Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes.

Area of Science:

• High-energy physics
• Quantum field theory
• Collider physics

Background:

• Theoretical predictions at high-energy colliders require efficient computational methods.
• Existing methods can struggle with ultraviolet and infrared singularities at higher orders.
• Understanding scattering and decay processes necessitates robust theoretical frameworks.

Purpose of the Study:

• To propose multiloop vacuum amplitudes within the loop-tree duality (LTD) framework as optimal building blocks.
• To demonstrate the causal and singularity-free properties of this novel approach.
• To develop a new differential representation for cross sections and decay rates.

Main Methods:

• Utilizing the loop-tree duality (LTD) representation of vacuum amplitudes.
• Leveraging the manifestly causal properties inherent in the LTD framework.
• Developing a novel differential representation for cross sections and decay rates based on LTD residues.

Main Results:

• Multiloop vacuum amplitudes in LTD are identified as efficient building blocks for collider predictions.
• The LTD causal unitary approach yields a differential representation free of UV and IR singularities at all orders.
• The method naturally incorporates gauge invariance and wave function renormalization.
• The local functional form of initial-state collinear splitting functions is conjectured for the first time.

Conclusions:

• The LTD causal unitary method provides a theoretically sound and well-defined description of differential observables at colliders.
• This approach offers a significant advancement in calculating scattering and decay processes with high precision.
• The framework paves the way for new theoretical insights into fundamental particle interactions.