The [Formula: see text] massive operator matrix elements of [Formula: see text] for the structure function [Formula:...

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Particle Physics

Background:

• Heavy flavor Wilson coefficients are crucial for describing particle interactions.
• Understanding anomalous dimensions is key to perturbative quantum field theory.
• Previous calculations were limited in scope or precision.

Purpose of the Study:

• To compute contributions to massive operator matrix elements for heavy flavor Wilson coefficients.
• To determine structure functions and transversity for general Mellin variable N.
• To provide an independent calculation of 3-loop anomalous dimensions.

Main Methods:

• Utilizing advanced summation technologies for nested sums.
• Employing products of hypergeometric terms with harmonic sums.
• Handling generalized harmonic sums as intermediate results.

Main Results:

• Complete results obtained for two specific massive operator matrix elements.
• Contributions to 3-loop anomalous dimensions computed independently.
• Final results expressed in terms of nested harmonic sums.

Conclusions:

• The study provides a comprehensive calculation of key quantities in heavy flavor physics.
• The methods used allow for precise analytical results.
• This work advances the understanding of perturbative calculations in quantum field theory.