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Flavor Nonsinglet Splitting Functions at Four Loops in QCD: Fermionic Contributions
B A Kniehl1, S Moch1, V N Velizhanin1
1II. Institute for Theoretical Physics, Hamburg University, D-22761 Hamburg, Germany.
Physical Review Letters
|September 10, 2025
Summary
We calculated fourth-order contributions to quark distribution evolution in quantum chromodynamics. These findings detail flavor differences and have implications for particle physics, including Higgs boson production.
Area of Science:
- High-energy particle physics
- Quantum Chromodynamics (QCD)
Background:
- Understanding quark distribution functions is crucial for particle physics.
- Perturbative QCD provides a framework for these calculations.
- Flavor differences in quark distributions require precise theoretical treatment.
Purpose of the Study:
- To determine fourth-order n_{f} contributions to splitting functions for quark distribution evolution.
- To present analytic forms in N and x space for a general gauge group.
- To analyze small-x and large-x limits and their implications.
Main Methods:
- Calculations within perturbative quantum chromodynamics.
- Derivation of analytic forms for splitting functions in Mellin N and momentum-fraction x space.
- Analysis of contributions in small-x and large-x limits.
Main Results:
- Fourth-order n_{f} contributions to splitting functions for all flavor differences were determined.
- Analytic forms in N and x space are provided for a general gauge group.
- Small-x rise is confined to extremely small values (x≲10^{-6}), and large-x limit includes four-loop anomalous dimension.
Conclusions:
- The results offer precise insights into quark distribution evolution.
- Implications extend to gluonic quantities and threshold-enhanced logarithms from soft-gluon emission.
- Applications include calculations for Higgs boson production in gluon-gluon fusion.
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