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Two-loop anomalous-dimension matrix for soft-gluon exchange.

S Mert Aybat1, Lance J Dixon, George Sterman

  • 1C.N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794-3840, USA.

Physical Review Letters
|October 10, 2006
PubMed
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Researchers computed the matrix of anomalous dimensions for quantum chromodynamics (QCD) hard scattering at two loops. This matrix is proportional to the one-loop matrix, enabling closed-form resummation of higher-order logarithms.

Area of Science:

  • High-energy physics
  • Quantum chromodynamics (QCD)
  • Perturbative QCD

Background:

  • Resummation of soft-gluon exchange is crucial for QCD hard scattering calculations.
  • Anomalous dimensions matrix is essential for this resummation process.
  • Previous calculations were limited in scope or order.

Purpose of the Study:

  • To compute the anomalous dimensions matrix for arbitrary 2-->n massless processes at two-loop order for the first time.
  • To establish the relationship between one-loop and two-loop anomalous dimensions matrices.
  • To enable the closed-form resummation of higher-order logarithms and poles.

Main Methods:

  • Direct computation of the anomalous dimensions matrix at two loops.
  • Utilizing color-generator notation.

Related Experiment Videos

  • Employing dimensional regularization.

    • Main Results:

    • The two-loop anomalous dimensions matrix is proportional to the one-loop matrix.
    • This proportionality holds for arbitrary 2-->n massless processes.
    • The results reproduce known pole terms in 2-->2 amplitudes and predict new ones.

    Conclusions:

    • The proportionality simplifies higher-order calculations in perturbative QCD.
    • This work provides a pathway for closed-form resummation of next-to-next-to-leading logarithms.
    • The findings are applicable to a wide range of 2-->n scattering processes.