Next-to-leading order evolution of structure functions without PDFs

Area of Science:

• High-energy particle physics
• Quantum Chromodynamics (QCD)
• Perturbative QCD

Background:

• Deeply inelastic scattering experiments probe the structure of hadrons.
• Parton distribution functions (PDFs) are conventionally used to describe this structure.
• Factorization scale and scheme dependence can introduce ambiguities in theoretical predictions.

Purpose of the Study:

• To develop and numerically solve the DGLAP evolution equations directly for physical, observable structure functions.
• To provide an unambiguous method for comparing theoretical predictions with experimental data in high-energy physics.
• To investigate the advantages of using a physical basis for evolution equations.

Main Methods:

• Formulation and numerical solution of the DGLAP evolution equations at next-to-leading order.
• Direct evolution of 6 physical, observable structure functions.
• Comparison of results obtained in the physical basis with conventional PDF evolution.

Main Results:

• The DGLAP evolution equations were successfully solved directly in a basis of physical structure functions.
• Expressing evolution in the physical basis eliminates factorization scale and scheme dependence.
• This method provides an unambiguous confrontation of perturbative QCD predictions with experimental measurements.

Conclusions:

• Solving DGLAP equations directly for observable structure functions offers a more direct and unambiguous comparison with experimental data.
• The physical basis approach avoids the complexities associated with unobservable parton distribution functions.
• This work validates a new approach for theoretical predictions in perturbative Quantum Chromodynamics.