C.J. Bomhof

The construction of gauge-links in arbitrary hard processes

Transverse momentum dependent parton distribution and fragmentation functions are described by hadronic matrix elements of bilocal products of field operators off the light-cone. These bilocal products contain gauge-links, as required by gauge-invariance. The gauge-links are path-ordered exponentials connecting the field operators along a certain integration path. This integration path is process-dependent, depending specifically on the short-distance partonic subprocess. In this paper we present the technical details needed in the calculation of the gauge-links, and a calculational scheme is provided to obtain the gauge invariant distribution and fragmentation correlators corresponding to a given partonic subprocess.

Gauge link structure in quark–quark correlators in hard processes

Abstract Distribution functions in hard processes can be described by quark–quark correlators, nonlocal matrix elements of quark fields. Color gauge invariance requires inclusion of appropriate gauge links in these correlators. For transverse momentum dependent distribution functions, in particular important for describing T -odd effects in hard processes, we find that new link structures containing loops can appear in Abelian and non-Abelian theories. In transverse moments, e.g., measured in azimuthal asymmetries, these loops may enhance the contribution of gluonic poles. Some explicit results for the link structure are given in high-energy leptoproduction and hadron–hadron scattering.

Single spin asymmetries in hadron-hadron collisions

We study weighted azimuthal single spin asymmetries in hadron-hadron scattering using the diagrammatic approach at leading order and assuming factorization. The effects of the intrinsic transverse momenta of the partons are taken into account. We show that the way in which T-odd functions, such as the Sivers function, appear in these processes does not merely involve a sign flip when compared with semi-inclusive deep inelastic scattering, such as in the case of the Drell-Yan process. Expressions for the weighted scattering cross sections in terms of distribution and fragmentation functions folded with hard cross sections are obtained by introducing modified hard cross sections, referred to as gluonic-pole cross sections.

Non-universality of transverse momentum dependent parton distribution functions

Abstract In the field theoretical description of hadronic scattering processes, single transverse-spin asymmetries arise due to gluon initial and final state interactions. These interactions lead to process dependent Wilson lines in the operator definitions of transverse momentum dependent parton distribution functions. In particular for hadron–hadron scattering processes with hadronic final states this has important ramifications for possible factorization formulas in terms of (non)universal TMD parton distribution functions. In this paper we will systematically separate the universality-breaking parts of the TMD parton correlators from the universal T -even and T -odd parts. This might play an important role in future factorization studies for these processes. We also show that such factorization theorems will (amongst others) involve the gluonic pole cross sections, which have previously been shown to describe the hard partonic scattering in weighted spin asymmetries.

Sivers Single-Spin Asymmetry in Photon-Jet Production

We study a weighted asymmetry in the azimuthal distribution of photon-jet pairs produced in the process pp-->gamma jet X with a transversely polarized proton. We focus on the contribution of the Sivers effect only, considering experimental configurations accessible at the Relativistic Heavy Ion Collider. We show that predictions for the asymmetry, obtained in terms of gluonic-pole cross sections calculable in perturbative QCD, can be tested and clearly discriminated from those based on a generalized parton model, involving standard partonic cross sections. Experimental measurements of the asymmetry will therefore test our present understanding of single-spin asymmetries.

Gluonic pole cross sections and single spin asymmetries in hadron-hadron scattering

The gauge-links connecting the parton field operators in the hadronic matrix elements appearing in the transverse momentum dependent distribution functions give rise to T-odd effects. Due to the process-dependence of the gauge-links the T-odd distribution functions appear with different prefactors. A consequence is that in the description of single spin asymmetries the parton distribution and fragmentation functions are convoluted with gluonic pole cross sections rather than the basic partonic cross sections. In this paper we calculate the gluonic pole cross sections encountered in single spin asymmetries in hadron-hadron scattering. The case of back-to-back pion production in polarized proton-proton scattering is worked out explicitly. It is shown how T-odd gluon distribution functions originating from gluonic pole matrix elements appear in twofold.

Spin asymmetries in jet-hyperon production at LHC

Abstract We consider polarized Λ hyperon production in proton–proton scattering, p p → ( Λ ↑ jet ) jet X , in the kinematical region of the LHC experiments, in particular the ALICE experiment. We present a new Λ polarization observable that arises from the Sivers effect in the fragmentation process. It can be large even at midrapidity and therefore, is of interest for high energy hadron collider experiments. Apart from its potential to shed light on the mechanisms behind the phenomenon of Λ polarization arising in unpolarized hadronic collisions, the proposed observable in principle also allows to test the possible color flow dependence of single spin asymmetries and the (non)universality of transverse momentum dependent fragmentation functions.

UNIVERSALITY OF SINGLE SPIN ASYMMETRIES IN HARD PROCESSES

We discuss the use of time reversal symmetry in the classification of parton correlators. Specifically, we consider the role of (small) intrinsic transverse momenta in these correlators and the determination of the proper color gauge link. The transverse momentum weighted correlators in hard processes can be expressed as a product of universal gluonic pole matrix elements and gluonic pole cross sections.

Sivers Effect Asymmetries in Hadronic Collisions

We argue that weighted azimuthal single spin asymmetries in back‐to‐back jet or pion production in polarized proton‐proton scattering can be written as convolutions of universal distribution and fragmentation functions with gluonic pole cross sections as hard functions. Gluonic pole cross sections are gauge‐invariant weighted sums of Feynman diagrams. The weight factors are a direct consequence of the (diagram‐dependence of) gauge links. The best known consequence of the gauge links is the generation of the Sivers effect that is a source for single‐spin asymmetries. Moreover, due to the dependence of the gauge links on the color‐flow of the hard diagram the Sivers effect in SIDIS enters with opposite sign as it does in Drell‐Yan scattering. The weight factors in the gluonic pole cross sections are the appropriate generalizations to more complicated processes of this relative sign difference. Furthermore, it is argued that the gluon‐Sivers effect appears in twofold.