Dispersion relations for hadronic light-by-light scattering in triangle kinematics

Jan Lüdtke, Massimiliano Procura, Peter Stoffer (Corresponding author)

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We present a new strategy for the dispersive evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon aμ. The new approach directly applies in the kinematic limit relevant for aμ: one of the photons is treated as an external electromagnetic field with vanishing momentum, so that the kinematics corresponds to a triangle. We derive expressions for the relevant single-particle intermediate states, as well as the tensor decompositions of the two-pion sub-processes that appear in addition to those needed in the established dispersive approach. The existing approach is based on a set of dispersion relations for the hadronic light-by-light tensor in four-point kinematics. At present it is not known how to consistently include in this framework resonant intermediate states of spin 2 or larger, due to the appearance of kinematic singularities that can be traced back to the redundancy of the tensor decomposition. We show that our new approach circumvents this problem and enables dispersion relations in the limit of triangle kinematics that are manifestly free from kinematic singularities, paving the way towards a data-driven evaluation of all relevant exclusive hadronic intermediate states.
Original languageEnglish
Article number125
Number of pages45
JournalJournal of High Energy Physics
Issue number4
Publication statusPublished - Apr 2023

Austrian Fields of Science 2012

  • 103012 High energy physics


  • Chiral Lagrangian
  • Effective Field Theories
  • Nonperturbative Effects
  • Precision QED

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