Gluonic Pole Research Articles

Archetypal factorization and gluon poles in semi-exclusive reactions

Abstract Within the archetypal factorization procedure, we study the gluon pole contributions manifesting in the nucleon–lepton hard processes of hadron production. We prove the dominant role of gluon pole contributions in such processes. We analyze the different sources of complexity associated with the gluon pole functions. As a practical application, we derive a new single spin asymmetry directly related to the gluon poles that can be studied experimentally.

Erratum to: Gluon poles and photon distribution amplitudes in Drell-Yan-like processes

Erratum to: Gluon poles and photon distribution amplitudes in Drell-Yan-like processes

Gluon poles and photon distribution amplitudes in Drell-Yan-like processes

We calculate the hadron tensor related to the photon-induced Drell-Yan process, with incoming nucleon being transversally polarised. We predict the new single spin asymmetry which probes gluon poles and which is expressed in terms of photon (both chiral-odd and chiral-even) distribution amplitudes and chiral-odd nucleon function stemming from the nucleon transverse polarization.

Study of Spin through Gluon Poles

Based on the use of contour gauge and collinear factorization, we propose a new set of single spin asymmetry which can be measured in polarized Drell-Yan process by SPD@NICA. We stress that all of discussed single spin asymmetries exist owing to the gluon poles manifesting in the twist-3 or twist-2⊗twist-3 parton distributions related to the transverse-polarized Drell-Yan process.

Angular distributions in pion-nucleon Drell-Yan process

We study the Drell-Yan process in the polarized pion-nucleon scattering. We calculate the U(1)em gauge invariant hadron tensors. To this end, we have to take into account two diagrams—the standard diagram and an additional one—both diagrams are required to get the gauge invariant hadron tensor. We obtain a new single transverse spin asymmetry that probes gluon poles and chiral-odd distribution functions. The process of pion-nucleon scattering in the limit of large Feynman x is described by a convolution of two non-collinear exclusive-channel distribution amplitudes, which demonstrates the duality between different factorization regimes.

Drell-Yan-like processes and duality

We calculate the gauge invariant Drell-Yan-like hadron tensors. In connection with new COMPASS results, we predict the new single spin asymmetry which probes gluon poles together with chiral-odd and time-odd functions. The relevant pion production as a particular case of the Drell-Yan-like process has been discussed. For the meson-induced Drell-Yan (DY) process, we model an analog of the twist-3 distribution function, which is a collinear function in inclusive channel, by means of two noncollinear distribution amplitudes which are associated with exclusive channel. This modeling demonstrates the fundamental duality between different factorization regimes.

Drell-Yan hadron tensor: Contour gauge and gluon propagator

We consider the gauge invariant Drell-Yan hadron tensor which includes the standard and non-standard diagram contributions. The non-standard diagram contribution is appeared owing to the complexity of the twist three $B^V(x_1,x_2)$-function where the gluon pole manifests. We use the contour gauge conception which allows us to fix easily the spurious uncertainties in the gluon propagator. The contour gauge condition is generated by the corresponding Wilson lines in both the standard and non-standard diagrams. We demonstrate the substantial role of the non-standard diagram for forming of the relevant contour in the Wilson path-ordered exponential that leads to the spurious singularity fixing.

Single spin asymmetry in forward pA collisions. II. Fragmentation contribution

We compute the twist-three fragmentation contribution to the transverse single spin asymmetry (SSA) in light hadron production $p^\uparrow p\to hX$ and $p^\uparrow A\to hX$ including the gluon saturation effect in the unpolarized nucleon/nucleus. Together with the results in our previous paper, this completes the full evaluation of the SSA in this process in the "hybrid" formalism. We argue that the dependence of SSAs on the atomic mass number in the forward region can elucidate the relative importance of the soft gluon pole contribution from the twist-three quark-gluon-quark correlation in the polarized nucleon and the twist-three fragmentation contribution from the final state hadron.

