Rapidity distribution at soft-virtual and beyond for n-colorless particles to LO in QCD

Area of Science:

• High Energy Physics
• Quantum Chromodynamics
• Collider Physics

Background:

• Understanding particle production at hadronic colliders is crucial for testing the Standard Model and searching for new physics.
• Threshold contributions and rapidity distributions are key observables in high-energy scattering processes.
• Precision calculations in perturbative Quantum Chromodynamics (QCD) are essential for interpreting experimental results.

Purpose of the Study:

• To develop a systematic framework for studying threshold contributions to differential rapidity distributions in hadronic colliders.
• To introduce universal operators for calculating soft virtual differential cross sections and performing threshold resummation.
• To provide analytical results for specific processes like Higgs boson production and Drell-Yan production.

Main Methods:

• Utilizing the universality of soft enhancements and factorization properties of the differential cross section.
• Developing a universal soft-collinear operator for next-to-next-to-next-to-next-to-leading order (N^4LO) calculations in perturbative QCD.
• Employing a universal operator for threshold resummation to next-to-next-to-next-to-leading logarithmic (N^3LL) accuracy.
• Extending the framework to include next-to-threshold contributions.

Main Results:

• A systematic framework for threshold contributions to differential rapidity distributions is established.
• A universal soft-collinear operator for N^4LO calculations and a universal operator for N^3LL resummation are presented.
• Approximate analytical results for rapidity distributions at N^4LO and N^3LL accuracy are derived for Higgs boson production (gluon fusion, bottom quark annihilation) and Drell-Yan production.
• The framework is extended to include next-to-threshold contributions for diagonal partonic channels.

Conclusions:

• The developed framework provides a powerful tool for precise theoretical predictions in high-energy hadronic collisions.
• The universal operators and analytical results enhance the accuracy of calculations for important Standard Model processes.
• This work contributes to a deeper understanding of perturbative QCD dynamics near threshold and facilitates precise comparisons with experimental data.