P.J. Mulders

Time reversal odd distribution functions in leptoproduction

We consider the various asymmetries, notably single spin asymmetries, that appear in leptoproduction as a consequence of the presence of time-reversal odd distribution functions. This could facilitate experimental searches for time-reversal odd phenomena.

Universality of T-odd effects in single spin and azimuthal asymmetries

We analyze the transverse-momentum-dependent distribution and fragmentation functions in space-like and time-like hard processes involving at least two hadrons, in particular, 1-particle inclusive leptoproduction, the Drell–Yan process and two-particle inclusive hadron production in electron–positron annihilation. As is well known, transverse momentum dependence allows for the appearance of unsuppressed single spin azimuthal asymmetries, such as Sivers and Collins asymmetries. Recently, Belitsky, Ji and Yuan obtained fully color-gauge-invariant expressions for the relevant matrix elements appearing in these asymmetries at leading order in an expansion in the inverse hard scale. We rederive these results and extend them to observables at the next order in this expansion. We observe that at leading order one retains a probability interpretation, contrary to a claim in the literature and show the direct relation between the Sivers effect in single spin asymmetries and the Qiu–Sterman mechanism. We also study fragmentation functions, where the process-dependent gauge link structure of the correlators is not the only source of T-odd observables and discuss the implications for universality.

Semi-inclusive deep inelastic scattering at small transverse momentum

We study the cross section for one-particle inclusive deep inelastic scattering off the nucleon for low transverse momentum of the detected hadron. We decompose the cross section in terms of structure functions and calculate them at tree level in terms of transverse-momentum-dependent parton distribution and fragmentation functions. Our results are complete in the one-photon exchange approximation at leading and first subleading twist accuracy, with both beam and target polarization.

Modelling quark distribution and fragmentation functions

The representation of quark distribution and fragmentation functions in terms of non-local operators is combined with a simple spectator model. This allows us to estimate these functions for the nucleon and the pion ensuring correct crossing and support properties. We give estimates for the unpolarized functions as well as for the polarized ones and for subleading (higher twist) functions. Furthermore, we can study several relations that are consequences of Lorentz invariance and of C, P, and T invariance of the strong interactions.

No generalized transverse momentum dependent factorization in the hadroproduction of high transverse momentum hadrons

It has by now been established that standard QCD factorization using transverse momentum dependent parton distribution functions fails in hadroproduction of nearly back-to-back hadrons with high transverse momentum. The essential problem is that gauge-invariant transverse momentum dependent parton distribution functions cannot be defined with process-independent Wilson line operators, thus implying a breakdown of universality. This has led naturally to proposals that a correct approach is to instead use a type of generalized transverse momentum dependent factorization in which the basic factorized structure is assumed to remain valid, but with transverse momentum dependent parton distribution functions that contain nonstandard, process-dependent Wilson line structures. In other words, to recover a factorization formula, it has become common to assume that it is sufficient to simply modify the Wilson lines in the parton correlation functions for each separate hadron. In this paper, we will illustrate by direct counterexample that this is not possible in a non-Abelian gauge theory. Since a proof of generalized transverse momentum dependent factorization should apply generally to any hard hadroproduction process, a single counterexample suffices to show that a general proof does not exist. Therefore, to make the counter-argument clear and explicit, we illustrate with a specific calculation for a double spin asymmetry in a spectator model with a non-Abelian gauge field. The observed breakdown of generalized transverse momentum dependent factorization challenges the notion that the role of parton transverse momentum in such processes can be described using separate correlation functions for each external hadron.

Transverse momentum dependence in gluon distribution and fragmentation functions

We investigate the twist two gluon distribution functions for spin-1/2 hadrons, emphasizing the intrinsic transverse momentum of the gluons. These functions are relevant in leading order in the inverse hard scale in scattering processes such as inclusive leptoproduction or Drell-Yan scattering, or more generally in hard processes in which at least two hadrons are involved. They show up in azimuthal asymmetries. For future estimates of such observables, we discuss specific bounds on these functions. ©2001 The American Physical Society.

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.

Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum

This talk reports on recent work where we studied the connection between the description of semi-inclusive DIS at high transverse momentum (based on collinear factorization) and low transverse momentum (based on transverse-momentum-dependent factorization). We used power counting to determine the leading behavior of the structure functions at intermediate transverse momentum in the two descriptions. When the power behaviors are different, two distinct mechanisms are present and there can be no matching between them. When the power behavior is the same, the two descriptions must match. An explicit calculation however shows that for some observables this is not the case, suggesting that the transverse-momentum-dependent-factorization description beyond leading twist is incomplete.

Intrinsic transverse momentum and the polarized Drell-Yan process

In this paper we study the cross section at leading order in 1/Q for polarized Drell-Yan scattering at measured lepton-pair transverse momentum QT. We find that for a hadron with spin 1/2 the quark content at leading order is described by six distribution functions for each flavor, which depend on both the lightcone momentum fraction x, and the quark transverse momentum k 2 . These functions are illustrated for a free-quark ensemble. The cross sections for both longitudinal and transverse polarizations are expressed in terms of convolution integrals over the distribution functions.

Evolution of transverse momentum dependent distribution and fragmentation functions

We use Lorentz invariance and the QCD equations of motion to study the evolution of functions that appear at leading order in a I / Q expansion in azimuthal asymmetries. This includes the evolution equation of the Collins fragmentation function. The moments of these functions are matrix elements of known twist two and twist three operators. We present the evolution in the large N-c limit, restricting to non-singlet for the chiral-even functions