Numerical solution of DGLAP equations using Laguerre polynomials expansion and Monte Carlo method

Area of Science:

• High Energy Physics
• Computational Physics

Background:

• The Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations are fundamental in describing parton distribution functions (PDFs) in quantum chromodynamics.
• Previous studies often relied on analytical approximations or semi-analytical methods for solving DGLAP equations.

Purpose of the Study:

• To present a fully numerical method for solving DGLAP evolution equations at leading-order (LO) and next-to-leading-order (NLO) approximations.
• To demonstrate the efficiency and accuracy of a Monte Carlo-based approach for extracting evolved parton distributions.

Main Methods:

• Utilizing a Laguerre polynomial expansion for the theoretical framework, building upon the work of Furmanski et al.
• Implementing a Monte Carlo method for all computational stages of parton distribution extraction.
• Developing algorithms in FORTRAN for efficient numerical computation.

Main Results:

• Achieved evolved parton densities through a complete numerical calculation process.
• Demonstrated that the numerical solutions are obtained in a practical wall clock time.
• Obtained results for evolved parton densities that show good agreement with established phenomenological models.

Conclusions:

• The fully numerical approach offers a viable and efficient alternative for solving DGLAP equations.
• The employed numerical techniques and algorithms show potential for broader applications in computational physics.
• The study validates the accuracy of the numerical method by comparing its results favorably against other numerical calculations and phenomenological models.