Time-Like heavy-flavour thresholds for fragmentation functions: the light-quark matching condition at NNLO

Area of Science:

• High Energy Physics
• Quantum Chromodynamics
• Particle Physics

Background:

• Matching conditions are essential for describing fragmentation functions during factorization scale evolution.
• Accurate descriptions of observables with identified final-state hadrons require next-to-next-to leading order (NNLO) accuracy in quantum chromodynamics.
• The NNLO matching condition for light-flavour to hadron fragmentation functions was previously missing.

Purpose of the Study:

• To present the analytical form of the matching condition for light-flavour to hadron fragmentation function at NNLO.
• To incorporate the first non-trivial heavy-quark effects into light-quark fragmentation functions.
• To provide a complete framework for NNLO calculations in quantum chromodynamics.

Main Methods:

• Extended the formalism used for next-to-leading order matching conditions to NNLO.
• Utilized $$ annihilation cross sections in the derivation.
• Performed calculations and presented results in Mellin space.

Main Results:

• Derived the analytical NNLO matching condition for light-flavour to hadron fragmentation functions.
• Identified and quantified the first non-trivial heavy-quark effects in light-quark fragmentation functions.
• Obtained results in Mellin space, facilitating further theoretical and phenomenological applications.

Conclusions:

• The derived NNLO matching condition is a critical component for precise predictions in quantum chromodynamics.
• This work completes the necessary ingredients for NNLO calculations involving identified hadrons.
• The inclusion of heavy-quark effects enhances the accuracy and scope of fragmentation function studies.