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Flavor Nonsinglet Splitting Functions at Four Loops in QCD: Fermionic Contributions.

B A Kniehl1, S Moch1, V N Velizhanin1

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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.

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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.