmetries

We investigate the relative size of various twist-3 quark-gluon correlation functions relevant to single transverse spin asymmetries (SSAs) in a quark-diquark model of the nucleon. We calculate the quark-gluon correlation function ${T}_{q,F}(x,x)$ that is responsible for the gluonic pole contribution to the SSAs, as well as ${T}_{q,F}(0,x)$ and ${T}_{\ensuremath{\Delta}q,F}(0,x)$ responsible for the fermionic pole contributions. We find in both cases of a scalar diquark and an axial-vector diquark that at the first nontrivial order only the ${T}_{q,F}(x,x)$ is finite while all other quark-gluon correlation functions vanish. Using the same model, we evaluate quark Sivers function and discuss its relation to the ${T}_{q,F}(x,x)$. We also discuss the implication of our finding to the phenomenological studies of the SSAs.

Transverse momentum dependent quark distributions and polarized Drell-Yan processes

We study the spin-dependent quark distributions at large transverse momentum. We derive their transverse momentum behaviors in the collinear factorization approach in this region. We further calculate the angular distribution of the Drell-Yan lepton pair production with polarized beams and present the results in terms of the collinear twist-three quark-gluon correlation functions. In the intermediate transverse momentum region, we find that the two pproaches: the collinear factorization and the transverse momentum dependent factorization approaches are consistent in the description of the lepton pair angular distributions.

QCD evolution of the transverse momentum dependent correlations

We study the QCD evolution for the twist-three quark-gluon correlation functions associated with the transverse momentum odd quark distributions. Different from that for the leading twist quark distributions, these evolution equations involve more general twist-three functions beyond the correlation functions themselves. They provide important information on nucleon structure, and can be studied in the semi-inclusive hadron production in deep inelastic scattering and Drell-Yan lepton pair production in pp scattering process.

Drell–Yan lepton pair azimuthal asymmetry in hadronic processes

We study the azimuthal asymmetry (cos2ϕ) in the Drell–Yan lepton pair production in hadronic scattering processes at moderate transverse momentum region, taking into account the contributions from the twist-three quark–gluon correlations from the unpolarized hadrons. The contributions are found to dominate the asymmetry, and are not power suppressed by q⊥/Q at small q⊥ where q⊥ and Q are the transverse momentum and invariant mass of the lepton pair. Accordingly, the Lam–Tung relation will be violated at this momentum region, and its violation depends on the twist-three functions. However, at large transverse momentum q⊥∼Q, the Lam–Tung relation still holds because all corrections are power suppressed by Λ2/q⊥2∼Λ2/Q2 where Λ is the typical nonperturbative scale.