Single spin asymmetry in forwardpAcollisions

We compute the transverse single spin asymmetry in light hadron production $p^\uparrow p\to hX$ and $p^\uparrow A\to hX$ including the gluon saturation effect in the unpolarized nucleon/nucleus. In the forward (large-$x_F$) region, the dominant contribution comes from the so-called derivative term associated with the soft gluonic pole. This leads to the cancellation of nuclear effects in $A_N$ which can be tested at RHIC. We also show that the soft fermionic pole disappears in the saturation environment.

Factorization theorem, gluon poles and new contributions in semi-inclusive processes

We discuss the role of gluon poles and the gauge invariance for the hadron tensors of Drell-Yan and direct photon production processes with the transversely polarized hadron.

Novel effects in twist-three SSA

We discuss the role of gluon poles and the gauge invariance for the hadron tensors of Drell-Yan and direct photon production processes with the transversely polarized hadron. These hadron tensors are needed to construct the corresponding single spin asymmetries. For the Drell-Yan process, we perform our analysis within both the Feynman and axial-type (contour) gauges for gluons. In both the Feynman and contour gauges, we demonstrate that the gauge invariance leads to the need of the new (non-standard) diagrams. Moreover, in the Feynman gauge, we argue the absence of gluon poles in the correlators 〈̄ψγ⊥A+ ψ〉 related traditionally to dT(x,x)/dx. As a result, these terms disappear from the final QED gauge invariant Drell-Yan hadron tensor. For the direct photon production, by using the contour gauge for gluon fields, we find that there are new twist-3 terms present in the hadron tensor of the considering process in addition to the standard twist-3 terms.

Constraining gluon poles

In this letter, we revise the QED gauge invariance for the hadron tensor of Drell–Yan type processes with the transversely polarized hadron. We perform our analysis within the Feynman gauge for gluons and make a comparison with the results obtained within the light-cone gauge. We demonstrate that QED gauge invariance leads, first, to the need of a non-standard diagram and, second, to the absence of gluon poles in the correlators 〈ψ¯γ⊥A+ψ〉 related traditionally to dT(x,x)/dx. As a result, these terms disappear from the final QED gauge invariant hadron tensor. We also verify the absence of such poles by analyzing the corresponding light-cone Dirac algebra.

New contributions to gluon poles in direct photon production

We consider the direct photon production in two hadron collision with one of the hadrons being transversely polarized. By using the contour gauge for gluon fields, we find that there are new twist-$3$ terms present in the hadron tensor of the considering process in addition to the standard twist-$3$ terms. In this work, we demonstrate that the significance of these new terms are two-fold: first, they are crucial to both the QED and QCD gauge invariance and, second, their contributions to the hadron tensor are at least the same as those from the standard ones. We also study the resuting effects which are responsible for the universality breaking of the corresponding twist-$3$ parton distributions.

Generalized universality of definite rank gluon transverse momentum dependent correlators

Transverse momentum dependent (TMD) parton correlators describing the partonic structure of hadrons contain gauge links, required by color gauge invariance. The required gauge links enter in the matrix elements that contain the parton fields and depend on the color flow in the hard process. The correlators are expanded in terms of transverse momentum dependent parton distribution functions, referred to as TMD PDFs, or in short TMDs. In this paper, we introduce gluon TMDs of definite rank, by making an expansion of the TMD gluon correlator with the help of irreducible tensors built from the transverse momenta. The process dependence is isolated in gauge link dependent gluonic pole factors multiplying the TMDs. It is important to account for the different possibilities in the color structure within the matrix elements, leading to multiple TMDs at a given rank. In this way we are able to write the leading tree level result for a hard process in terms of process dependent gluon correlators which are expressed in a finite set of universal TMDs. We tabulate the gluonic pole factors for various gauge links, among them those that are relevant for 2 to 2 processes.

Generalized universality of higher transverse moments of quark transverse momentum dependent correlators

The color gauge-invariant transverse momentum dependent (TMD) quark correlators contain process dependent gauge links in the bilocal matrix elements. In this paper, we split these process dependent correlators into universal TMD correlators, which in turn can be parametrized in universal TMD distribution functions. The process dependence is contained in gluonic pole factors, of which the value is determined by the gauge link. The operator structures of the universal TMD correlators are identified using transverse moments. In this paper, specific results for double transverse weighting of quark TMDs are given. In particular, we show that for a spin 1/2 target one has three universal time-reversal even leading `pretzelocity distributions', two of which involve double gluonic pole matrix elements and come with process dependent gluonic pole factors. We generalize the results for single and double weighting to TMD correlators of any specific rank, illustrating it for unpolarized, spin 1/2 and spin 1 targets.

