Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order.

Area of Science:

• High Energy Physics
• Quantum Chromodynamics (QCD)
• Particle Physics Phenomenology

Background:

• Anomalous dimensions are crucial for understanding particle interactions in Quantum Chromodynamics (QCD).
• Higher-order calculations are essential for precise theoretical predictions in high-energy physics.
• Previous studies have calculated anomalous dimensions to lower orders, necessitating further investigation.

Purpose of the Study:

• To compute the quark and gluon rapidity anomalous dimensions to fourth order in QCD.
• To perform the resummation of the energy-energy correlation in the back-to-back limit at N4LL precision.
• To assess the impact of higher-order calculations on theoretical uncertainties.

Main Methods:

• Calculation of N3LO rapidity anomalous dimensions using dimensional regularization.
• Application of the soft and rapidity anomalous dimension correspondence.
• Incorporation of N4LO threshold anomalous dimensions.
• Resummation of energy-energy correlations using the N4LO rapidity anomalous dimension.

Main Results:

• The quark and gluon rapidity anomalous dimensions are obtained to fourth order in QCD.
• Generalized Casimir scaling is demonstrated to relate these anomalous dimensions at four loops.
• The energy-energy correlation is resummed to N4LL for the first time.
• Numerical results show a reduction in perturbative uncertainties to below 1%.

Conclusions:

• The fourth-order calculation provides a significant advancement in QCD theory.
• The achieved N4LL resummation offers improved precision for event shape observables.
• The findings reduce theoretical uncertainties, enhancing the predictive power of QCD.