The construction of gauge-links in arbitrary hard processes

Abstract

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.

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

“…The partonic and gluonic pole cross sections are, then, no longer necessarily proportional to each other. In that case the use of gluonic pole cross sections comes as a natural definition since, as was already mentioned earlier, the gluonic pole strengths C [D] G depend solely on the structure of the gauge-link which, in turn, is fixed by the color-flow structure of the Feynman diagram D [14,15]. In what follows we will summarize how they can be calculated.…”

“…In what follows we will summarize how they can be calculated. Using the results of [15] we will give all gluonic pole factors and the corresponding gluonic pole cross sections that can appear in the tree-level contributions to single spin asymmetries in hadron-hadron scattering. The expressions dσ [D] that appear in the sums (6) and (7) [18,19]:…”

“…Hence, the description of the gluon contribution to T -odd effects involves two different gluonic pole cross sections, one containing the gluonic pole factors C (d) G and one containing the factors C (f ) G . Using the results of [15] we can give all gluonic pole strengths C G appearing in 2→2 scattering processes with external gluons. They are listed in Tables III-VI.…”

“…They are related by time-reversal and, correspondingly, the T -odd distribution functions appear with opposite sign. When going beyond these processes one may encounter more complicated gauge-link structures [13,14,15]. Consequently, the simple sign relation between T -odd effects in SIDIS and DY generalizes to color-dependent factors, called gluonic pole factors.…”

“…[14]. All the gauge-links appearing at tree-level in such processes were calculated in [15]. Using these results we will give all gluonic pole factors in section III after introducing the general formalism in section II.…”