We discuss the evolution of the eight leading twist transverse momentum dependent parton distribution functions, which turns out to be universal and spin independent. By using the highest order perturbatively calculable ingredients at our disposal, w
e perform the resummation of the large logarithms that appear in the evolution kernel of transverse momentum distributions up to next-to-next-to-leading logarithms (NNLL), thus obtaining an expression for the kernel with highly reduced model dependence. Our results can also be obtained using the standard CSS approach when a particular choice of the $b^*$ prescription is used. In this sense, and while restricted to the perturbative domain of applicability, we consider our results as a prediction of the correct value of $b_{rm max}$ which is very close to $1.5 {rm GeV}^{-1}$. We explore under which kinematical conditions the effects of the non-perturbative region are negligible, and hence the evolution of transverse momentum distributions can be applied in a model independent way. The application of the kernel is illustrated by considering the unpolarized transverse momentum dependent parton distribution function and the Sivers function.
Transverse momentum dependent parton distribution functions (TMDPDFs) encode information about the intrinsic motion of quarks inside the nucleon. They are important non-perturbative ingredients in our understanding of, e.g., azimuthal asymmetries and
other qualitative features in semi-inclusive deep inelastic scattering experiments. We present first calculations on the lattice, based on MILC gauge configurations and propagators from LHPC. They yield polarized and unpolarized transverse momentum dependent quark densities and enable us to test the assumption of factorization in x and transverse momentum. The operators we employ are non-local and contain a Wilson line, whose renormalization requires the removal of a divergence linear in the cutoff 1/a.
Modifications to quark and antiquark fragmentation functions due to quark-quark (antiquark) double scattering in nuclear medium are studied systematically up to order cal{O}(alpha_{s}^2)$ in deeply inelastic scattering (DIS) off nuclear targets. At t
he order $cal{O}(alpha_s^2)$, twist-four contributions from quark-quark (antiquark) rescattering also exhibit the Landau-Pomeranchuck-Midgal (LPM) interference feature similar to gluon bremsstrahlung induced by multiple parton scattering. Compared to quark-gluon scattering, the modification, which is dominated by $t$-channel quark-quark (antiquark) scattering, is only smaller by a factor of $C_F/C_A=4/9$ times the ratio of quark and gluon distributions in the medium. Such a modification is not negligible for realistic kinematics and finite medium size. The modifications to quark (antiquark) fragmentation functions from quark-antiquark annihilation processes are shown to be determined by the antiquark (quark) distribution density in the medium. The asymmetry in quark and antiquark distributions in nuclei will lead to different modifications of quark and antiquark fragmentation functions inside a nucleus, which qualitatively explains the experimentally observed flavor dependence of the leading hadron suppression in semi-inclusive DIS off nuclear targets. The quark-antiquark annihilation processes also mix quark and gluon fragmentation functions in the large fractional momentum region, leading to a flavor dependence of jet quenching in heavy-ion collisions.
We present preliminary numerical studies in Lattice QCD related to the intrinsic transverse momentum distribution of partons in the nucleon. We employ non-local operators, consisting of spatially separated quark creation and annihilation operators co
nnected by a straight Wilson line. A clear signal is already obtained from a small number of configurations at a pion mass of about 600 MeV. As an example, we demonstrate that we can obtain the first x-moment of the transverse momentum dependent parton distribution function f_1^{n=1}(k_T) from our data. Our results, which are not renormalized, show a Gaussian-like distribution. The root mean squared transverse momentum is about 560 MeV for a Gaussian fit, close to phenomenological values.
