Transverse momentum distributions inside the nucleon from lattice QCD

Abstract

SummaryNucleons, i.e., protons and neutrons, are composed of quarks and gluons, whose interactions are described by the theory of quantum chromodynamics (QCD), part of the standard model of particle physics. This work applies lattice QCD to compute quark momentum distributions in the nucleon. The calculations make use of lattice data generated on supercomputers that has already been successfully employed in lattice studies of spatial quark distributions ("nucleon tomography"). In order to be able to analyze transverse momentum dependent parton distribution functions, this thesis explores a novel approach based on non-local operators. One interesting observation is that the transverse momentum dependent density of polarized quarks in a polarized nucleon is visibly deformed. A more elaborate operator geometry is required to enable a quantitative comparison to high energy scattering experiments. First steps in this direction are encouraging. ZusammenfassungNukleonen, also Protonen und Neutronen, bestehen aus Quarks und Gluonen, deren Wechselwirkung durch die Quantenchromodynamik (QCD) innerhalb des Standardmodells der Teilchenphysik beschrieben wird. Diese Arbeit nutzt Gitter-QCD zur Berechnung von QuarkImpulsverteilungen im Nukleon. Dabei wird auf Gitterdaten zurückgegriffen, die auf Hochleistungsrechnern erstellt und bereits erfolgreich für die Analyse der räumlichen Quarkverteilung ("Nukleontomographie") eingesetzt wurden. Für die Untersuchung von Transversalimpulsabhängigen Partonverteilungsfunktionen stellt diese Arbeit ein neuartiges Verfahren, basierend auf nicht-lokalen Operatoren, vor. Die Ergebnisse zeigen u.a. eine sichtbare Verformung der Transversalimpuls-abhängigen Dichte polarisierter Quarks im polarisierten Nukleon. Ein quantitativer Vergleich mit Streuexperimenten erfordert kompliziertere Operatorgeometrien. Erste Schritte in diese Richtung sind vielversprechend.

Relating transverse structure of various parton distributions

“…Considering the spin pointing along zdirection and nucleon polarized in transverse x-direction, S ⊥ = (1, 0), the p ⊥ -densities of quarks in the two dimensional transverse momentum plane are plotted in figure (2). In our model the unpolarized distributions, the unpolarized nucleon having unpolarized quarks inside, are symmetric for both u and d quarks as predicted from lattice data in [23,24]. The values of p 2 ⊥ ρ U U = 0.0569 GeV 2 for u and p 2 ⊥ ρ U U = 0.0725 GeV 2 for d quarks.…”

“…In figure 1, we have compared our model with the corresponding lattice results [23,24]. It is interesting to note that the above three lattice moments are almost identical when normalized to one at l 2 ⊥ = 0.…”

“…(5.10). This also may be the the reason of approximate "factorization" of x and p ⊥ dependence of TMDs which is not contradicting to lattice QCD data [23,24,29]. Such factorization ansatz is also used in the phenomenological parameterizations and experimental extractions of the TMDs [30][31][32].…”

“…In lattice QCD the hadronic matrix elements can be parametrized by the invariant amplitudesà i (l 2 ; P, S) as [23,24] …”

Transverse structure of a proton in a light-front quark-diquark model

“…phenomenological extraction [23], Lattice QCD [31,32] etc. In the Gaussian ansatz the unpolarized TMDs are written asf…”