Number Density Interpretation of Dihadron Fragmentation Functions.

Area of Science:

• Quantum Field Theory
• Particle Physics
• High-Energy Physics

Background:

• Fragmentation functions are crucial for understanding particle production in high-energy collisions.
• Existing definitions of dihadron fragmentation functions (DiFFs) lack a clear physical interpretation.
• Phenomenological studies utilize extended DiFFs, but their nature as number densities is not fully established.

Purpose of the Study:

• To develop a rigorous quantum field-theoretic definition for fully unintegrated dihadron fragmentation functions (DiFFs) and generalize it to n-hadron fragmentation functions.
• To establish that these new definitions are consistent with a number density interpretation and satisfy relevant sum rules.
• To derive the evolution equations for the extended DiFFs used in phenomenological analyses.

Main Methods:

• Development of a novel quantum field-theoretic framework for fragmentation functions.
• Demonstration of sum rule satisfaction for the proposed DiFF definition.
• Derivation of evolution equations for extended DiFFs.

Main Results:

• A new, consistent quantum field-theoretic definition for fully unintegrated dihadron fragmentation functions (DiFFs) and n-hadron fragmentation functions is presented.
• The proposed DiFF definition satisfies key sum rules, confirming its interpretation as a number density.
• Extended DiFFs used in current phenomenological studies are shown to be number densities, and their evolution equations are derived.

Conclusions:

• The new framework provides a clear physical meaning for DiFFs obtained from experimental measurements.
• This work unifies theoretical definitions with phenomenological applications of fragmentation functions.
• The established number density interpretation enhances the predictive power and understanding of particle production processes.