Double Parton Distributions in the Nucleon on the Lattice

Item type:	Thesis of the University of Regensburg (PhD)
Open Access Type:	Primary Publication
Date:	3 November 2020
Referee:	Prof. Dr. Andreas Schäfer
Date of exam:	28 October 2020
Institutions:	Physics > Institute of Theroretical Physics > Chair Professor Schäfer > Group Andreas Schäfer
Keywords:	lattice QCD, double parton distributions, four point functions, parton correlations
Dewey Decimal Classification:	500 Science > 530 Physics
Status:	Published
Refereed:	Yes, this version has been refereed
Created at the University of Regensburg:	Yes
Item ID:	44056

Abstract (English)

Modern scattering experiments involving hadrons are sensitive to parton correlations, which can be parameterized by double parton distributions (DPDs). These are non-perturbative objects, which are largely unknown in theory, detailed experimental access is quite challenging. This thesis provides a first non-perturbative study from first principles of light quark DPDs in the nucleon in the ...

Abstract (English)

Modern scattering experiments involving hadrons are sensitive to parton correlations, which can be parameterized by double parton distributions (DPDs). These are non-perturbative objects, which are largely unknown in theory, detailed experimental access is quite challenging. This thesis provides a first non-perturbative study from first principles of light quark DPDs in the nucleon in the framework of lattice QCD. First of all, a brief review of Quantum Chromodynamics (QCD) is given, followed by definitions and relations regarding double parton distributions. After that, the evaluation of hadronic matrix elements in the framework of lattice QCD is explained. DPDs are related to two-current matrix elements, which can be calculated on the lattice by evaluating four-point functions. We describe the corresponding Wick contractions for the case of the proton and give details on the techniques being used for their simulation. These are performed on 990 configurations of the CLS ensemble H102 with β = 3.4, which corresponds to a lattice spacing of 0.0856 fm, and pseudoscalar masses m(π) = 355 MeV and m(K) = 441 MeV. The data is converted to the MS-bar scheme at a renormalization scale of μ = 2 GeV. Results of the bare Wick contractions, as well as physical combinations for specific flavor, are presented for the two-current matrix elements < V⁰ V⁰ > and < A⁰ A⁰ >, where also lattice artifacts are explored. The data of two-current matrix elements is used for the determination of twist-2 functions, which are related to the first DPD Mellin moment for a specific quark polarization. Consistence of the results with the DPD number sum rule is verified. The dependence on the quark flavor and polarization is analyzed for the twist-2 functions, as well as for the extracted DPD Mellin moments. A further aspect to be investigated is the validity of factorization hypotheses which are often assumed in order to decompose DPDs in terms of single parton distribution functions (PDFs). This is e.g. the case in the well known pocket formula of double parton scattering. To this end, we derive factorized expressions for hadronic matrix elements of two operators, where we obtain convolutions of proton form factors, which can be obtained from lattice calculations. We implement two versions, the corresponding results are compared to those obtained from two-current matrix elements.

Translation of the abstract (German)

Die vorliegende Dissertation beinhaltet eine erste nicht-perturbative Studie von sogenannten Doppel-Parton-Verteilungen (engl. double parton distributions (DPDs)) unter Verwendung von Gitter-QCD-Simulationen. Mithilfe dieser DPDs lassen sich Parton-Korrelationen in Hadronen parametrisieren, welche in modernen Streuexperiementen relevant sind. DPDs stehen im Zusammenhang mit ...

Translation of the abstract (German)

Die vorliegende Dissertation beinhaltet eine erste nicht-perturbative Studie von sogenannten Doppel-Parton-Verteilungen (engl. double parton distributions (DPDs)) unter Verwendung von Gitter-QCD-Simulationen. Mithilfe dieser DPDs lassen sich Parton-Korrelationen in Hadronen parametrisieren, welche in modernen Streuexperiementen relevant sind. DPDs stehen im Zusammenhang mit zwei-Strom-Matrixelementen, welche auf dem Gitter über vier-Punkt-Funktionen berechnet werden können. Auf die zugehörigen Wick-Kontraktionen für den Fall des Protons sowie auf technische Details der Gittersimulation wird eingegangen. Es werden Ergebnisse der einzelnen Wick Kontraktionen sowie der physikalisch relevanten Kombinationen gezeigt, wobei auch Gitterartefakte untersucht werden. Aus den Daten der zwei-Strom-Matrixelemente können sogenannte twist-2-Funktionen berechnet werden, welche im Zusammenhang mit Mellin-Momenten von DPDs stehen. Bei der zugehörigen Berechnung werden Abhängigkeiten der Ergebnisse von Quark-Flavor und -Polarisation diskutiert. Ein weiterer wichtiger Aspekt ist die Gültigkeit von Faktorisierungsannahmen, welche oft verwendet werden, um DPDs mittels einfacher Parton-Verteilungsfunktionen (engl. parton distribution functions (PDFs)) darzustellen. Ein entsprechend faktorisierter Ausdruck der zwei-Strom-Matrixelemente wird hergeleitet, woraus eine Faltung von Proton-Formfaktoren resultiert. Die zugehörigen Ergebnisse werden mit denen der zwei-Strom-Matrixelemente verglichen.

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