Undergraduate Research at Jefferson Lab

Impact of Moment Calculations on Constraining Parametrizations of Parton Distribution Functions from Lattice QCD

Student: Zaki Panjsheeri

School: University of Virginia

Mentored By: David Richards

Quantum Chromodynamics (QCD) is the theory of the strong interaction, which describes the binding of protons and neutrons to form nuclei and the binding of quarks and gluons to form hadrons such as the proton, neutron, and pion. The distribution of the momentum fraction x carried by the quarks and gluons within hadrons is represented by Parton Distribution Functions (PDF’s), which can be related to quantities that can be calculated from first principles using Lattice QCD. Lattice QCD solves QCD through large scale numerical calculation called Lattice Gauge Theory. Determining the distribution of the momentum of hadrons between the quarks and gluons that constitute them directly from lattice calculations is an ongoing area of research. We use Bayesian statistical methods to relate the quantities computed on the lattice to the PDF’s describing the underlying physics. Here we investigate the extent to which independent calculations of the moments with respect to x can be used to provide further constraints on the parametrization of PDF’s. Until recently, the only way of obtaining information about the PDF’s was through calculation of their moments. New methods allow the x-dependence to be computed directly. However, it is important to understand whether moment calculations contribute useful additional insight. A precise knowledge of PDF’s is pivotal to the interpretation of experimental programs across high energy and nuclear physics. Furthermore, an understanding of the internal structure of hadrons within QCD is at the core of nuclear physics, and Lattice QCD plays an essential role in understanding that structure, providing a more complete picture than can be obtained from experiment alone.

[Watch the presentation on YouTube]