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Soft-gluon effective coupling and cusp anomalous dimension.

Stefano Catani1, Daniel de Florian2, Massimiliano Grazzini3

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We extend the CMW effective coupling for Quantum Chromodynamics (QCD) beyond leading order. This research uncovers a new perturbative relation between soft-gluon couplings and the cusp anomalous dimension.

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Area of Science:

  • High Energy Physics
  • Quantum Chromodynamics (QCD)
  • Perturbative Quantum Field Theory

Background:

  • Soft-gluon resummation is crucial for precise predictions in QCD hard-scattering processes.
  • The Collins-Masterelli-Webber (CMW) effective coupling provides a framework for this resummation.
  • Extending this framework beyond leading-logarithmic accuracy is essential for higher precision.

Purpose of the Study:

  • To propose and analyze extensions of the CMW soft-gluon effective coupling to all perturbative orders.
  • To investigate the behavior of these extended couplings in d-dimensional spacetime.
  • To uncover all-order perturbative relations with fundamental QCD quantities like the cusp anomalous dimension.

Main Methods:

  • Developing two novel proposals for soft-gluon effective couplings.
  • Analyzing these couplings in d-dimensional spacetime, including the conformal point where the QCD $\beta$-function vanishes.
  • Calculating explicit expressions for the couplings up to N$^3$LL in d-dimensions and N$^4$LL in 4-dimensions.

Main Results:

  • Two well-defined soft-gluon effective couplings are presented, extending the CMW coupling to all orders.
  • An all-order perturbative relation is found: the 4D cusp anomalous dimension equals the d-dimensional effective coupling at the conformal point.
  • Explicit expressions for the couplings are derived, confirming previous results and establishing new relations with the cusp anomalous dimension.

Conclusions:

  • The proposed effective couplings offer a robust framework for higher-order soft-gluon resummation in QCD.
  • The discovered relation with the cusp anomalous dimension provides new insights into the structure of QCD observables.
  • These findings pave the way for more precise theoretical predictions in high-energy physics.