Analytical Soft Functions for Heavy-Quark Final States at Hadron Colliders

Area of Science:

• High Energy Physics
• Quantum Chromodynamics
• Collider Physics

Background:

• Precision predictions are crucial for understanding heavy-quark production at hadron colliders.
• Soft functions are key components in calculating scattering amplitudes in quantum chromodynamics.

Purpose of the Study:

• To compute the complete two-loop, fully differential soft function for heavy-quark pair production with a color-singlet system.
• To provide analytic results for transverse-momentum-dependent and threshold soft functions.
• To decompose the soft function into color correlators for broader applications.

Main Methods:

• Two-loop perturbative calculations in quantum chromodynamics.
• Derivation of analytic expressions for generic kinematics.
• Decomposition into dipole and tripole color correlators.

Main Results:

• The first computation of the complete two-loop, fully differential soft function for this process.
• Novel analytic results for transverse-momentum-dependent and threshold soft functions.
• A decomposition into dipole and tripole color correlators.

Conclusions:

• The computed soft function is a significant advancement for precision heavy-quark physics at the LHC.
• The results provide essential building blocks for processes involving heavy quarks and jets.
• This work enables more accurate theoretical predictions for experimental analyses.