Analysis of the Double Parton Distribution Functions in Quantum Chromodynamics

Open Access
Author:
Snyder, Zachary Steven
Area of Honors:
Physics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Anna Stasto, Thesis Supervisor
  • Richard Wallace Robinett, Honors Advisor
Keywords:
  • QCD
  • Parton
  • DPDF
  • quantum field theory
  • quantum chromodynamics
Abstract:
We demonstrate the mathematical formalism for the construction of consistent initial conditions for the double parton distribution functions in the collinear approximation. The initial conditions within this framework have an important property that they exactly and simultaneously satisfy both the momentum sum rule and the quark number sum rule. Furthermore, in this formalism, the double parton distribution's functional behavior is related to the single parton distribution functions. We find that this condition imposes certain relations on the large and small x behavior of both single and double parton distribution functions. By making use of the Mellin transformation we analytically solve the evolution equation at leading logarithmic order for the gluon channel double parton distribution function. Furthermore, we illustrate the double parton correlations for the gluon channel and show how they change with the evolution scale.