Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation.

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Collider Physics

Background:

• Transverse-momentum resummation is crucial for precise predictions in high-energy particle collisions like Drell-Yan and Higgs production.
• Understanding soft functions is essential for accurately calculating scattering amplitudes in quantum chromodynamics (QCD).

Purpose of the Study:

• To compute a specific soft function relevant for transverse-momentum resummation up to three loops.
• To extract the rapidity anomalous dimension associated with this soft function.
• To investigate potential relationships between different anomalous dimensions in QCD.

Main Methods:

• Utilized the bootstrap technique for perturbative calculations.
• Employed supersymmetric decomposition to simplify the soft function computation.
• Performed calculations in the expansion of the strong coupling constant.

Main Results:

• The soft function was successfully computed to three-loop accuracy.
• The rapidity anomalous dimension was extracted from the computed soft function.
• An unexpected relationship was discovered between anomalous dimensions for transverse-momentum and threshold resummation.

Conclusions:

• The three-loop computation provides a significant advancement in the precision of theoretical predictions for Drell-Yan and Higgs production.
• The identified relation between anomalous dimensions suggests deeper underlying structures in QCD.
• This work opens new avenues for theoretical research in particle physics resummation.