GENERALIZED UNIVERSALITY FOR TMD DISTRIBUTION FUNCTIONS

Azimuthal asymmetries in high-energy processes, most pronounced showing up in combination with single or double (transverse) spin asymmetries, can be understood with the help of transverse momentum dependent (TMD) parton distribution and fragmentation functions. These appear in correlators containing expectation values of quark and gluon operators. TMDs allow access to new operators as compared to collinear (transverse momentum integrated) correlators. These operators include nontrivial process dependent Wilson lines breaking universality for TMDs. Making an angular decomposition in the azimuthal angle, we define a set of universal TMDs of definite rank, which appear with process dependent gluonic pole factors in a way similar to the sign of T-odd parton distribution functions in deep inelastic scattering or the Drell-Yan process. In particular, we show that for a spin 1/2 quark target there are three pretzelocity functions.

Higher twist parton distributions from light-cone wave functions

We explore the possibility to construct higher-twist parton distributions in a nucleon at some low reference scale from convolution integrals of the light-cone wave functions (WFs). To this end we introduce simple models for the four-particle nucleon WFs involving three valence quarks and a gluon with total orbital momentum zero, and estimate their normalization (WF at the origin) using QCD sum rules. We demonstrate that these WFs provide one with a reasonable description of both polarized and unpolarized parton densities at large values of the Bjorken variable $x\ensuremath{\ge}0.5$. Twist-three parton distributions are then constructed as convolution integrals of $qqqg$ and the usual three-quark WFs. The cases of the polarized structure function ${g}_{2}(x,{Q}^{2})$ and single transverse spin asymmetries are considered in detail. We find that the so-called gluon pole contribution to twist-three distributions relevant for single spin asymmetry vanishes in this model, but is generated perturbatively at higher scales by the evolution, in the spirit of Gl\"uck-Reya-Vogt parton distributions.

Gauge invariance, gluonic poles and single spin asymmetry in Drell-Yan processes

We explore the electromagnetic gauge invariance of the hadron tensor of the Drell-Yan process with one transversely polarized hadron. The special role is played by the contour gauge for gluon fields. The prescription for the gluonic pole in the twist 3 correlator is related to causality property and compared with the prescriptions for exclusive hard processes. As a result we get the extra contributions, which naively do not have an imaginary phase. The single spin asymmetry for the Drell-Yan process is accordingly enhanced by the factor of two.

Model independent analysis of gluonic pole matrix elements and universality of transverse-momentum-dependent fragmentation functions

Gluonic pole matrix elements explain the appearance of single spin asymmetries (SSA) in high-energy scattering processes. They involve a combination of operators which are odd under time reversal (T-odd). Such matrix elements appear in principle both for parton distribution functions and parton fragmentation functions. We show that for parton fragmentation functions these gluonic pole matrix elements vanish as a consequence of the analytic structure of scattering amplitudes in Quantum Chromodynamics. This result is important in the study of the universality of transverse momentum dependent (TMD) fragmentation functions.

ANALYTIC PROPERTIES OF MULTI-PARTON POLE MATRIX ELEMENTS AND UNIVERSALITY OF FRAGMENTATION FUNCTIONS

Gluonic pole matrix elements explain the appearance of single spin asymmetries (SSA) in high-energy scattering processes. They involve a combination of operators which are odd under time reversal (T-odd). Such matrix elements appear in principle both for parton distribution functions and parton fragmentation functions. We show that for parton fragmentation functions these gluonic pole matrix elements vanish as a consequence of the analytic structure of scattering amplitudes in Quantum Chromodynamics. We extend this analysis to the case of multi-partonic pole matrix elements. This result is important in the study of the universality of transverse momentum dependent (TMD) fragmentation functions.