Compact multigluonic scattering amplitudes with heavy scalars and fermions.

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Particle Physics

Background:

• Scattering amplitudes are fundamental in quantum field theory for describing particle interactions.
• Recursion relations offer a powerful method for calculating these amplitudes, but can become complex.
• Understanding relationships between different particle types, like scalars and fermions, is crucial for theoretical consistency.

Purpose of the Study:

• To derive a compact and efficient expression for scattering amplitudes of massive scalar-antiscalar pairs with positive helicity gluons.
• To establish a foundational building block for calculating other helicity configurations using recursion relations.
• To verify theoretical predictions, specifically SUSY-like Ward identities, by comparing scalar and fermion-gluon scattering amplitudes.

Main Methods:

• Combined the Berends-Giele and on-shell recursion relations.
• Developed an analytical expression for the scattering amplitude.
• Performed explicit calculations to compare scalar and fermion amplitudes.

Main Results:

• Obtained an extremely compact expression for the scattering amplitude of a complex massive scalar-antiscalar pair and positive helicity gluons.
• Demonstrated that this expression serves as a fundamental component for constructing other helicity configurations.
• Showed that the scattering amplitude of massive fermions to positive helicity gluons is proportional to the scalar one.

Conclusions:

• The derived compact expression simplifies the calculation of specific scattering amplitudes.
• The proportionality between scalar and fermion amplitudes confirms predicted SUSY-like Ward identities.
• This work provides a key tool for further theoretical investigations in particle physics.