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Register a new userTransverse momentum distributions of quarks from the lattice using extended gauge links
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Authors
Bernhard U. Musch
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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 connected 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.
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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.
This work applies lattice QCD to compute quark momentum distributions in the nucleon. We explore a novel approach based on non-local operators in order to analyze transverse momentum dependent parton distribution functions, which encode information about the intrinsic motion of quarks inside the nucleon. Our calculations are based on MILC gauge configurations and domain wall fermion propagators from LHPC. One interesting observation is that the transverse momentum dependent density of polarized quarks in a polarized nucleon is visibly deformed. Moreover, we can test the assumption that longitudinal and transverse momentum dependence factorize within a certain kinematical region. A more elaborate operator geometry is required to enable a quantitative comparison to azimuthal asymmetries observable in experiments such as semi-inclusive deeply inelastic scattering, and to study time-reversal odd distributions such as the Sivers function. First steps in this direction are encouraging.
We discuss in detail a method to study transverse momentum dependent parton distribution functions (TMDs) using lattice QCD. To develop the formalism and to obtain first numerical results, we directly implement a bi-local quark-quark operator connected by a straight Wilson line, allowing us to study T-even, process-independent TMDs. Beyond results for x-integrated TMDs and quark densities, we present a study of correlations in x and transverse momentum. Our calculations are based on domain wall valence quark propagators by the LHP collaboration calculated on top of gauge configurations provided by MILC with 2+1 flavors of asqtad-improved staggered sea quarks.
This work presents the first calculation in lattice QCD of three moments of spin-averaged and spin-polarized generalized parton distributions in the proton. It is shown that the slope of the associated generalized form factors decreases significantly as the moment increases, indicating that the transverse size of the light-cone quark distribution decreases as the momentum fraction of the struck parton increases.
A better understanding of transverse momentum (k_T-) dependent quark distributions in a hadron is needed to interpret several experimentally observed large angular asymmetries and to clarify the fundamental role of gauge links in non-abelian gauge theories. Based on manifestly non-local gauge invariant quark operators we introduce process-independent k_T-distributions and study their properties in lattice QCD. We find that the longitudinal and transverse momentum dependence approximately factorizes, in contrast to the behavior of generalized parton distributions. The resulting quark k_T-probability densities for the nucleon show characteristic dipole deformations due to correlations between intrinsic k_T and the quark or nucleon spin. Our lattice calculations are based on N_f=2+1 mixed action propagators of the LHP collaboration.
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